Evidence that artificial intelligence is increasing the impact, but narrowing the scope, of research

There is growing evidence of positive impacts of generative artificial intelligence on productivity. This includes productivity in research (see this post, for example), including my own. However, some have questioned whether increasing research productivity comes at a cost of narrowing the scope of research.

So, I was interested to read this article by Qianyue Hao (Tsinghua University) and co-authors, published in the prestigious journal Nature (ungated earlier version here) late last year. They look at the impact of AI tools (not limited to generative AI) on the productivity of researchers and the quality of research. Specifically, they look at authors publishing in six representative fields: biology, medicine, chemistry, physics, materials science, and geology, across three 'eras': (1) the 'machine learning era ' (from 1980 to 2014), the 'deep learning era' (from 2015 to 2022), and the 'generative AI era' (from 2023 onwards). Hao et al. compare authors who publish 'AI augmented papers' with those who do not. An 'AI augmented paper' is one that uses methods such as:

...support vector machines and principal component analysis from the machine learning era, and convolutional neural networks and generative adversarial networks from the deep learning era. Large language models, which have emerged in recent years, also rank among the most frequently used methods...

Using a dataset that includes over 27 million papers with complete records that were published between 1980 and 2025, of which about 310,000 were 'AI augmented', Hao et al. find that:

...annual citations to AI papers are 98.70% higher than those to non-AI papers on average...

So, AI augmented research gathers more citations, which suggests that authors using AI in their research achieve greater impact. This is reinforced by evidence that AI augmented papers are published in higher quality journals (with Q1 journals being the highest ranked). Hao et al. report that:

...the proportion of AI papers in Q1 journals is 18.60% higher than that of non-AI papers in all journals; in Q2 journals, the AI proportion is 1.59% higher; whereas Q3 and Q4 journals hold a relatively lower proportion of papers with AI... These results indicate a heterogeneous distribution of AI-augmented papers across journals, with a higher prevalence in high-impact journals.

And AI appears to make authors more productive, as:

On average, researchers adopting AI annually publish 3.02 times more papers... and garner 4.84 times more citations... than those not adopting AI, with consistency.

All of these results seem to hold across all of the disciplines that Hao et al. consider. However, it is not all good news. Hao et al. use machine learning to create a measure of the 'breadth of scholarly attention'. Using that measure, they find that:

Compared with conventional research, AI research is associated with a 4.63% contracted median collective knowledge extent across science, which is consistent across all six disciplines... Moreover, when dividing these disciplines into more than two hundred sub-fields, the contraction of knowledge extent can be observed in more than 70% of them...

Of course, some of the differences here may be due to selection, as the types of researchers, and the types of research, involving AI use may be meaningfully different from those that don't. However, putting the selection issues aside, Hao et al. note that there is a tension between the individual researcher's incentive to produce a greater quantity of research that has higher impact, which would suggest greater use of AI, and the social incentive to produce a greater breadth of research.

So, the takeaway from this paper is that we need to consider researcher incentives, not just productivity. Specifically, this research suggests that the use of AI in research is leading to a 'prisoners' dilemma' outcome: each individual researcher acting in their own best interests (and using AI in their research) leads to an outcome that is worse for society overall (less breadth of research and more incremental gains).

Hao et al. conclude that:

The substantial academic benefits of AI use may be a driving force behind its accelerated rate of adoption; however, we also find unintended consequences from the increased prevalence of AI-augmented research. In all fields, AI-augmented research focuses on a narrower scope of scientific topics and reduces the scientific engagement of follow-on research, leading to more overlapping research work that slows the expansion of knowledge. Further, with a greater concentration of collective attention to the same AI papers, the adoption of AI seems to induce authors to converge on the same solutions to known problems rather than create new ones.

So, what is the solution here? Society probably wants research to be higher quality and have a broad scope. But individual researchers' incentives to use AI in their research appears inconsistent with that outcome. The traditional prisoners' dilemma is a repeated game (see here or here, for example), and the players of that game can avoid the worst outcome by cooperating. In this case, the researchers could cooperate by agreeing not to use AI in their research. The problem is that every researcher has an incentive to cheat on that agreement, since if they use AI, then that will be good for their career. This prisoners' dilemma is more difficult to ensure cooperation in than the traditional game, because there are not just two players who need to cooperate, but thousands (or millions). Ensuring cooperation in a prisoners' dilemma game with many players, each of whom is far better off cheating than cooperating, is almost impossible (which is why solving the problem of climate change is so difficult).

My own view is that the answer is not to keep AI out of research. That is not realistic, in the same way that it's not realistic to expect students not to use generative AI. The incentives need to be redesigned, but this will be no easy task. As long as universities, research funders, and publishers reward researchers for quantity, citations, and publication in top-ranked outlets, then we should expect more AI-augmented work, with a narrower scope than society might prefer. If we want AI to expand knowledge rather than simply accelerate competition within narrow foci, then we need institutions that also reward novelty, breadth, and the discovery of new questions. That is the economic challenge we must face up to.

[HT: Marginal Revolution]

The economics of pricing LLM tokens

Ethan Ding had a really interesting post on Substack last month, discussing his view on the future costs of tokens for large language models (LLMs), and what that means for the viability of subscription-based generative AI. I want to focus on two aspects of Ding's post. First, this (the lack of capitalisation is Ding's style):

the math has fundamentally broken.

prisoner’s dilemma for everyone else

this leaves everyone else in an impossible position.

every ai company knows usage-based pricing would save them. they also know it would kill them. while you're being responsible with $0.01/1k tokens, your vc-funded competitor offers unlimited for $20/month.

guess where users go?

classic prisoner's dilemma:

• everyone charges usage-based → sustainable industry
• everyone charges flat-rate → race to the bottom
• you charge usage, others charge flat → you die alone
• you charge flat, others charge usage → you win (then die later)

so everyone defects. everyone subsidizes power users.

Ok, so let's look at this prisoners' dilemma. Consider two AI firms (Firm A and Firm B), each with two strategies to choose from (Usage-based pricing, or flat-rate pricing). The game is outlined in the payoff table below. The payoffs are expressed in +'s and -'s, with more +'s obviously being better.

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If Firm B chooses usage-based pricing, Firm A's best response is to choose flat-rate pricing (since ++ is a better payoff than +) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If Firm B chooses flat-rate pricing, Firm A's best response is to choose flat-rate pricing (since - is a better payoff than --);
3. If Firm A chooses usage-based pricing, Firm B's best response is to choose flat-rate pricing (since ++ is a better payoff than +); and
4. If Firm A chooses flat-rate pricing, Firm B's best response is to choose flat-rate pricing (since - is a better payoff than --).

Note that Firm A's best response is always to choose flat-rate pricing. This is their dominant strategy. Likewise, Firm B's best response is always to choose flat-rate pricing, which makes it their dominant strategy as well. The single Nash equilibrium occurs where both players are playing a best response (where there are two ticks), which is where both firms choose flat-rate pricing.

Notice that both players would be unambiguously better off if they chose usage-based pricing. However, both will choose flat-rate pricing, which makes them both worse off. This is a prisoners' dilemma game (it's a dilemma because, when both players act in their own best interests, both are made worse off).

