Social dilemmas in multistrategy evolutionary potential games

The nature of social dilemmas is studied in n-strategy evolutionary potential games on a square lattice with nearest-neighbor interactions and the logit rule. For symmetric games with symmetric payoff matrices there are no dilemmas because of the coincidence of individual and common interests. The dilemmas are caused by the antisymmetric parts of the self- and cross-dependent payoff components if it modifies the preferred Nash equilibrium. The contentment of players and the emergence of dilemmas in the preferred Nash equilibria are illustrated on some two-dimensional cross sections of the parameter space.