Prisoner’s dilemma

The evolution of cooperation is frequently analysed in terms of the repeated Prisoner s Dilemma game. Computer simulations show that the emergence of cooperation is a robust phenomenon. However, the strategy which eventually gets adopted in the population seems to depend sensitively on fine details of the modelling process, so that it becomes difficult to predict the evolutionary outcome in real populations. 

One can, of course, adopt the evolutionary viewpoint again. It reduces to drowning by numbers have lots of players play lots of Prisoner s Dilemma games for lots and lots of gen-... 

Thus we ought also to study the iterated Prisoner s Dilemma when the players have to take turns. The slight modification in such an alternating Prisoner s Dilemma game can affect the interaction to a considerable extent. For instance, if two Tit For Tat players engage in a Prisoner s Dilemma of the usual simultaneous kind, and if one of them defects by mistake, both players will subsequently cooperate and defect in turns. On the other hand, if two Tit For Tat players engage in an alternating Prisoner s Dilemma, and a unilateral defection occurs inadvertently, then the outcome will be an unbroken sequence of mutual defections. 

In an interesting series of experiments, Claus Wedekind and Manfred Milinski have tested humans (more specifically, first year students) in both the simultaneous and the alternating Prisoner s Dilemma (see Wedekind and Milinski, 1996). In both cases the sub-... 

Boyd, R. (1989), Mistakes Allow Evolutionary Stability in the Repeated Prisoner s Dilemma Game, Journal of Theoretical Biology 136, 47—56. 

Frean, M.R. (1994), The Prisoner s Dilemma without synchrony, Proceedings of the Royal Society London B, 257, 75-79. 

Nowak, M. and Sigmund, K. (1994), The alternating Prisoner s Dilemma, Journal of Theoretical Biology 168, 219-26. 

Wedekind, C. and Milinski, M. (1996), Human cooperation in the simultaneous and the alternating Prisoner s Dilemma Pavlov versus Generous Tit For Tat. Proceedings of the National Academy of Science of the USA, 93,2686-2689. 

Wu, J. and R. Axelrod (1995), How to cope with noise in the iterated Prisoner s Dilemma, Journal of Conflict Resolution 39, 183-9. 

In the best known of all games, the Prisoner s Dilemma, both players have a dominant strategy, that is, a strategy that is the best reply to all moves by the opponent ... 

There Ls another evolutionary theory of altruism that aims at explaining altruism toward strangers, and even toward members of different species. This account is dosely related to the theory of cooperation in repealed Prisoner s Dilemmas, further discussed in chapter XllI. 

Each traffic equilibrium is better for everyone than any other pattern of behavior. In the first erosion story, one equilibrium is worse for everyone, that, namely, in which no reforestation is undertaken. Fortunately, there is also another equilibrium, which is preferred by everybody to anything else they could do. In the Prisoner s Dilemma, there is only one equilibrium, which is worse for everybody than a cooperative (nonequilibrium > pattern. We can illustrate this case by a third erosion story, in which we suppose that erosion occurs on a given plot if and only if trees are cut down on both adjoining plots. Whatever others do, it is in the interest of the individual peasant to fell trees on his plot, since in doing that he harms only his neighbors, not himself. The equilibrium outcome is that the land is lost to the lake, unless a political solution is found. 

The Prisoner s Dilemma equilibrium differs from all the other equilibria mentioned so far, in that it is made up of aaions each of which is the best response to anything others could do, not just to their equilibrium behavior. Equilibrium then does not require a person to have correct expectations about what others will do, since he will take the same action whatever he expects them to do. (An action of this type is called a dominant strategy. 1 If he expects wrongly, he will be surprised, perhaps unpleasantly so, but he will not regret what he did. In such cases there can be unintended consequences in equilibrium. Usually, however, surprise and regret go together. 

Thereafter, some of the difficulties of forming effective teams were considered. First, the complexity of teams was examined in light of two little models the deciding-doing model and a model of the probabihty of team conflict. These led to discussion of the prisoner s dilemma problem recast as the teammate s dilemma problem to help understand why team cooperation is so difficult to achieve. Oftentimes, individuals who cooperate with the team goals are forced to carry freeloaders who choose to do less than their fair share. Understanding this dilemma adds force to the establishment of team ground rules and norms. 

For this distinction see Parfit, Tnidence, morality and the Prisoner s Dilemma". 

On the two person Prisoner s Dilemma see Rapoport aixl Chammah. Prhoner s DUemma. For the n-person case see Taylor, Atiarchif and Cooperation. 

---