Ding notes that this is a losing proposition for all generative AI firms, and is the position that they are all in right now. They could try to cooperate and shift to usage-based pricing, but there will always be a strong incentive for the firms to cheat on any agreement and instead offer flat-rate pricing. So, any agreement will not last. Especially since there are other strategies available, which Ding goes on to discuss. The one that caught my eye was this:

use ai as a loss leader to drive consumption of aws-competitive services. you're not selling inference. you're selling everything else, and inference is just marketing spend.

the genius is that code generation naturally creates demand for hosting. every app needs somewhere to run. every database needs management. every deployment needs monitoring. let openai and anthropic race inference to zero while you own everything else.

the companies still playing flat-rate-grow-at-all-costs? dead companies walking. they just have very expensive funerals scheduled for q4.

It makes sense to play the losing prisoners' dilemma strategy, if a firm can use it to be more profitable elsewhere. Using generative AI as a loss leader, and then making more profits by selling complementary services (hosting, data management, monitoring) may be more profitable overall for the generative AI firms.

For loss leading to be successful though, two conditions need to be met. First, the loss leading service should be price elastic. That means that when price is low, many consumers are attracted to the service. That seems likely to be the case for generative AI, because when the price increases, consumers can easily switch to one of the many other generative AI platforms. Second, there must be many other complementary services for the firm to sell. The three suggestions by Ding (hosting, data management, monitoring) are all complements to generative AI (or, at least, to the ways that generative AI is being used right now). So, it seems that loss leading with generative AI may be a profitable strategy for the generative AI firms, even though it means playing out the prisoners' dilemma on pricing.

[HT: Marginal Revolution]

Mobile phone providers and the repeated switching costs game

This week, my ECONS101 class covered pricing and business strategy, and one aspect of that is switching costs and customer lock-in. Switching costs are the costs of switching from one good or service to another (or from one provider to another). Customer lock-in occurs when customers find it difficult (costly) to change once they have started purchasing a particular good or service. The main cause of customer lock-in is, unsurprisingly, high switching costs.

As one example, consider this article from the New Zealand Herald last month:

A new Commerce Commission study has found the switching process between telecommunications providers is not working as well as it should for consumers...

The study found 50% of mobile switchers and 45% of broadband switchers ran into at least one issue when switching.

The experience was so bad that 29% of mobile switchers and 27% of broadband switchers said they wouldn’t want to switch again in future...

The commission’s latest consumer satisfaction report found that 31% of mobile consumers and 29% of broadband consumers have not switched because it requires ‘too much effort to change providers’...

Gilbertson said a lack of comprehensive protocols between the “gaining” service provider and the “losing” service provider was a central issue with the current switching process.

This led to a number of problems, including double billing, unexpected charges, and delays.

The difficulty of changing from one mobile phone provider to another is a form of switching cost. It's not a monetary cost, but the time, effort, and frustration experienced by consumers wanting to switch makes the process of switching costly. And because the process is costly, mobile phone consumers are locked into their current provider.

It is clear why a mobile phone provider would want to make it difficult (costly) for its consumers to switch away from it and use some other provider. However, why don't mobile phone providers try to make it easier to switch to using their service instead? Maybe they could have staff whose role is to help consumers to navigate the process of switching to their service. That would allow the mobile phone provider to attract consumers and capture a greater market share. The answer is provided by considering a little bit of game theory.

Consider the game below, with two mobile phone providers (A and B), each with two strategies ('Easy' to switch to, and 'Hard' to switch to). The payoffs are made-up numbers that might represent profits to the two providers.

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If Provider B chooses to make switching easy, Provider A's best response is to make switching easy (since 3 is a better payoff than 2) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If Provider B chooses to make switching hard, Provider A's best response is to make switching easy (since 8 is a better payoff than 6);
3. If Provider A chooses to make switching easy, Provider B's best response is to make switching easy (since 3 is a better payoff than 2); and
4. If Provider A chooses to make switching hard, Provider B's best response is to make switching easy (since 8 is a better payoff than 6).

Note that Provider A's best response is always to choose to make switching easy. This is their dominant strategy. Likewise, Provider B's best response is always to make switching easy, which makes it their dominant strategy as well. The single Nash equilibrium occurs where both players are playing a best response (where there are two ticks), which is where both providers make switching easy.

So, that seems to suggest that the mobile phone providers should be making switching to them easier. However, notice that both providers would be unambiguously better off if they chose to make switching hard (they would both receive a payoff of 6, instead of both receiving a payoff of 3). By both choosing to make switching easy, it makes both providers worse off. This is a prisoners' dilemma game (it's a dilemma because, when both players act in their own best interests, both are made worse off).

That's not the end of this story though, because the simple example above assumes that this is a non-repeated game. A non-repeated game is played once only, after which the two players go their separate ways, never to interact again. Most games in the real world are not like that - they are repeated games. In a repeated game, the outcome may differ from the equilibrium of the non-repeated game, because the players can learn to work together to obtain the best outcome.

So, given that this is a repeated game (because the providers are constantly deciding whether to make switching easier or not), both providers will realise that they are better off making switching harder, and receiving a higher payoff as a result. And unsurprisingly, that is what happens, and it doesn't require an explicit agreement between the players - the agreement is 'tacit' (it is understood by the providers without needing to be explicit). Each provider just needs to trust that the other providers will make switching hard (because there is an incentive for each provider to 'cheat' on this outcome). Any instance of cheating (by making switching easier) would be immediately known by the other providers, and the agreement would break down, making them all worse off. So, there is an incentive for all providers to keep switching hard for the consumers. Even a new entrant firm into the market, which might initially make it easy for consumers to switch to them in order to capture market share, would soon realise that they are then better off making switching more difficult (it is not so long ago (2009) that 2degrees was a new entrant in this market).

The Commerce Commission is correct that the difficulty of switching mobile phone providers (the switching cost) keeps consumers with their current provider (customer lock-in). The result is that the mobile phone providers can profit from increasing prices for their lock-in consumers. The only solution to this situation would be to find some way to force a breakdown of the tacit arrangement. Then the market would settle at the equilibrium of all providers making it easy to switch to them. This may be an instance where some regulation is necessary.

Why tit-for-tat tariffs may not work against Trump

Last week, my ECONS101 class covered game theory. At the end of the final lecture, after we had been covering repeated games and tit-for-tat strategies, a really perceptive student asked me about Trump's tariffs. A lot of the rhetoric about tariffs has been posed in terms of tit-for-tat (see here and here, for example). The student's question got me thinking though, about why a tit-for-tat strategy may not work in this case.

Before we get that far though, we need to think about the tariff game, as outlined in the payoff table below. There are two players: USA and 'Other Country'. Each player has two strategies: high tariffs, or low tariffs (which includes no tariffs). The payoffs are expressed as "+" for good outcomes (and "++" is particularly good), and "--" for bad outcomes (and "--" is particularly bad), while zero is a neutral payoff. 

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If the other country chooses high tariffs, USA's best response is to choose high tariffs (since "0" is better than "--" as a payoff) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If the other country chooses low tariffs, USA's best response is to choose high tariffs (since "++" is better than "+" as a payoff);
3. If USA chooses high tariffs, the other country's best response is to choose high tariffs (since "0" is better than "--" as a payoff); and
4. If USA chooses low tariffs, the other country's best response is to choose high tariffs (since "++" is better than "+" as a payoff).

