The law and economics (and game theory) of Survivor

As I mentioned in a post last year, I really love the reality show Survivor. One day I might even collate some of the cool economics-related examples from the show - comparative advantage, asymmetric information, risk and uncertainty, public goods, common resources, and lots and lots of game theory (coalitions, prisoners' dilemmas, repeated games, coordination games, and so on).

I recently ran across this 2000 working paper by Kimberley Mason and Maxwell Stearns (both George Mason University) on the law and economics of Survivor. It would probably be more correct if the title said it was about the game theory of Survivor, which is what it is. It was written soon after the conclusion of the first season of Survivor (which is currently showing its 37th season - David vs. Goliath). The paper is interesting in that it traces out all the strategic decision-making in the first season, and relates it to game theory and rational decision-making. Mason and Stearns also highlight the masterstroke of the eventual winner, Richard Hatch, in bowing out of the last immunity challenge:

The strenuous nature of the competition helped Richard to justify a decision that was ultimately a well disguised defection from his suballiance with Rudy. Recall that Richard withdrew from the competition, claiming that he knew he would not win. If one construes the Richard/Rudy suballiance as a commitment to do whatever they can to ensure that they emerge as the finalists... then by withdrawing, Richard defected. To see why consider how the game was necessarily played as a result of Richard’s decision. Had Rudy won the competition, he would have voted to keep Richard on as a finalist, consistent with his commitment to the suballiance. Because Kelly preferred Rudy to Richard (as shown in her first vote in cycle 13), this would have risked a 4 to 3 vote for Rudy by the jury. (This assumes that the remaining six jurors vote as they did.). But if Kelly won the game, then she would choose between Rudy and Richard. She knew that either of them would vote for the other as a juror. The only question from her perspective was who was more popular with the remaining jurors. As Richard likely knew, Rudy was more popular, meaning that if Kelly won, Richard would still be selected as a finalist. In contrast, if Richard stayed in the immunity contest and won, he faced another Catch-22. If he voted to keep Rudy, then Kelly would vote for Rudy as a juror, and as a result, Richard would lose (again assuming the other jurors voted as they did). And if he voted for Kelly, then he would violate the express terms of the suballiance with Rudy, and risk Rudy’s retribution. If Rudy also defected, then Kelly would win. The only way that Richard could reduce the likelihood of this result was to withdraw from the game. While he would remain a finalist regardless of whether Rudy or Kelly won, he hoped that Kelly would win because she would eliminate his toughest final competitor.

Kelly won the challenge, and Richard duly won Survivor by a vote of 4-3. Mason and Stearns conclude:

At the beginning of this essay, we posited that Survivor was played in a manner that was consistent with the predictions of rational choice theory. We certainly do not suggest that every player played in a manner that optimized his or her prospects for winning. Indeed, that is largely the point. At each step in the game, those who best positioned themselves to win were the ones who played in a rational and strategic manner.

Interestingly, the paper also contains a discussion of the optimal size of an alliance, based on theory from Gordon Tullock and Nobel Prize winner James Buchanan, which should be familiar to my ECONS102 students:

Professors Buchanan and Tullock present an optimal size legislature as a function of two costs, agency costs, which are negatively correlated with the number of representatives, and decision costs, which are positively correlated with the number of representatives... The optimum point, according to Buchanan and Tullock, is that which minimizes the sum of agency and decision costs...

These two conflicting costs, which are both a function of coalition size, pit the benefits of safety in numbers against the risks of disclosure to non-alliance members... As the size of the coalition increases, the members are increasingly protected against the risk that a member will defect in favor of an alternative coalition. Conversely, as coalition size increases, the members face an increased risk of disclosure, which could lead to a coalition breakdown.

The optimal size of an alliance is one that correctly balances the benefits of being large enough to be safe from the non-allied players voting you off (the marginal benefit of adding one more person to the alliance decreases as the alliance gets larger), against the costs of the alliance being revealed to all players (the marginal cost of adding one more person to the alliance increases as the alliance gets larger). The cost of having a large alliance also relates to the chance of defection - the chance that one or more members of the alliance switch sides and blindside someone. It is easier to maintain trust and cohesion in a smaller alliance.

Survivor is a great example of economics in action. If you aren't already a fan, you should start watching it!

Read more:

• The economics of Survivor

The debate over a well-cited article on online piracy

Recorded music on CDs and recorded music as digital files are substitute goods. So, when online music piracy was at its height in the 2000s, it is natural to expect that there would be some negative impact on recorded music sales. For many years, I discussed this with my ECON110 (now ECONS102) class. However, in the background, one of the most famous research articles on the topic actually found that there was essentially no statistically significant effect of online piracy on music sales.

