Pairwise Interaction-Comparison Dynamics

We introduce and study a class of evolutionary game dynamics -- named Pairwise Interact-and-Imitate Dynamics (PIID) -- where agents are matched in pairs, are engaged in a symmetric game, and possibly change behavior depending on relative payoffs in the pair. We provide a condition on the underlying game -- named Supremacy -- that ensures global asymptotic stability of the state where the whole population adopts the supreme action. We show the robustness of our result with respect to small changes in the revision protocol followed by agents. We then apply PIID to a number of issues that are typically studied in evolutionary game theory, obtaining survival of strictly dominated strategies, ineffectiveness of assortativity, evolution of maximin convention, and evolution of aggressive behavior.