Notice that USA chooses high tariffs no matter what the other country does, high tariffs is a dominant strategy for the USA. Similarly, since the other country chooses high tariffs no matter what the USA does, high tariffs is a dominant strategy for the other country. Both countries will choose to play their dominant strategy (because it is always better than the other strategy, not matter what the other country chooses to do). The outcome where both countries choose high tariffs is the Nash equilibrium in this game (it is also a dominant strategy equilibrium, because both countries have a dominant strategy).

However, I'm sure that you can clearly see that both countries would be better off with low tariffs (since the payoff for each country would be "+", instead of "0"). This game is an example of the prisoner's dilemma (it's a dilemma because, when both countries act in their own best interests, both are made worse off).

However, it is important to remember that this game is a repeated game. It is played more than once, with the same players, and the same strategy choices. When a game is repeated, then the outcome may differ from the equilibrium of the non-repeated game, because the players can learn to work together to obtain the best outcome.

In a repeated prisoners' dilemma game like this, each player can encourage the other to cooperate by using the tit-for-tat strategy. That strategy, identified by Robert Axelrod in the 1980s, works by initially cooperating (low tariffs), and then in each play of game after the first, the player does whatever the other player did last time. So, if the USA chooses high tariffs, then the other country should punish them and choose high tariffs in the next play of the game. And if the USA chooses low tariffs, then the other country should reward them and choose low tariffs in the next play of the game. The tit-for-tat strategy works because it encourages the other player to cooperate. And that is what many people have been expecting of Trump. If you punish the USA for high tariffs by setting your own high tariffs, eventually they will realise their error and start cooperating with low tariffs again.

But there is a problem. The whole edifice of the tit-for-tat strategy assumes that Trump knows that he is playing the game outlined above, where there is an unambiguously better outcome for both countries, if they both choose low tariffs. By his past statements, it is absolutely clear that Trump thinks that trade is a zero-sum game (for example, see here or here).

So, what does the game look like if you believe that trade is zero-sum? Instead of there being gains from the low-tariff/low-tariff outcome, the payoffs become zero, as shown in the payoff table below.

Solving this game for the Nash equilibrium, the best responses are:

1. If the other country chooses high tariffs, USA's best response is to choose high tariffs (since "0" is better than "--" as a payoff) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If the other country chooses low tariffs, USA's best response is to choose high tariffs (since "++" is better than "0" as a payoff);
3. If USA chooses high tariffs, the other country's best response is to choose high tariffs (since "0" is better than "--" as a payoff); and
4. If USA chooses low tariffs, the other country's best response is to choose high tariffs (since "++" is better than "0" as a payoff).

Notice that the game itself doesn't change. Imposing high tariffs is still a dominant strategy for both countries, and the outcome where both countries choose high tariffs is the only Nash equilibrium (and is also a dominant strategy equilibrium).

However, there is an important difference in this game when it is played as a repeated game. There is no incentive for players to cooperate. That's because cooperating results in a payoff of "0", just the same as not cooperating. And because of this, the tit-for-tat strategy would be pointless.

Which seems to be what other countries are finding, when dealing with Trump. Other countries may think they are playing the first game, where a tit-for-tat strategy may get Trump to reconsider. But if Trump thinks they are playing the second (zero-sum) game (and it seems that he does), then the tit-for-tat strategy is simply not going to work.

[HT: Sarah from my ECONS101 class]

Angola plays its dominant strategy in defecting against OPEC

The Financial Times reported last week (paywalled):

Angola, Africa’s second biggest oil producer, has said it is leaving Opec after disagreements over its production targets, delivering a blow to the oil cartel chaired by Saudi Arabia.

The decision comes after the producer group lowered Angola’s oil output target last month as part of a series of cuts led by Saudi Arabia to help prop up prices.

OPEC is an example of a cartel. Cartels can arise when a market is an oligopoly - a market where there are many buyers, but few sellers. A cartel essentially acts like a monopoly seller - it is able to use market power to extract greater economic rent from the market (in the form of higher profits, arising from higher prices), than the countries would be able to extract if they were competing with each other. The cartel can be maintained because there are few sellers, so it is relatively easy for them to coordinate their actions. In this case, OPEC coordinates to raise prices by restricting production.

However, there is always an incentive for each cartel member to cheat on the cartel agreement, or to leave the cartel entirely (as Angola has done). To see why, we can apply some game theory. Let's say that there are two players - Angola and 'the rest of OPEC'. Each player has two strategies - high production (which leads to lower prices and lower profits for oil producers), or low production (which leads to higher prices and higher profits). If one player has high production and the other low production, the high production player benefits more. However, if both players have high production, both are worse off. These outcomes and payoffs are illustrated in the diagram below (the payoff numbers represent profits, but are just made up to illustrate this example).

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If the rest of OPEC chooses high production, Angola's best response is to choose high production (since 2 is a better payoff than 0) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If the rest of OPEC chooses low production, Angola's best response is to choose high production (since 4 is a better payoff than 3);
3. If Angola chooses high production, the rest of OPEC's best response is to choose high production (since 10 is a better payoff than 9); and
4. If Angola chooses low production, the rest of OPEC's best response is to choose high production (since 15 is a better payoff than 12).

Note that Angola's best response is always to choose high production. This is their dominant strategy. Likewise, the rest of OPEC's best response is always to choose high production, which makes it their dominant strategy as well. The single Nash equilibrium occurs where both players are playing a best response (where there are two ticks), which is where all of OPEC (including Angola) chooses high production.

Notice that both players would be unambiguously better off if they chose low production. However, both will choose high production, which makes them both worse off. This is a prisoners' dilemma game (it's a dilemma because, when both players act in their own best interests, both are made worse off).

That's not the end of this story though, because the simple example above assumes that this is a non-repeated game. A non-repeated game is played once only, after which the two players go their separate ways, never to interact again. Most games in the real world are not like that - they are repeated games. In a repeated game, the outcome may differ from the equilibrium of the non-repeated game, because the players can learn to work together to obtain the best outcome.

And that is what happens when a cartel forms. If all of OPEC (including Angola) works together and agrees to choose low production, both players benefit. That is what they were doing, up until Angola chose to leave OPEC. The problem here is that both players choosing low production is not an equilibrium. If Angola knows that the rest of OPEC is choosing low production, it is better off defecting from the agreement and choosing high production. Angola profits more that way (at least, in the short term).

So essentially, by leaving OPEC (and thereby choosing high production), Angola is simply playing its dominant strategy.

Read more:

• The oil price war is actually just a return to equilibrium

The prisoners' dilemma, with real prisoners (and the Camorra)

I've written a number of posts about the prisoners' dilemma (most recently here). In the prisoners' dilemma, all players have a dominant strategy, which is a strategy that is always better for the player, no matter what any of the other players choose to do. However, if each player acts in their own self-interest, the outcome leads to payoffs that are worse for everyone, than if they had cooperated. Robert Frank has described these games as leading to behaviour that is 'smart for one, dumb for all'.

