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.

More evidence that movie production incentives don't pay off

An anonymous reader pointed me to this 2020 article by John Bradbury (Kennesaw State University), published in the journal Contemporary Economic Policy (ungated earlier version here), on the impacts of state-level movie production incentives in the US. This is a topic I have blogged about before, and something I retain an interest in (not least because our government is very keen on providing large subsidies to foreign movie production firms).

Bradbury collates the data on movie production incentives (MPIs) over the period from 2000 to 2015, during which time:

...44 states enacted MPIs, seven states ended their programs, and four states suspended their programs temporarily... Several states also expanded and reduced incentives for filming over time...

That provides sufficient variation to determine the relationship between incentives and economic growth, especially as the variable of interest (MPIs) could be defined as a continuous variable. However, instead:

MPI is equal to zero or one, where one reflects the state having any active state-funded film incentives in place during any part of the year of observation or it denotes a certain incentive threshold for in-state spending on film projects...

So, essentially this is an analysis at the extensive margin of MPIs (comparing states with, and without, MPIs), or at the intensive margin at particular thresholds. Bradbury does note (in a footnote) that using a continuous measure of MPIs "did not produce meaningfully different estimates", but that just makes me wonder why those results weren't presented as the primary results. To deal with the potential endogeneity of MPIs and economic growth (which would arise, for example, if characteristics of states that affect economic growth also affect whether the state offers MPIs), Bradbury employs an instrumental variables approach. Specifically, he instruments for MPIs using the age of the state's film commission and whether neighbouring states have MPIs. Those seem like sensible instruments, and they are good predictors of MPIs and pass the usual tests for weak instruments in the first stage of the estimation.

As an outcome variable, Bradbury looks at income per capita (in levels and growth rate), as well as Gross State Product (GSP) per capita (the state-level equivalent of GDP per capita, again in levels and growth rate). He also looks at GSP specific to the film industry alone. In the main results, he finds that:

Estimates of having any MPI program are not statistically significant for any measure of economic performance, which is not indicative of a large multiplier that enhances economic development. Estimates of the economic impact of MPI implementation on the film industry are also insignificant, which does not indicate an industry-specific effect.

So, not only is there no effect of MPIs on the economy overall, there is not even a statistically significant effect on the film industry. Bradbury then goes on to look at different types of incentives and different levels of incentives, and there is no clear pattern of significant positive effects on the economy (the few statistically significant effects he finds would probably not survive an adjustment for multiple hypothesis testing, and to highlight them would simply be a case of cherry-picking of results).

So, in addition to not paying off in terms of tax revenue, it seems that movie production incentives don't pay off in terms of economic growth. You might wonder why these incentives don't pay off. There are a number of potential reasons. Perhaps movie production crowds out other economic activities. However, if that were the case then Bradbury would have found an increase in GSP in the film industry, and there would have been an offsetting decline in other industries. Alternatively, perhaps movie production (at some level) would have happened in the state anyway, and the incentives simply become a transfer from the state government to the movie production firms. On that point, Bradbury notes (in discussing an earlier study) that there may be:

...a “crowding out” effect due to many states offering incentives in a zero-sum game, where film production companies move (or threaten to move) to competitor states unless appropriate incentives are offered. If many states offer incentives, then film companies ultimately end up filming in their desired location (where they would have located absent subsidies) with a significant subsidy.

That strikes me as likely to be the case. If your state was the only state offering an incentive, then it is likely to attract movie productions that would have otherwise occurred elsewhere. However, if most states are offering incentives, then Tiebout competition kicks in, and the movie production firms simply play off states against each other. Only the movie production firms benefit from that situation.

Bradbury concludes that:

...it appears that MPIs divert tax revenue to the film industry from other economic sectors (public and private) without generating corresponding economic growth, which calls into question the popular use of film incentives to promote economic development...

