INB-Lunch-Seminar

Prisoner's Dilemma on a sizeable network: experiment and theory

Jelena Grujic, Department of Mathematics, Universidad Carlos III de Madrid

Recently, we have designed and performed an experiment to test the emergence of cooperation in the presence of an underlying structure [1]. In our experiment human subjects played a PD on a sizable network, with a setup as close as possible to the one of Nowak and May simulations [2]. We observed that population is heterogeneous, consisting of  emergence of three different strategies: cooperators, defectors and conditional cooperators. Cooperators and defectors, respectively cooperate or defect, with high probability independently of their previous action as well as the actions of their neighbors. On the other hand, conditional cooperators change the probability of cooperation depending of the previous actions, theirs as well as their neighbors.

Here we are trying to provide a plausible evolutionary explanation of the strategies observed in the experiments. Specifically, we use replicator dynamics to evolve similar set of strategies to the one observed in the experiment, but in the simplest case, where players play basic Prisoner Dilemma with each of the opponents separately.

We find, two attractors, one with full defection and the other one in interior with frequencies of each population similar to the one we observe in the experiment. The full defection attractor has much smaller area of attraction, therefore the stable point which correspond to the finding in the experiment is significantly more probable outcome of the evolution.

[1] Grujic J, Fosco C, Araujo L, Cuesta JA, Sanchez A, (2010) Social Experiments in the Mesoscale: Humans Playing a Spatial Prisoner's Dilemma. PLoS ONE 5, e13749.
[2] Nowak MA, May RM (1992) Evolutionary games and spatial chaos. Nature 359: 826–829.