Sunday, 25 November 2018

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!

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