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Martin Peterson (ed.), The Prisoner’s Dilemma

Shaun P. Hargreaves Heap
p. 165-168
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Martin Peterson (ed.), The Prisoner’s Dilemma, Cambridge: Cambridge University Press, 2015, 298 pages, ISBN 978-110736017-4

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1The Prisoners’ dilemma, without any apparent effort on my part, almost always generates a bit of wonder in the class. You can hear and see an attentive form of bristling. You can see it on the students’ faces: some blink, some frown. Others pull themselves up in their seats with a deep breath or an unnaturally loud sigh. I don’t have to pose the question in the class for it to be felt: how can what seems rational produce such a stupid result?

2The first few chapters of this volume discuss this “paradox of rationality”. There are contributions from Binmore, Gauthier and Hausman, and also some later ones by Bicchieri, Sontuoso, and Bonanno that address the question from different angles. My reading of them as a group yields what seems to me to be the conventional wisdom now on this matter. It is as follows.

3In standard game theoretic terms, it is not rational to cooperate in a one shot Prisoners’ dilemma. If, however, we (appear to) observe cooperation, then three inferences are possible.

  1. People are guided in their actions by a different kind of rationality to that found in game theory (or not by rationality at all).

  2. The interaction has been wrongly described as a Prisoner’s dilemma because individuals are motivated in, possibly various, non-selfish ways with the result that the interaction is better described by another game where “cooperation” is game theoretically rational.

  3. The interaction may be part of an indefinitely repeated Prisoners’ dilemma in which it can be rational to cooperate.

4There may be some overlaps between 1) and 2) because, for instance, some accounts of social norms can both challenge the game theoretic account of rationality and the description of the pay-offs in an interaction. 3) may also be less of a solution to the paradox than its substitution for another. This is because, while placing the interaction in a repeated setting may explain how cooperation is rationally possible, it creates another puzzle or problem: these repeated games have multiple equilibria and conventional game theory cannot explain how one is selected. This point is made trenchantly by both Binmore in his opening chapter and in a later chapter by Northcott and Alexandrova on the explanatory power of the Prisoners’ dilemma.

5The question that naturally arises is: What should one make of this conventional wisdom regarding the Prisoners’ dilemma? It is unfortunate, but perhaps not unsurprising in an edited volume, that it is difficult to find a direct or settled answer or a clear outline of the debate over this question. Peterson has a good introductory chapter on the dilemma but there is no similar conclusion. The last chapter by Weirich is titled the “Lesson of the Prisoner’s Dilemma” but it is focused more narrowly on what it might entail for rationality. So I will propose an answer and try to show how the other contributions relate to this.

6My answer is that the Prisoners’ dilemma is inescapably important (and centrally so for social science) in so far as many important interactions can plausibly be described under a selfish account of motives and the game theoretic view of rationality as a Prisoners’ dilemma. This is so for one of two reasons (A and B) depending on whether we observe cooperation or not in such settings.

7If we don’t cooperate, then we need to construct institutions for collective action (and subordinate individual freedom in these areas to these institutions) in so far as we wish to achieve the Pareto improvement that comes from cooperation. A) This is a first order political inference from the Prisoners’ dilemma. (There is little on this in the volume.)

8If, alternatively we do cooperate in such settings, then we need to redirect our intellectual efforts away from the game theoretic account of rationality, a presumption of selfishness or towards understanding how an equilibrium is selected. B) This is a first order agenda setting insight for social science from the dilemma. (There is more on this.)

9Thus, it does not really matter for the importance of the Prisoners’ dilemma whether individuals (appear) to cooperate in one shot prisoners’ dilemma or not. Whichever is the case, there is an important insight. It is just the nature of the insight that changes. I have spelled this out because, if anything, the overall tone of the volume is an encouragement to the thought that the Prisoners’ dilemma has been over-rated. To my mind, for the reasons I have just sketched, this would only be warranted if one doubted whether the “many” and “plausible” parts of the “in so far as many important interactions can plausibly be described under a selfish account of motives and the game theoretic view of rationality as a Prisoners’ dilemma” statement above were satisfied.

