Human Behavior and Network Games

Cooperation and defection are the two strategies that are at the heart of every social dilemma. While cooperators contribute to the collective welfare at a personal cost, defectors choose not to. The Prisoner's Dilemma (PD) game, in particular, has been widely used to model a situation in which mutual cooperation leads to the best outcome in social terms, but defectors can benefit the most individually. Due to the lower individual fitness of cooperators, selection pressure acts in favor of defectors so that, according to the principles of Darwinian selection, cooperation extinction is inevitable. However, cooperation is indeed observed in biological and social systems alike: the evolutionary origin of cooperation remains a unsolved puzzle. 

A key point is that the way in which individuals adapt their behavior (usually referred to as evolutionary dynamics or strategy update) is unknown a priori. Most theoretical studies in this field build on update rules based on payoff comparison, which fit in the framework of biological evolution where payoff is understood as fitness and thus reproductive success. However they are questionable for a socio/economic context where individuals aware of others' actions but often do not know how much they benefit from them. Indeed, large-scale experiments with humans playing a spatial PD game show that humans do not consider neighbors' payoffs when making their decisions. Rather, they respond to the cooperation that they observe in a reciprocal manner: they are more likely to cooperate if, in the previous round, many of their neighbors and themselves did so – a behavior known as moody conditional cooperation (MCC), while they ignore the context and free-ride with high probability if they did not.

In this work we studied how MCC could arise from evolution. We performed an extensive analysis of different evolutionary dynamics for players' behavioral traits, from imitative rules where players simply copy the strategies of others if they get higher payoffs, to rational strategies in which players adopt the Best Response to what others do, and Reinforcement Learning strategies where players use their experience to choose or avoid certain actions based on their consequences. We find that MCC can be explained only by people learning from what they experience, and not for instance from the information they may gather on others. Another important outcome of experiments is that the shape of the network of interactions among players does not influence cooperative behavior. In this work we showed that the absence of network reciprocity is a general consequence of evolutionary dynamics that do not take neighbors' payoffs into account. 

Evolution of the level of cooperation for different evolutionary dynamics: Proportional Imitation, Fermi Rule, Death-Birth rule, Unconditional Imitation.
Evolution of the level of cooperation for different evolutionary dynamics: Voter Model, Best Response, Reinforcement and Adaptive Learning.

Evolutionary Network Games

Network Games are used to model contexts, ranging from public goods provision to information collection, where a player’s well-being depends on own action as well as on the actions taken by her neighbors. Many of the game-theoretic applications studied in the economic literature can be classified into two canonical types of interactions:

A relevant question for in this context is how the network of social connections shapes the choices that individuals make. The classic approach is to look at the Nash equilibria (the situations where no player has anything to gain by changing only her own strategy) in one-shot games, or at the Bayes-Nash equilibria when players are assumed to have only limited local information on the network. Another possible route is to consider network games from an evolutionary perspective, by looking at the attractors of the dynamics and selecting among the large multiplicity of Nash equilibria in a spirit very close to that of biological evolution. Theoretical and simulation results for strategy updating rules based on imitation and rational deduction show that, for Strategic Substitutes, imitation leads necessarily to full defection (which in non-Nash), whereas, rational deduction allows players to self-organize into a variety of Nash equilibria. For Strategic Substitutes instead the outcome depends mainly on the incentive to cooperate, with a phase transition between a fully defective Nash equilibrium and full cooperation. Notably, the transition point vanishes for infinitely large scale-free networks, meaning that cooperative equilibria arise for any value of the incentive to cooperate. 

Coordination game with Proportional Imiation dynamics for scale-free networks: Stationary cooperation level versus the incentive to cooperate times the probability to find a cooperator following a randomly chosen link, for various system sizes. The vertical solid line identifies the critical value equal to the cost of cooperation.