Normal Behavior, Altruism and Aggression in Cooperative Game Dynamics

The paper introduces a local cooperation pattern for repeated bimatrix games: the players choose a mutually acceptable strategy pair in the next round. A mutually acceptable strategy pair provides each player with a payoff no smaller than that expected, in average, at a historical distribution of players' actions recorded up to the latest round. It may happen that at some points mutually acceptable strategy pairs do not exist. A game round at such "still" points indicates that at least one player revises his/her payoffs and switches from normal behavior to abnormal. We consider payoff switches associated with altruistic and aggressive behaviors, and define measures of all combinations of normal, altruistic and aggressive behaviors on every game trajectory. These behavior measures serve as criteria for the global analysis of game trajectories. Given a class of trajectories, one can identify the measures of desirable and undesirable behaviors on each trajectory and select optimal trajectories, which carry the minimum measure of undesirable behaviors. In the paper, the behavior analysis of particular classes of trajectories in the repeated Prisoner's Dilemma is carried out.