10The “many” and “plausible” are non-trivial conditions and several of the contributions do address their likelihood, but often indirectly or only in passing. There is, for instance, a chapter by Bermudez on the relation between the Prisoners’ dilemma and Newcomb’s problem that is interesting in its own right but can be viewed also as a reflection on whether the Prisoners’ dilemma is always the appropriate way of thinking about interactive dilemmas. Peterson’s own contribution extends the dilemma to intra-subagent interactions. Brennan and Brooks consider whether Public Goods interactions only differ from the two-person Prisoner’s dilemma through a simple numbers or scale effect. They offer some novel insights with respect to the complicated effects of increasing the numbers in the interaction. Binmore refers in passing to the significant claim in the literature that the Stag-Hunt game is more often the key encapsulation of the social dilemmas that we face. The Bovens chapter is an exception because it directly addresses the applicability of these conditions by examining whether the n person Prisoners’ dilemma captures the Tragedy of the Commons and so is the chapter by McLean on the application of the Prisoners’ dilemma to the problem of climate change. Northcott and Alexandrova also address the issue centrally. Their chapter is perhaps the most significant source in the volume for my earlier remark about “the Prisoners’ dilemma is over-rated” tone. Their argument, using the “live-and-let-live” norm in the WWI trenches as the key illustration, is that the Prisoners’ dilemma is often misapplied or is too loosely attributed to interactions. Their analysis of the norm is very interesting and it correctly suggests that the Prisoners’ dilemma itself does not tell us why the norm occurred in some places and not others, or why it disappeared. However, these are not doubts about whether the basic interaction between combatants in trenches (over whether, as it were, to “shoot-to-kill” or “shoot-for-show”) corresponds to a Prisoners’ dilemma. They are a complaint about the absence of an account regarding equilibrium selection once this interaction is indefinitely repeated (see the comment about inference 3. above). This is a reasonable complaint to make about game theory. It is not a complaint about the applicability of the prisoners’ dilemma. Indeed, the complaint only takes the form that it does once we accept the appropriateness of the dilemma as a description the interaction between combatants.

11For these reasons, I’m not inclined on the basis of this volume to doubt that the “many” and “plausibly” conditions apply and so I hold to the view that the Prisoners’ dilemma is central to social science. The question therefore that follows concerns the way that it is central (is it A. or B.?); and, as I have suggested, this turns on whether people tend to cooperate or not in these dilemmas. This is where the chapter by Holt, Johnson and Schmidtz on the experimental evidence on how people play the Prisoner’s dilemma in the laboratory is helpful. The standard experimental result has surprisingly high cooperation in one shot games. But, this falls with both stranger and partner matching in finitely repeated versions of the game. Thus, the experimental evidence suggests that the Prisoners’ dilemma is likely to be important both for collective action institution formation and for the account of what makes people tick (i.e., both A) and B)). It is in this context that Holt et al. is particularly useful because they consider some of what we know affects the level of cooperation. In particular, they focus on the experiments where cooperation is sustained better when individuals can choose who they interact with and they report on a new experiment of their own in this vein.

12The experimental results are actually more extensive on this topic. There are related results that find that “social closeness” of subjects or their membership of the same group in a multi-group setting in the lab also promotes cooperation. Experiments also find that the capacity to punish affects the level of cooperation (usually beneficially) and that inequality typically hinders cooperation. There have also been experiments that seem to support the “parochial altruism” conjecture regarding the origins of altruism, broadly understood, within a group (i.e., that it depends on a conflict or competition between groups). These are all interesting and potentially important insights; and it is a pity they are largely overlooked.

13So, this is a good volume to go to if you want to read some of the work of some of the important contributors to the debate over the Prisoner’s dilemma. It is less good, and this is perhaps in the nature of an edited volume that relies in this way on important contributions, if you want a clear view of where the debate now stands over the importance of the Dilemma.

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Shaun P. Hargreaves Heap, « Martin Peterson (ed.), The Prisoner’s Dilemma », Œconomia, 9-1 | 2019, 165-168.

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Shaun P. Hargreaves Heap, « Martin Peterson (ed.), The Prisoner’s Dilemma », Œconomia [En ligne], 9-1 | 2019, mis en ligne le 01 mars 2019, consulté le 27 juin 2019. URL :

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Shaun P. Hargreaves Heap

King’s College, London

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