There have been a number of studies of decision-making in the prisoners' dilemma. It is an important game to study, because it can tell us a lot about cooperation, particularly when we compare different population groups. Following that theme, this 2018 article by Annamaria Nese, Niall O’Higgins (both University of Salerno), Patrizia Sbriglia (University of Campania Luigi Vanvitelli), and Maurizio Scudiero (Ministry of Justice, Italy), published in the journal European Economic Review (ungated earlier version here), compares behaviour in the prisoners' dilemma between ordinary prisoners, Camorristi (Mafiosi from Naples), and students (an ordinary control group used in many experiments, in psychology and economics). Nese et al. set out to test three things:

First, to test whether Camorra participants have a greater tendency to cooperate in the Prisoners’ Dilemma game than ordinary criminals or students. Second, to test whether Camorra members differ from members of the other two groups in their reaction to the presence of external sanctions, and third, when the possibility of third party punishment is introduced, to analyse how the application of sanctions by members of the different groups under study varies.

Their sample is made up of 109 students from the University of Campania-Luigi Vanvitelli, 129 Camorra from Secondigliano jail in Naples, and 109 ordinary criminals from another prison in the same province as the university. Nese et al. explain the experiment as follows:

The experiment comprised two different designs: a one-shot Prisoners’ Dilemma (PD) and a one-shot Prisoners dilemma with third party punishment (PD-TPP)... In the PD design, at the beginning of the sessions, each subject was provided with an envelope that was labelled A or B and a number that identified the subject... A (B) subjects were endowed with 10 tokens and were paired with B (A) subjects. The (A and B) subjects had to (simultaneously) determine whether to keep the tokens or send them to the partner. If subjects sent the tokens to their (anonymous) partner, the researcher would triple the amount. Thus, the game had four possible outcomes: (10, 10), (40, 0), (0, 40), (30, 30).

So, this is a classic prisoners' dilemma, because both players have a dominant strategy to keep the tokens. If you doubt this, skip ahead to the end of this post [*], where I show the Nash equilibrium for this game (but make sure you come back to here afterwards!). Continuing with the explanation of the experiment:

The PD-TPP had a two-stage design involving three types of subject (A, B and C). The first stage corresponded to the PD and our procedures were precisely the same; the fundamental difference being that A and B were aware that the C player could intervene at the second stage and could thus influence their final payoff by awarding deduction points to one (or both) of them. In fact, at the beginning of the second stage, after A and B had determined whether or not to send the tokens, player C was endowed with 40 tokens and had to decide whether to keep the tokens or spend some or all of their endowment so as to deduct points from A and/or B. One deduction point would decrease A and B’s total payoff by three tokens... Thus, C was asked to indicate on the decision sheet how many deduction points he would allocate for each of the four possible outcomes in the PD: (CC), (DD), (CD), (DC).

In the outcomes in that last sentence, C refers to 'cooperate' (send the tokens), and D refers to 'defect' (keep the tokens). Nese et al. ran this experiment with the students, and each group of prisoners, separately - that is, there is no mixing between the groups. Their key results are summarised in Figure 1 in the paper:

In the ordinary prisoners' dilemma, students cooperate significantly more than ordinary criminals. However, Camorristi cooperate significantly more than either of the other two groups. Introducing the possibility of punishment increases cooperation among ordinary criminals, but decreases cooperation among students and Camorristi. In terms of punishment behaviour, Nese et al. found that:

...all three groups punished defectors in roughly equal measure when their co-respondent also defected. Camorra inmates punished defectors - when their counterpart co-operated - significantly more and more often than the other two groups... In contrast to students, both types of prisoner sometimes punish co-operators as well as defectors; the tendency being slightly more pronounced amongst ordinary criminals than Camorristi.

Nese et al. then take things a bit further, looking at how the results vary for participants who have different levels of cooperativeness, reciprocity, and locus of control (all measured by a survey). They find that:

...(a) across the three different samples, rather unsurprisingly, the main driver of pro-social behaviour, is a cooperative attitude; and, (b) perhaps more significantly, the greater tendency towards co-operation shown by Camorristi compared to either students or ordinary criminals remains statistically significant, even controlling for individual attitudes towards co-operation.

And in terms of punishment behaviour:

Controlling for individual preferences... a more co-operative attitude and a stronger internal locus of control negatively affect the size of punishment whilst being a reciprocator tends to increase it...

Introducing terms for individual preferences towards cooperation, reciprocity and locus of control, it emerges that amongst Camorristi the tendency to punish increases with the belief in the appropriateness of reciprocity –particularly positive reciprocity –and with a more internal locus of control (regarding good events), but falls as the tendency towards co-operation increases. Again, for ordinary criminals, the sign of the effects is typically reversed: subjects with a strong internal locus are less likely to punish, as are (especially positive) reciprocators whilst those who are more oriented towards co-operation punish more.

Taking these results all together, Nese et al. conclude that:

Camorristi inmates demonstrate a high degree of cooperativeness and a strong tendency to punish defectors. Moreover, the attachment to co-operative (in-group) norms of behaviour amongst Camorristi is completely reversed when such norms are externally imposed –leading to a significant reduction in co-operation once an external ‘judge’ is introduced.

This behaviour is quite different from that observed amongst ordinary criminals who are less willing to co-operate with each other than either students or Camorristi in the absence of a referee, but who become more co-operative under the threat of externally imposed punishment. The behaviour of ordinary criminals suggests an element of opportunism which is entirely lacking - or perhaps more accurately - completely overwhelmed by the more honour-bound mores of the Camorra, with its emphasis on the negative nature of betrayal and the rejection of external authority, accompanied by the threat of severe sanctioning of within-group rule breakers.

Interesting. I wonder what sort of results we would get for gang members in New Zealand?

[HT: Marginal Revolution, back in January]

*****

[*] The game is outlined in the payoff table below.

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If B chooses to keep the tokens, A's best response is to keep the tokens (since 10 is a better payoff than 0) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If B chooses to send the tokens, A's best response is to keep the tokens (since 40 is a better payoff than 30);
3. If A chooses to keep the tokens, B's best response is to keep the tokens (since 10 is a better payoff than 0); and
4. If the Police chooses to send the tokens, B's best response is to keep the tokens (since 40 is a better payoff than 30).

Note that A's best response is always to choose to keep the tokens. This is their dominant strategy. Likewise, B's best response is always to choose to keep the tokens, which makes it their dominant strategy as well. The single Nash equilibrium occurs where both players are playing a best response (where there are two ticks), which is where both A and B choose to keep the tokens. Notice that by both playing their dominant strategy and keeping the tokens, both players are worse off than they would be if they had both sent the tokens. This is a prisoners' dilemma game because, when both players act in their own best interests, both are made worse off.

This ain't a (crime)scene, it's an arms race

Gun violence has been in the news a lot recently, with incidents in Hamilton and Auckland among others, and predictably that has reignited the debate over the arming of police in New Zealand. However, we should resist the temptation. To see why, let's apply a little bit of game theory.

The arms race game is a variation of the prisoners' dilemma. For simplicity, let's assume that there are two players in our game, the police and the criminals. Both players have two strategies, to arm themselves or to disarm (or not arm). Both police and criminals are best off if they are armed and the other group is not, but if both are armed this escalates the potential for violent confrontation. Both players are making their decisions at the same time, making this a simultaneous game. The game is outlined in the payoff table below.