That 2007 article was written by Felix Oberholzer-Gee (Harvard) and Koleman Strumpf (Kansas University), and published in the Journal of Political Economy (one of the Top Five journals I blogged about last week; ungated earlier version here). Oberholzer-Gee and Strumpf used 17 weeks of data from two file-sharing servers, matched to U.S. album sales. The key issue with any analysis like this is:

...the popularity of an album is likely to drive both file sharing and sales, implying that the parameter of interest γ will be estimated with a positive bias. The album fixed effects vi control for some aspects of popularity, but only imperfectly so because the popularity of many releases in our sample changes quite dramatically during the study period.

The standard approach for economists in this situation is to use instrumental variables (which I have discussed here). Essentially, this involves finding some variable that is expected to be related to U.S. file sharing, but shouldn’t plausibly have a direct effect on album sales in the U.S. Oberholzer-Gee and Strumpf use school holidays in Germany. Their argument is that:

German users provide about one out of every six U.S. downloads, making Germany the most important foreign supplier of songs... German school vacations produce an increase in the supply of files and make it easier for U.S. users to download music.

They then find that:

...file sharing has had only a limited effect on record sales. After we instrument for downloads, the estimated effect of file sharing on sales is not statistically distinguishable from zero. The economic effect of the point estimates is also small.... we can reject the hypothesis that file sharing cost the industry more than 24.1 million albums annually (3 percent of sales and less than one-third of the observed decline in 2002).

Surprisingly, this 2007 article has been a recent target for criticism (although, to be fair, it was also a target for criticism at the time it was published). Stan Liebowitz (University of Texas at Dallas) wrote a strongly worded critique, which was published in the open access Econ Journal Watch in September 2016. Liebowitz criticises the 2007 paper for a number of things, not least of which is the choice of instrument. It is worth quoting from Liebowitz's introduction at length:

First, I demonstrate that the OS measurement of piracy—derived from their never-released dataset—appears to be of dubious quality since the aggregated weekly numbers vary by implausibly large amounts not found in other measures of piracy and are inconsistent with consumer behavior in related markets. Second, the average value of NGSV (German K–12 students on vacation) reported by OS is shown to be mismeasured by a factor of four, making its use in the later econometrics highly suspicious. Relatedly, the coefficient on NGSV in their first-stage regression is shown to be too large to possibly be correct: Its size implies that American piracy is effectively dominated by German school holidays, which is a rather farfetched proposition. Then, I demonstrate that the aggregate relationship between German school holidays and American downloading (as measured by OS) has the opposite sign of the one hypothesized by OS and supposedly supported by their implausibly large first-stage regression results.

After pointing out these questionable results, I examine OS’s chosen method. A detailed factual analysis of the impact of German school holidays on German files available to Americans leads to the conclusion that the extra files available to Americans from German school holidays made up less than two-tenths of one percent of all files available to Americans. This result means that it is essentially impossible for the impact of German school holidays to rise above the background noise in any regression analysis of American piracy.

I leave it to you to read the full critique, if you are interested. Oberholzer-Gee and Strumpf were invited to reply in Econ Journal Watch. However, instead they published a response in the journal Information Economics and Policy (sorry, I don't see an ungated version online) the following year.  However, the response is a great example of how not to respond to a critique of your research. They essentially ignored the key elements of Liebowitz's critique, and he responded in Econ Journal Watch again in the May 2017 issue:

Comparing their IEP article to my original EJW article reveals that their IEP article often did not respond to my actual criticisms but instead responded, in a cursorily plausible manner, to straw men of their own creation. Further, they made numerous factual assertions that are clearly refuted by the data, when tested.

In the latest critique, Liebowitz notes an additional possible error in Oberholzer-Gee and Strumpf's data. It seems to me that the data error is unlikely (it is more likely that the figure that represents the data is wrong), but since they haven't made their data available to anyone, it is impossible to know either way.

