Modified snowdrift games for multi-robot water polo matches

In this paper, using game theoretic ideas, we propose a modified snowdrift game to study the emergence and evolution of cooperation among robots in multi-robot water polo matches. We first formulate a game setting in which groups of robots play matches repeatedly that are modeled by modified snowdrift games. Then by introducing a cooperation coefficient we investigate how evolutionary stability is affected by cooperation efficiency through replicator dynamics in infinite populations. We identify evolutionarily stable strategies (ESS) under different fixed values of the cooperation coefficient. We further study the co-evolution of the cooperation efficiency with game dynamics using simulations of Fermi processes in finite populations. It is found that the cooperation efficiency improves when robots are capable to learn.