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If the criminals choose to arm, the Police's best response is to arm (since -5 is a better payoff than -10) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If the criminals choose to disarm, the Police's best response is to arm (since 10 is a better payoff than 5);
3. If the Police choose to arm, the criminals' best response is to arm (since -5 is a better payoff than -10); and
4. If the Police choose to arm, the criminals' best response is to arm (since 10 is a better payoff than 5).

Note that the Police's best response is always to choose to arm. This is their dominant strategy. Likewise, the criminals' best response is always to choose to arm, which makes it their dominant strategy as well. The single Nash equilibrium occurs where both players are playing a best response (where there are two ticks), which is where both the Police and criminals choose to arm. This leads to escalation of violence and is worse off for everyone than if both players chose to disarm. That demonstrates that the arms race is a type of prisoners' dilemma game (it's a dilemma because, when both players act in their own best interests, both are made worse off). If both police and criminals follow their dominant strategies, eventually we will end up in a situation like the U.S., with growing militarisation of police, which makes both police and citizens worse off.

How do we avoid this outcome? First, we need to recognise that the arms race game outlined above is not a one-shot game, it is a repeated game. That means that it is effectively played not once, but many times. In repeated games, the players are more likely to be able to work together to move away from the Nash equilibrium, and ensure a better outcome for all.

Let's assume for the sake of argument that the game is played weekly, and decisions are made simultaneously each week. Both police and criminals recognise that it is in their long-run interests to disarm. If they choose not to arm, and can trust the other player also not to arm, everyone benefits (or, rather, everyone faces a lower cost, since crime would continue, but it wouldn't be aggravated to the same extent by firearms).

Can each side really trust the other? That's the problem. In a repeated prisoners' dilemma game like this, each player can encourage the other to cooperate by using the tit-for-tat strategy. That strategy, identified by Robert Axelrod in the 1980s, works by initially cooperating (disarming), and then in each play of game after the first, you do whatever the other player did last time. So, if the criminals armed last week, the Police arm this week. And if the criminals disarmed last week, the Police disarm this week. Essentially, that means that each player punishes the other for not cooperating, by themselves choosing not to cooperate in the next play of the game. It also means that each player rewards the other for cooperating, by themselves choosing to cooperate in the next play of the game. However, the tit-for-tit strategy doesn't eliminate the incentive for either side to cheat. Can the Police trust the criminals not to arm, if they knew for sure that the Police would not arm?

A more severe form of punishment strategy is the grim strategy. This involves initially cooperating (like the tit-for-tat strategy), when the other player chooses not to cooperate, you switch to not cooperating and never cooperate again. You can see that this strategy essentially locks in the worst outcome in the game. And unfortunately, arming the police is a type of grim strategy if it is difficult to back out of once the decision is made (which, judging by the experience in the U.S., may well be the case).

We need another option. If the criminals are going to arm, and Police can't trust them not to, and we want to avoid the grim strategy, we end up in the outcome where Police (and society more generally) have the worst outcome, and criminals have the best. To encourage criminals not to arm, Police need to be armed at least some of the time. At least enough of the time that the long-run best outcome is for criminals not to arm all of the time. If criminals get a payoff of 10 for sure each week, they would surely arm. But if they get a payoff of 10 some weeks, but -5 in other weeks, then they might be better off on average to not arm.

The challenge in this approach is that the Police need to find the right balance. If criminals are arming more often (as appears to be the case right now), then Police need to arm a little bit more as a deterrent. This doesn't mean that having all Police routinely armed is the right solution, only that a little movement in that direction might help to restore an uneasy but preferable outcome.

Let's not finish on such a gloomy note. Time for a musical interlude, courtesy of Fall Out Boy (since I ripped off their song title for the title of this post, it seems only fair):

Spotify and the musicians' dilemma

Yesterday I posted an example of the prisoners' dilemma, applied to supermarkets' pricing behaviour in New Zealand. These are strategic situations where each player (decision maker), acting in their own self-interest, creates an outcome (and payoffs) that are worse for all of the players. There are many real world examples of the prisoners' dilemma (such as this one, or this one). However, I want to concentrate on an example from this January article in The Conversation, by John Hawkins, Ben Freyens, and Michael Walsh (all University of Canberra):

Streaming now accounts for more than half of recorded music revenue. Spotify has about a third of the subscribers paying for music streaming. Playlists overtook albums as the preferred way of listening to sequences of songs about five years ago.

Appearing on a prominent Spotify playlist is therefore a big deal...

With so much power, what will Spotify do next?

The answer, apparently, is to run a pay-to-play “experiment”, dropping Spotify’s “crystal clear” commitment in 2018 that “no one can pay to be added to one of Spotify’s editorial playlists”. But now there’s this:

In this new experiment, artists and labels can identify music that’s a priority for them, and our system will add that signal to the algorithm that determines personalised listening sessions.

The catch is musicians must accept a lower payment — a “promotional recording royalty rate” — on any song streamed as a result.

So, essentially, Spotify is asking musicians so accept a lower royalty rate in exchange for having their music promoted more intensively. Why does this provide an example of the prisoners' dilemma? Hawkins et al. explain:

The musician’s dilemma is that the best cooperative outcome is all artists refusing Spotify’s offer. No one gains, but no one loses either.

But who’s going to organise that, given the understandable fear of repercussions for going against Spotify?

Best placed to resist are Spotify’s superstars — the likes of Eilish, Taylor Swift, Ariana Grande, Ed Sheeran, Drake and Bad Bunny, with billions of streams between them. They have diversified marketing and revenue sources, and are cash cows Spotify doesn’t want to lose.

The most likely outcome is many or most musicians accepting lower song payments from Spotify, putting the squeeze on struggling musicians who refuse while making little difference to the prominence super streamers get from Spotify’s algorithms.

In other words, all of the musicians could work together and disagree with Spotify's generous offer of promotion. However, every musician then has an incentive to sign up to the programme, knowing that their music would have greater visibility while every other musician's music would not. So, even if there was an agreement between the musicians, the agreement would quickly break down. This is the problem that all cartels face - all of the members of the cartel have an incentive to 'cheat' on their agreement to get themselves a better deal.

Cooperation is hard. As I note in my ECONS101 class, it requires trust between the players. And trust usually requires developing a reputation for being trustworthy. And each musician would need to be able to trust all (or at least most) of the other musicians, before it would be worthwhile agreeing to forego the deal with Spotify. That seems unlikely.

The musicians' dilemma is clearly something that Spotify has thought through. Spotify might back down for any of the superstars (see above), but the average musician will just have to take what they can get, which already isn't a whole lot.

New Zealand's supermarket duopoly and coordinated behaviour

The National Business Review reported yesterday (probably gated):

Consumer and food manufacturer representatives say accommodating behaviour between the two dominant supermarket groups is a “major risk”,  that it is “highly likely”,  and that growth in private label products should be thoroughly investigated.

Foodstuffs and Woolworths, meanwhile, have played down any concerns in the hundreds of pages of submissions made on the Commerce Commission’s proposed scoped of its study into the country’s retail grocery market, saying it is “intensely competitive”...

A key feature of the preliminary issues paper was the proposed investigation of whether the country’s grocery sector is vulnerable to “accommodating” or “coordinated” behaviour, which it cites as a potential outcome in oligopolies.

The commission said such conduct does not necessarily require an explicit agreement or express coordination.

