Working memory constrains human cooperation in the Prisoner’s Dilemma

Many problems in human society reflect the inability of selfish parties to cooperate. The “Iterated Prisoner’s Dilemma” has been used widely as a model for the evolution of cooperation in societies. Axelrod’s computer tournaments and the extensive simulations of evolution by Nowak and Sigmund and others have shown that natural selection can favor cooperative strategies in the Prisoner’s Dilemma. Rigorous empirical tests, however, lag behind the progress made by theorists. Clear predictions differ depending on the players’ capacity to remember previous rounds of the game. To test whether humans use the kind of cooperative strategies predicted, we asked students to play the iterated Prisoner’s Dilemma game either continuously or interrupted after each round by a secondary memory task (i.e., playing the game “Memory”) that constrained the students’ working-memory capacity. When playing without interruption, most students used “Pavlovian” strategies, as predicted, for greater memory capacity, and the rest used “generous tit-for-tat” strategies. The proportion of generous tit-for-tat strategies increased when games of Memory interfered with the subjects’ working memory, as predicted. Students who continued to use complex Pavlovian strategies were less successful in the Memory game, but more successful in the Prisoner’s Dilemma, which indicates a trade-off in memory capacity for the two tasks. Our results suggest that the set of strategies predicted by game theorists approximates human reality.

Human cooperation in the simultaneous and the alternating Prisoner's Dilemma: Pavlov versus Generous Tit-for-Tat.

The iterated Prisoner's Dilemma has become the paradigm for the evolution of cooperation among egoists. Since Axelrod's classic computer tournaments and Nowak and Sigmund's extensive simulations of evolution, we know that natural selection can favor cooperative strategies in the Prisoner's Dilemma. According to recent developments of theory the last champion strategy of "win--stay, lose--shift" ("Pavlov") is the winner only if the players act simultaneously. In the more natural situation of players alternating the roles of donor and recipient a strategy of "Generous Tit-for-Tat" wins computer simulations of short-term memory strategies. We show here by experiments with humans that cooperation dominated in both the simultaneous and the alternating Prisoner's Dilemma. Subjects were consistent in their strategies: 30% adopted a Generous Tit-for-Tat-like strategy, whereas 70% used a Pavlovian strategy in both the alternating and the simultaneous game. As predicted for unconditional strategies, Pavlovian players appeared to be more successful in the simultaneous game whereas Generous Tit-for-Tat-like players achieved higher payoffs in the alternating game. However, the Pavlovian players were smarter than predicted: they suffered less from defectors and exploited cooperators more readily. Humans appear to cooperate either with a Generous Tit-for-Tat-like strategy or with a strategy that appreciates Pavlov's advantages but minimizes its handicaps.

Types of evolutionary stability and the problem of cooperation.

The evolutionary stability of cooperation is a problem of fundamental importance for the biological and social sciences. Different claims have been made about this issue: whereas Axelrod and Hamilton's [Axelrod, R. & Hamilton, W. (1981) Science 211, 1390-1398] widely recognized conclusion is that cooperative rules such as "tit for tat" are evolutionarily stable strategies in the iterated prisoner's dilemma (IPD), Boyd and Lorberbaum [Boyd, R. & Lorberbaum, J. (1987) Nature (London) 327, 58-59] have claimed that no pure strategy is evolutionarily stable in this game. Here we explain why these claims are not contradictory by showing in what sense strategies in the IPD can and cannot be stable and by creating a conceptual framework that yields the type of evolutionary stability attainable in the IPD and in repeated games in general. Having established the relevant concept of stability, we report theorems on some basic properties of strategies that are stable in this sense. We first show that the IPD has "too many" such strategies, so that being stable does not discriminate among behavioral rules. Stable strategies differ, however, on a property that is crucial for their evolutionary survival--the size of the invasion they can resist. This property can be interpreted as a strategy's evolutionary robustness. Conditionally cooperative strategies such as tit for tat are the most robust. Cooperative behavior supported by these strategies is the most robust evolutionary equilibrium: the easiest to attain, and the hardest to disrupt.