Film incentives represent another example of an economic development strategy that fails to promote growth, which provides further evidence that industry-specific incentives to lure business offer an uncertain path to economic improvement.

I think we would do well to take this as a warning against these incentives, and we certainly shouldn't be overly concerned about losing productions to other countries.

Read more:

• Lord of the Rings, tourism arrivals and harvesting
• More on hobbits and tourism
• Movie production incentives don't pay off

What pandemic schooling tells us about online learning

I've made online teaching and learning a regular theme of this blog (see the long list of links at the end of this post). I'm still of the opinion that online teaching creates a learning deficit among less-motivated or low-ability students, although on average the outcomes are similar for different teaching and learning modes. I desperately want someone to convince me that there is a solution that will at least lead to similar outcomes as we observe in face-to-face teaching, across the entire ability distribution. I'm yet to find it.

Most of the literature I have read relates to teaching and learning in the university context. That makes sense - until recently, online teaching and learning has been much more prevalent in tertiary education. However, the pandemic forced online teaching at all levels of schooling, providing a broad natural experiment on the impacts of online learning. So, I was interested to read this new working paper by Rebecca Jack (University of Nebraska-Lincoln), Clare Halloran (Brown University), James Okun (MIT), and Emily Oster (Brown University), which focuses on online teaching of US students in Grades 3 to 8. Specifically, Jack et al. combine exhaustively-collected data on school learning mode by school district across 11 states, with data from standardised tests conducted in 2016 to 2019, and in 2021 (with no testing being conducted in 2020 due to the pandemic). They distinguish three types of schooling mode:

...1) "in-person" (all or most students had access to traditional, 5-day-per-week, in-person instruction); 2) "virtual" (all or most students received instruction online, five days a week); and 3) "hybrid" (schooling modes that did not fall into one of these approaches).

Jack et al. then measure the percentage of school days in each schooling mode for each school district, and test the relationship between schooling mode (as a continuous variable) and pass rates (at the school district level) in English language arts (ELA) and maths. They find that:

The coefficients are quite stable across specifications and highly significant in all of them. In terms of magnitude, these regressions suggest that moving a district from fully virtual to 100% access to in-person learning would have reduced pass rate losses in Spring 2021 by 13 to 14 percentage points in math and about 8 percentage points in ELA. Moving from fully virtual to fully hybrid would have reduced pass rate losses by about 7 percentage points in math and 5 to 6 percentage points in ELA. Focusing on within-state, within-commuting zone variation in schooling mode, we estimate districts with full in-person learning had an average decline of 13.4 percentage points less in math and 8.3 percentage points less in ELA.

Those declines are quite substantial, and Jack et al. also find (what I characterise as) suggestive evidence that the effects are larger in school districts with a greater share of African American students, although they find no difference in impact between school districts with a greater or lesser share of low-income students (as measured by eligibility for free or reduced price school lunches). Also of interest, when looking at each grade individually, they find that:

In general, we see higher impacts in younger grades. This is especially true for in-person learning. This may reflect a greater benefit of consistent in-person time for younger students, although based on these data alone it is difficult to fully elucidate mechanisms.

One possible mechanism is that older students may be more self-directed in their learning than younger students are, and therefore better able to negotiate the online learning environment. That would accord with the limited difference in the literature in learning outcomes (on average) between online and face-to-face learning at tertiary level. However, it would be interesting to know whether there was heterogeneity in the effect of online learning between students at different levels in the ability distribution at this level (as observed in tertiary education). However, without longitudinal data on individual students (rather than aggregate data at the school district level), it would be difficult to investigate that heterogeneity.

Taking this study alongside others (particularly at the tertiary level), it seems to me that we need to understand more about how academic self-efficacy (or how self-directed students are) interacts with online teaching and learning. It would also be good to understand more about how academic self-efficacy can be promoted in the online environment, particularly among students in the bottom half of the ability distribution.