“Coordinated behaviour involves firms recognising that they can reach a more profitable outcome if they act to limit their rivalry when taking each other’s actions into account (such as by following a rival’s price increases),” the paper said.

The two Foodstuffs cooperatives have more than 400 retail stores nationwide predominantly under the New World, Pak’n’Save and Four Square banners, serving more than three million customers a week...

A market with two firms is a duopoly (and when there are more than two firms, but not many, the market is an oligopoly). The thing about duopoly markets (and oligopoly markets) is that the firms can more easily act to coordinate their behaviour, in terms of pricing or 'market splitting', to lower competition. Lower competition means higher profits for the firms.

To see how this works, consider the game laid out in the table below. There are two players (firms) - Foodstuffs and Woolworths. Each player has two strategies - price high, or price low. If both firms price low, then there is a price war and both are worse off. If both firms price high, then both are better off. The outcomes and payoffs are illustrated in the table (the payoff numbers represent profits, but are just made up to illustrate this example).

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If Woolworths chooses to price low, Foodstuffs' best response is to price low (since 50 is a better payoff than 25) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If Woolworths chooses to price high, Foodstuffs' best response is to price low (since 180 is a better payoff than 80);
3. If Foodstuffs chooses to price low, Woolworths' best response is to price low (since 50 is a better payoff than 25); and
4. If Foodstuffs chooses to price high, Woolworths' best response is to price low (since 180 is a better payoff than 80).

Note that Woolworths' best response is always to choose to price low. This is their dominant strategy. Likewise, Foodstuffs' best response is always to choose to price low, which makes it their dominant strategy as well. The single Nash equilibrium occurs where both players are playing a best response (where there are two ticks), which is where both firms choose to price low.

Notice that both firms would be unambiguously better off if they chose to price high. However, both will choose to price low, which makes them both worse off. This is a prisoners' dilemma game (it's a dilemma because, when both players act in their own best interests, both are made worse off).

So, it makes sense for the firms to try and find some way to avoid the bad (low price) outcome, and come to an 'arrangement' that ensures they get the better (high price) outcome. The NBR article gives suggestions of how this might be playing out:

Consumer NZ’s submission said it believed accommodating behaviour was a “major risk” in the market, particularly regarding price.

It detailed investigations it had made comparing prices between Woolworths’ private label brands sold at Countdown here and Woolworths in Australia, and found that New Zealand consumers paid 30% more for the same basket of 20 items...

Note that this type of behaviour doesn't actually require the two firms to collude. They can coordinate their actions even if they aren't directly communicating with each other. However, the structure and payoffs of the game haven't changed, so there will always be an incentive to 'cheat' on this sort of arrangement, and throw in a low price occasionally. Interesting, even that behaviour seems that it may be baked into the 'arrangement':

Consumer NZ’s supermarket price surveys, meanwhile, found that stores appeared to have ‘turns’ offering specials on the same products – for example, a particularly brand of cheese might be on special at one supermarket one week and then be on special at another the following.

Notice that in the game above, players colluding to set a high price would get a payoff of 80 each. However, if the game was played over and over again, and the two firms alternated who would have the low price, each firm would get 180 in the low price week, and 25 in the high price week, for a total of 205 (compared with 160 for sticking with high prices all of the time).

And this brings us to the idea of a repeated game. In a repeated game, the outcome may differ from the equilibrium of the non-repeated game, because the players can learn to work together to obtain the best outcome. And this could be what is happening. If Woolworths and Foodstuffs work together to alternate their low prices, both firms benefit. Both firms have a short-term incentive to 'cheat' (by setting a low price when the other firm does), but if they were to do so the arrangement could break down and both firms would end up back at the low price Nash equilibrium.

This is one of the aspects that the Commerce Commission is investigating as part of its market study into the grocery sector. Unsurprisingly, the supermarket firms are denying that any of this is going on. Maybe it isn't, or maybe it is and they just think that everyone is naive enough to believe them.

Book review: The Winner-Take-All Society

As I mentioned earlier in the week, I've been reading The Winner-Take-All Society by Robert Frank and Philip Cook. The book focuses on what Frank and Cook refer to as 'positional arms races' - the tendency for winner-take-all markets to lead to a prisoners' dilemma, where people engage in costly, but ultimately fruitless, investment in order to win the arms race. These winner-take-all markets (and the positional arms races they incentivise) have led to a number of negative consequences, as they summarise in the introduction:

Winner-take-all markets have increased the disparity between rich and poor. They have lured some of our most talented citizens into socially unproductive, sometimes even destructive, tasks. In an economy that already invests too little for the future, they have fostered wasteful patterns of investment and consumption. They have led indirectly to greater concentration of our most talented college students in a small set of elite institutions. They have made it more difficult for "late bloomers" to find a productive niche in life. And winner-take-all markets have molded our culture and discourse in ways many of us find deeply troubling.

That paragraph neatly summarises several chapters of the book, which look at the effects of winner-take-all markets in all of those areas. And far from simply looking at the 'superstar and tournament effects' that exist at the very top of the income distribution, Frank and Cook devote an entire chapter to 'minor-league superstars' such as doctors, administrators, and accountants (no mention of economists, though!).

For someone like myself, who has read a lot of Robert Frank books, there is little that is new. That isn't surprising, because this book was published in 1995, and I have read a lot of more recent work by Frank. The examples, while dated, still do a good job of illustrating the points that are being made (although I wonder how many younger readers would know about the Lorena Bobbitt story, without looking it up. The book has some very quotable bits, such as this:

Social critics have long identified advertising as perhaps the largest and most conspicuous example of pure social waste in a market economy.

And this critique of the free market:

...although Adam Smith's invisible hand assures that markets do a speedy and efficient job of delivering the goods and services people desire, it tells us nothing about where people's desires come from in the first place. If tastes were fixed at birth, this would pose no problem. But if culture shapes tastes, and if market forces shape culture, then the invisible hand is untethered. Free marketeers have little to cheer about if all they can claim is that the market is efficient at filling desires that the market itself creates.

The latter sections of the book discuss ways that society has adapted to curtail positional arms races, including through rules, social norms, contracts, and public policy. However, clearly those attempts have not been entirely successful, or there would be no need for the book!

The most disappointing aspect of the book may be the proposed solutions to the problems, where Frank and Cook focus on progressive consumption taxes. To me, they ignore the obvious problems of such a tax. It isn't as simple as taking a person's (or household's income) and subtracting savings in order to work out their consumption, because people (or households) could consume from past accumulated savings (in which case, the tax authority has to be able to determine how much savings the person (or household) had at the start and the end of the year), or from capital gains (in which case, the tax authority needs to be able to assess all realised capital gains). While they make their proposal seem very simple in theory, it would turn out to be anything but simple in practice.

Nevertheless, this is a good book that covers one of the sources of higher inequality over the last couple of decades, and is important source material for understanding more recent books by Robert Frank, such as the excellent Falling Behind: How Rising Inequality Harms the Middle Class.

The students' grade scaling dilemma

One of the sad things about teaching online is that I miss out on some of the more interesting conversations with students. I can almost never anticipate some of the truly interesting questions they come up with, and many of them unfortunately cannot be answered with the simple tools of introductory economics. Sometimes though, they can. Consider this example (paraphrased from a real question I was asked recently, but not by a current student of mine): If every paper is going to have its grades scaled to match past semesters, why should anyone do any of the coursework at all?