Overall, this debate is a lesson in two things. First, it demonstrates how not to respond to reasonable criticism - that is, by avoiding the real questions and answering some straw man arguments instead. Related to that is making your data available. Restricting access to the data (except in cases where the data are protected by confidentiality requirements) makes it seem as if you have something to hide! In this case, the raw data might have been confidential, but the weekly data used in the analysis are derivative and may not be. Second, as Leibowitz notes in his first critique, most journal editors are simply not interested in publishing comments on articles published in their journal, where the comments might draw attention to flaws in the original articles. I've struck that myself with Applied Economics, and ended up writing a shortened version of a comment on this blog instead (see here). It isn't always the case though, and I had a comment published in Education Sciences a couple of months ago. The obstructiveness of authors and journal editors to debate on published articles is a serious flaw in the current peer reviewed research system.

In the case of Oberholzer-Gee and Strumpf's online piracy article, I think it needs to be seriously down-weighted. At least until they are willing to allow their data and results to be carefully scrutinised.

Drinking increases the chances of coming to an agreement?

Experimental economics allows researchers to abstract from the real world, presenting research participants with choices where the impact of individual features of the choice can be investigated. Or sometimes the context in which choices are made can be manipulated to test their effects on behaviour.

In a 2016 article published in the Journal of Economic Behavior & Organization (I don't see an ungated version, but it looks like it might be open access anyway), Pak Hung Au (Nanyang Technological University) and Jipeng Zhang (Southwestern University of Finance and Economics) look at the effect of drinking alcohol on bargaining.

They essentially ran three experiments, where participants drank either: (1) a can of 8.8% alcohol-by-volume beer; (2) a can of non-alcoholic beer; or (3) a can of non-alcoholic beer (and where they were told it was non-alcoholic). They then got participants to play a bargaining game where each participant was given a random endowment of between SGD1 and SGD10, then paired up with another and:

...chose whether to participate in a joint project or not. If either one subject in the matched pair declined to participate in the joint project, they kept their respective endowments. If both of them agreed to start the joint project, the total output of the project was equally divided between them. The project’s total output was determined by the following formula: 1.2 × sum of the paired subjects’ endowment.

So, if Participant X had an endowment of 4 and Participant Y had an endowment of 8, and they both chose to participate in the joint project, they would each receive $7.20 (12 * 1.2 / 2). So, it should be easy to see that participants with a low endowment are more likely to be better off participating than participants with a high endowment (who will be made worse off, like Participant Y in the example above, unless the person they are paired with also has a high endowment). Au and Zhang show that participating in the joint project should only be chosen by those with an endowment of 3 or less.

Using data from 114 NTU students, they then find that:

...[w]hen the endowment is between 1 and 4 dollars, almost all subjects participate in the alcohol treatment and a large proportion (around 90–95%) of the subjects join the project in the two nonalcohol treatments. When the endowment is above 8 dollars, the participation ratio drops to around 0.2...

...subjects in the alcohol treatment are more likely to join the project at almost all endowment levels, compared with their counterparts in the two nonalcohol treatments.

Importantly, they show that drinking alcohol has no effect on altruism or risk aversion, ruling out those as explanations for the effect, leading them to conclude that:

...in settings in which skepticism can lead to a breakdown in negotiation, alcohol consumption can make people drop their guard for each others’ actions, thus facilitating reaching an agreement.

Drinking makes people more likely to come to an agreement. I wonder how you could reconcile those results with the well-known effects of alcohol on violent behaviour? Perhaps alcohol makes people more likely to agree to engage in violent confrontation?

Read more:

• Drunk people are more impatient and less generous

Tauranga's beggar ban, and the economics of panhandling

Tauranga City Council has just passed a ban on begging. The New Zealand Herald reports:

The council voted 6-5 to ban begging and rough sleeping within five metres of the public entrances to retail or hospitality premises in the Tauranga City, Greerton and Mount Maunganui CBDs.

The bans will become law on April 1, 2019, as part of the council's revised Street Use and Public Places Bylaw...

[Councillor Terry] Molloy said the measures of success would be a marked reduction in beggars and rough sleepers in the targeted areas, the community feeling a higher level of comfort with their security in those areas, happier retailers and no proof the problem had moved elsewhere.

Becker's rational model of crime applies here. Panhandlers (or beggars) weigh up the costs and benefits of panhandling when they decide when (and where) to panhandle. If you increase the costs of panhandling (for example, by penalising or punishing panhandlers), you can expect there to be less of it (at least, in the areas where the penalties are being enforced). How much less? I'll get to that in a moment.

You may doubt that panhandlers are rational decision-makers. However, a new paper by Peter Leeson and August Hardy (both George Mason University) shows that panhandlers do act in rational ways. Using data from 258 panhandlers, observed on 242 trips to Washington D.C. Metrorail stations, Leeson and Hardy find that:

Panhandlers solicit more actively when they have more human capital, when passersby are more responsive to solicitation, and when passersby are more numerous. Panhandlers solicit less actively when they encounter more panhandling competition. Female panhandlers also solicit less actively...

