On Derivation and Evolutionary Classification of Social Dilemma Games

We propose an axiomatic derivation and a classification of multiperson social dilemma games. For the two-person symmetric games, the axiomatization leads to three types of the social dilemmas only: the Prisoner's Dilemma (PD) game, the Chicken (Snowdrift) game and the Stag Hunt game. The popular multiperson games, such as for example the N-person PD, the Public Goods, the Tragedy of the Commons, the Volunteer's Dilemma and the Assurance game, are included in the proposed frame. For general social dilemma games with arbitrary payoffs, their simple classification is proposed, based on the number of stable equilibria of the corresponding replicator dynamics.