First, some context. The COVID-19 crisis has caused considerable disruption to university teaching, and the move to teaching and learning online has without doubt disadvantaged many students. There is justifiable concern that students' grades will be negatively affected. Some universities will be automatically scaling up all grades (e.g. University of Auckland). At Waikato, our Vice-Chancellor has announced that there will be no automatic scaling, but individual grades, and grade distributions for papers, will be compared with past trimesters, and adjusted to ensure they compare fairly with those past trimesters.

Now, as a student, if you know that grades will be scaled, then the incentive for you to work hard are lowered somewhat. Now think about the incentives for the class as a whole. If you could coordinate with all of the other students in your class as a 'cooperative', you could all agree to do no coursework at all. At the end of the trimester, you would all have your grades scaled up. And since the grade distribution needs to be similar to past years, most students in the cooperative would pass, without having to do any work at all.

So, why won't this happen? This is essentially an example of the prisoners' dilemma from game theory (see here for another example). The problem for the student cooperative is that the social incentive (to work together, do no coursework, and be scaled into a passing grade) doesn't match the private incentive. The private incentive for each student is to work slightly harder than the students in the cooperative, so that after the scaling you are at the top of the distribution, and get an easy A+ grade.

In fact, working slightly harder is a dominant strategy - it makes you better off if all of the other students do no coursework (since you get an easy A+), and it makes you better off if all the other students work slightly harder as well (since otherwise you fall behind and drop down the grade distribution, and are at risk of failing even after the grades are scaled). [*]

So, no student would agree to join the 'no-coursework cooperative', unless they could be sure that every other student would join as well. And no student could trust the other students to follow through on the cooperative, since every one of them could get an easy A+ by working slightly harder.

Cooperation is hard. As I note in my ECONS101 class, it requires trust between the players. And trust usually requires developing a reputation for being trustworthy. Unless you know the other students in your class really well, you probably have no reason to trust that they will follow through on a no-coursework agreement.

And so, that's why students should continue to do some coursework.

*****

[*] This doesn't quite extend to a strategy of 'working crazy hard' being a dominant strategy, because at some point the costs of increasing how hard you work on a paper begin to outweigh the benefits of doing so. We could easily make this much more complicated than necessary, so let's stick to two strategies - 'doing no coursework', and 'working slightly harder'.

CEOs playing games

Experimental economics is incredibly useful, because it allows economists to study decision-making in circumstances when basically all of the key parameters to the decision are controlled. However, one of the main problems with experimental economics is that the study population is often made up of students (see here and here for previous posts on this topic). So, it's particularly interesting when experimental economics makes us of samples made up of 'real people'.

For instance, in a new article (open access) published in the journal Experimental Economics, Håkan Holm (Lund University), Victor Nee (Cornell University), and Sonja Opper (Lund University), report on an experiment they conducted with Chinese CEOs and "comparable people in professional roles". Their sample size is quite large for this type of study - they have 200 CEOs and 200 other professionals.

Their experiment involves game theory - essentially, the research participants were asked to choose actions in three games: (1) the prisoners' dilemma (which I have written about before, most recently here); (2) a 'battle of the sexes' coordination game (I have written about coordination games too, see for example here); and (3) a chicken game (which I have also written about before, see here). They also asked the research participants about their beliefs about what the other research participants would choose.

Now, you might be thinking that CEOs have good strategic minds, and so they should be able to do well in game theoretic settings. You might also think that CEOs would be more selfish and more aggressive in these games. In those two hypotheses, you would only be partly correct. Holm et al. find that:

...substantial differences in behavior between the CEOs and the control group, but not in the way many would expect. The CEOs were not in general closer to the Nash equilibrium prediction (assuming selfish preferences). On the contrary, the average control group behavior was closer to the Nash equilibrium in the majority of the games and did not best respond less frequently to their beliefs. The most striking and consistent pattern was that the CEOs had higher expected earnings than the comparison group in all the games. The CEOs cooperated more and played less hawkishly compared to the control group, no matter how the game was framed (abstractly or with a narrative). Compared to the control group the CEOs’ also had significantly higher average beliefs that others would cooperate in the Prisoner’s Dilemma.

More specifically, the CEOs were between 13 and 25 percentage points more likely to choose the cooperative (prisoners' dilemma) or less aggressive (battle of the sexes, or chicken) option that the control group of professionals were. Because of (or perhaps in spite of) this, they earned more overall in the games. So, it appears that CEOs really do act differently than other (otherwise similar) people. Just not in the way that we might expect.

Holm et al. argue that this may be because less aggressive choices may be helpful because they allow the CEO "to mobilize support and loyalty from employees and business partners". I think we would need a lot more research before we can draw any conclusions about the mechanisms that explain these observed differences. Hopefully, there is more research on this to come.

[HT: Marginal Revolution, last year]

Coronavirus contact tracing and conditional cooperation

In a new article in The Conversation yesterday, Stefan Volk (University of Sydney) discusses coronavirus contact tracing in terms of the prisoners' dilemma (or what he terms a 'social dilemma'):

As governments look to ease general social-distancing measures and instead use more targeted strategies to stop coronavirus transmission, we face a social dilemma about the limits of cooperative behaviour...

Economists define a social dilemma as a situation where individual interests conflict with collective interests. More specifically, it is a situation in which there is a collective benefit from widespread cooperation but individuals have an incentive to “free ride” on the cooperation of others...

That is very similar to the point I made last month in relation to the coronavirus lockdown:

These people aren't stupid. They are selfish, and acting in their own self-interest. Which is why we needed to go into full lockdown, and early, if we wanted to curtail the spread of coronavirus. Any voluntary or partial measures would simply be subject to the prisoners' dilemma.

Lockdown or contact tracing, both are subject to the prisoners' dilemma. Volk then goes on to make a very interesting point in relation to real-world behaviour in prisoners' dilemma situations:

My research (with behavioural economist Christian Thöni of the University of Lausanne) confirms this.

Based on reviewing 17 social dilemma studies involving more than 7,000 individuals, we estimate no more than 3% of the population can be relied on to act cooperatively out of altruism – independent of what others do.

About 20% can be expected to act selfishly (i.e. free ride).

The majority – about 60% – are “conditional cooperators”. They cooperate if they believe others will cooperate.

Another 10% are so-called “triangle cooperators”. They behave similarly to conditional cooperators, but only to the point where they believe enough people are cooperating. They then reduce their cooperation.

The remainder – about 7% – behave unpredictably.

The majority of people are 'conditional cooperators'. In the context of a lockdown, they'll obey the rules if they believe most other people are obeying the rules. In terms of contact tracing, they'll download an app and give it access to their location, if they believe that many others are also doing so. Volk makes the point that this has implications for how the lockdown, or contact tracing, is executed. He notes that:

...we must be assured others aren’t getting away with uncooperative behaviour. In other words, free riding must be swiftly and visible punished.

Without these conditions, an expectation of widespread cooperative behaviour is merely a hope.