[HT: Marginal Revolution]

Read more:

• Online vs. blended vs. traditional classes
• Flipped classrooms work well for top students in economics
• Flipped classrooms are still best only for the top students
• Online classes lower student grades and completion
• Online classes may also make better students worse off
• Meta-analytic results support some positive effects of using videos on student learning
• New review evidence on recorded lectures in mathematics and student achievement
• Meta-analytic results may provide some support for flipping the classroom
• The value of an in-person university education
• The pandemic may have revealed all we need to know about online learning
• Live streamed video lectures and student achievement
• Low-performing students, online teaching, and self-selection
• A slightly more optimistic take on online learning during the pandemic
• Research-based instructional strategies and flipped classrooms in economics
• Using microcommitments and social accountability to improve online and hybrid learning

Dani Rodrik on the benefits of economic populism

I just read an interesting 2018 article by Dani Rodrik (Harvard University), published in the AER Papers and Proceedings (ungated here). Rodrik starts by outlining a taxonomy of regimes, based on whether there are political restraints and/or restraints on economic policy, resulting in the following 2x2 matrix (Table 1 from the article):

*****

Rodrik describes the four possibilities in the 2x2 matrix as:

Personalized regimes such as Vladimir Putin’s in Russia or Tayyip Erdogan’s in Turkey are characterized by the absence of restraints in both the political and economic domains (box 1). But it is possible to conceive of autocratic regimes where important aspects of economic policy are placed on automatic pilot or delegated to technocrats (box 2). Pinochet’s regime in Chile provides an example.

Alternatively, a regime can be populist in the economic sense without rejecting liberal, pluralist norms in the political domain (box 3). Finally, a regime that is constrained in both politics and economics might be called a “liberal technocracy” (box 4). The European Union may be an example of the last type of regime: economic rules and regulations are designed at considerable distance from democratic deliberation at the national level, which accounts for the frequent complaint of a democratic deficit.

The rest of the article then mostly discusses the differences between regime (3) and regime (4), drawing an important distinction between two types of restraints on economic policy. First, there are:

...restraints on economic policy that take the form of delegation to autonomous agencies, technocrats, or external rules. As described, they serve the useful function of preventing those in power from shooting themselves in the foot by pursuing short-sighted policies.

Rodrik provides the example of delegating monetary policy to an independent central bank, or constraining trade policy through the use of free trade agreements. In terms of the second type of restraint on economic policy:

Commitment to rules or delegation may also serve to advance the interests of narrower groups, and to cement their temporary advantage for the longer run. Imagine, for example, that a democratic malfunction or random shock enables a minority to grab the reins of power. This allows them to pursue their favored policies, until they are replaced. In addition, they might be able to bind future majorities by undertaking commitments that restrain what subsequent governments can do.

Rodrik again uses the example of monetary policy, where a central bank's rigid adherence to inflation targeting can make us worse off, and to trade policy, where rules on intellectual property are exported and this extends the market power of holders of intellectual property rights.

Then comes the crux of Rodrik's argument - that economic populism, where the constraints on economic policy are relaxed or removed, may actually be beneficial in some cases. In particular, since:

...delegation to independent agencies (domestic or foreign) occurs in two different contexts: (i) in order to prevent the majority from harming itself in the future; and (ii) in order to cement a redistribution arising from a temporary political advantage for the longer term. Economic policy restraints that arise in the first case are desirable; those that arise in the second case are much less so.

Rodrik uses the substantial economic policy changes wrought by Franklin D. Roosevelt and the New Deal as an illustrative example. This paper presents an interesting framework to think about when constraining government economic policy may be a good idea, and when it may be better to relax the constraints. However, the short format of the article prevents a deeper examination of all of the implications of this framework. As described, I'm sure it could be used opportunistically to argue in favour of relaxing constraints in almost any situation. Hopefully, this is a topic that Rodrik is going to follow through on, as it really needs a book-length treatment (and I've quite enjoyed some of his other books - see reviews here and here).