Panhandlers are attracted to Metro stations where passersby are more responsive to solicitation and to stations where passersby are more numerous. Panhandlers are also attracted to Metro stations that are near a homeless shuttle-stop and are more numerous at stations that are near a homeless service.

In other words, if the benefits of panhandling increase (because passersby are more responsive, or more numerous), there will be more panhandling. If the costs of panhandling are higher (because the Metro station is further to travel to), there will be less panhandling. This is exactly what you would expect from rational panhandlers. As Leeson and Hardy note:

...panhandlers behave as homo economicus would behave if homo economicus were a street person who solicited donations from passersby in public spaces.

Interestingly, Leeson and Hardy also explain in economic terms how panhandling works:

...panhandler solicitation is generally regarded as a nuisance; it threatens to create “psychological discomfort…in pedestrians,” such as guilt, awkwardness, shame, even fear (Ellickson 1996: 1181; Skogan 1990; Burns 1992).5 Third, pedestrians are willing to pay a modest price to avoid this discomfort...

By threatening more discomfort, more active panhandler solicitation extracts larger payments through two channels. First, it makes passersby who would have felt the threat of some discomfort and thus paid the panhandler something even if he had solicited less actively feel a still greater threat and thus pay him more. Second, it makes passersby who would not have felt the threat of any discomfort and thus not paid the panhandler anything if he had solicited less actively feel a threat and thus pay him a positive amount.

An interesting question arises though. Panhandlers have imperfect information about how willing passersby are to pay to avoid this discomfort. They find this out through soliciting. So, in areas where passersby pay more (or more often), that might encourage panhandlers to be more active. I'm sure I'm not the only one who has been told not to pay panhandlers, because you just encourage more of the activity. It seems obvious. But is it true?

A new article by Gwendolyn Dordick (City College New York) and co-authors, published in the Journal of Urban Economics (ungated earlier version here), suggests probably not. They collected data from 154 walks through downtown Manhattan (centred around Broadway) in 2014 and 2015, where they observed the location and numbers of panhandlers. Importantly, their data collection occurred before and after several significant changes downtown, including the opening of One World Trade Center and its observation deck, and the increase in foot traffic associated with the September 11 Museum. This allowed them to evaluate how an increase in potential earnings (through more passersby, especially tourists) affects panhandling. They find that:

...the increase in panhandling was small and possibly zero (although our confidence intervals are not narrow enough to rule out relatively large changes). Panhandling moved from around Broadway toward areas where tourists were more common... We tentatively conclude that the supply elasticity of panhandling is low...

The moral hazard involved in giving to panhandlers seems to be small. More generally, the incidence of policy changes in places like Downtown Manhattan is likely to be pretty simple: a fairly constant group of panhandlers gains or loses; there is no “reserve army of panhandlers ”to eliminate any rise in returns by flooding in, and no shadowy “panhandling boss ”behind the scenes to soak up any gains by asking more money for right to panhandle in various locations (since control over even the best location is not worth much because substitute lo- cations are often vacant). Giving to panhandlers does not to any great extent encourage panhandling or a fortiori homelessness. 

In other words, when the expected earnings from panhandling increase, there isn't a sudden influx of new panhandlers, and existing panhandlers don't spend more time soliciting. Interestingly, they also find that:

Because the number of people who want to panhandle, even at the best times and places, is small, space is effectively free. Supply at zero price exceeds demand. Because space is free, so is courtesy, and so is abiding by norms.

There was little fighting among the panhandlers, because space was abundant. The main constraint to panhandling in Manhattan appeared to be that people didn't want to panhandle, not a lack of space to do so. This may also be because the panhandlers are 'target earners' - they only panhandle for long enough to earn what they wanted to for that day, so if the earnings are good they don't have to panhandle for very long (although Dordick et al.'s results cast some doubt on whether panhandlers actually are target earners).

What can Tauranga learn from the results of these two papers? Greater penalties on panhandlers will reduce panhandling, but it might also simply move it elsewhere. In these other locations, panhandlers will have to work even harder (perhaps being even more aggressive), and for longer, to achieve their target earnings. And because the best spaces for panhandling have been taken away from them, there may be even more conflict over the remaining spaces. I guess we'll see in due course.

[HT for the Leeson and Hardy paper: Marginal Revolution]