Punishment of the rule breakers during the lockdown appears to have been swift for some, but not all. And for the most part, New Zealanders appear to have been following the rules. However, it's hard to see how the government would enforce contact tracing - will we be fined for failing to keep a diary of all our daily contacts? It seems unlikely, which means that relying on conditional cooperation is going to be that much more difficult once the lockdown is lifted. That's why it's all the more important that the lockdown has been kept in place until the likelihood of further outbreaks has been reduced to near zero.

[Update: Read this follow-up post]

Read more:

• The prisoners' dilemma, and why we all have to be kept in lockdown

The prisoners' dilemma, and why we all have to be kept in lockdown

The prisoners' dilemma is probably the most famous example of game theory in action. I've written about it many times, in many different contexts (for example here, here, here, and here). In the prisoners' dilemma, all players have a dominant strategy, which is a strategy that is always better for the player, no matter what any of the other players choose to do. However, if each player acts in their own self-interest, the outcome leads to payoffs that are worse for everyone, than if they had cooperated. Robert Frank has described these games as leading to behaviour that is 'smart for one, dumb for all'.

And you can see this sort of behaviour all the time (once you know what to look for). Consider the current lockdown situation in New Zealand. If the lockdown was in any way voluntary (as it effectively was until Wednesday night), then each person has two options: (1) stay home; or (2) act normally. For most people, acting normally is a dominant strategy, at least in the early stages of the coronavirus spreading. They are better off acting normally if everyone else stays home (because they mostly get to go on with their lives as normal, and have low risk of catching the coronavirus; whereas staying home they would be giving up on things they like to do), and they are better off acting normally if everyone else is acting normally (because life goes on as normal, rather than giving up on things they like to do). So, individually people are better off acting normally. And so we saw things like this:

Hundreds of partygoers ignored the Government's advice and crowded into Wellington bars on Saturday night with no social distancing in sight.

Just hours after prime minister Jacinda Ardern confirmed the country was on a level two alert and urged people to work from home and keep a safe two metre distance from each other, young revellers took to bars around the country...

There were also reports of bars in other main cities including Auckland and Hamilton teeming with people.

And around the world:

Young German adults hold "corona parties" and cough towards older people.

A Spanish man leashes a goat to go for a walk to skirt confinement orders.

From France to Florida to Australia, kitesurfers, university students and others crowd the beaches...

"Some consider they're little heroes when they break the rules," French Interior Minister Christophe Castaner said. "Well, no. You're an imbecile, and especially a threat to yourself." 

These people aren't stupid. They are selfish, and acting in their own self-interest. Which is why we needed to go into full lockdown, and early, if we wanted to curtail the spread of coronavirus. Any voluntary or partial measures would simply be subject to the prisoners' dilemma. As I've noted before, in a repeated prisoners' dilemma (which this is, because we are essentially repeating it every day for the next four weeks), cooperation requires trust. And collectively, our behaviour up to this point hasn't earned that trust. We need to be locked down, so that the dominant strategy was no longer available to us.

Finally, an interesting research project for later would be to look at the difference in response, and the effectiveness of response, between countries that are more authoritarian and those that are more democratic, and between countries where the average 'respect for authority' (for want of a better term) is high or low. Even looking at the early data on the countries where the spread has been curtailed relatively quickly (China, South Korea) and those where it hasn't (Italy, Spain), I think we can see a pattern forming.

The oil price war is actually just a return to equilibrium

The 'war against coronavirus' may be just getting under way, but it wasn't the only war in the news in the past couple of weeks. Saudi Arabia and Russia have fired the first shots in an oil price war. The New Zealand Herald reported:

Expect to see petrol prices fall sharply in coming days after fears of a global price war sparked an historic collapse in crude oil barrel prices this morning

Oil prices plunged as much as 30 per cent as markets opened this morning - the biggest one day fall since the start of the first Iraq war in 1991.

Brent crude is currently down about 20 per cent.

But this follows falls of 10 per cent at the weekend on fears that Russia and Saudia [sic] Arabia will launch a full-scale price war.

Saudi Arabia slashed the price of its crude and upped production after Opec and Russia failed to agree on a supply response to coronavirus.

The industry had hoped that major players would agree on production cuts to mitigate the impact on global demand.

But talks in Vienna failed late on Saturday (NZT).

Global crude oil production is an example of an oligopoly - a market where there are many buyers, but few sellers. When there are few sellers, it is in the sellers' best interests to work together as a cartel. A cartel essentially acts like a monopoly seller - it is able to use market power to extract greater economic rent from the market (in the form of higher profits, arising from higher prices), than the countries would be able to extract if they were competing with each other.

This is another example of game theory in action. Let's say that there are two players - Saudi Arabia and Russia. Each player has two strategies - high production (which leads to lower prices and lower profits for oil producers), or low production (which leads to higher prices and higher profits). If one country has high production and the other low production, the high production country benefits more. However, if both countries have high production, both are worse off. These outcomes and payoffs are illustrated in the diagram below (the payoff numbers represent profits, but are just made up to illustrate this example).

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If Russia chooses high production, Saudi Arabia's best response is to choose high production (since 4 is a better payoff than 2) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If Russia chooses low production, Saudi Arabia's best response is to choose high production (since 10 is a better payoff than 8);
3. If Saudi Arabia chooses high production, Russia's best response is to choose high production (since 3 is a better payoff than 1); and
4. If Saudi Arabia chooses low production, Russia's best response is to choose high production (since 6 is a better payoff than 4).

Note that Russia's best response is always to choose high production. This is their dominant strategy. Likewise, Saudi Arabia's best response is always to choose high production, which makes it their dominant strategy as well. The single Nash equilibrium occurs where both players are playing a best response (where there are two ticks), which is where both countries choose high production.

Notice that both countries would be unambiguously better off if they chose low production. However, both will choose high production, which makes them both worse off. This is a prisoners' dilemma game (it's a dilemma because, when both players act in their own best interests, both are made worse off).

That's not the end of this story though, because the simple example above assumes that this is a non-repeated game. A non-repeated game is played once only, after which the two players go their separate ways, never to interact again. Most games in the real world are not like that - they are repeated games. In a repeated game, the outcome may differ from the equilibrium of the non-repeated game, because the players can learn to work together to obtain the best outcome.

And that is what happens when a cartel forms. If Saudi Arabia and Russia work together and both agree to choose low production, both countries benefit. That is what they were doing, up until a couple of weeks ago. The problem here is that both countries choosing low production is not an equilibrium. Each country individually realises that it can benefit by choosing high production (knowing that the other country is choosing low production), thereby cheating on the agreement. If both countries cheat, then the agreement breaks down and we end up at the Nash equilibrium (which appears to be what has happened). So essentially, the current oil 'price war' is simply a return to the equilibrium in this game.

However, it probably won't last. After a little while at the Nash equilibrium, it is likely that both countries will realise their folly, and work towards a new cartel agreement based on low production. And the cycle will begin all over again. Essentially, this has been the story of OPEC since soon after its formation - agreement by all (or most) parties, followed by selective cheating, followed by a breakdown in the agreement, followed by a new agreement.

So, make the most of low petrol prices. The coronavirus pandemic may keep them low for a while yet (due to low demand), but eventually Saudi Arabia and Russia will get their act together, and we'll be back to a world of higher oil prices (and consequently higher petrol prices).

[Updated 15/04/2020: To correct the positions of ticks and crosses in the payoff table]