Evolutionary snowdrift game with loners

Abstract

The effects of an additional strategy or character called loner in the snowdrift game are studied in a well-mixed population or fully-connected network and in a square lattice. The snowdrift game, which is a possible alternative to the prisoner's dilemma game in studying cooperative phenomena in competing populations, consists of two types of strategies, C (cooperators) and D (defectors). In a fully-connected network, it is found that either C lives with D or the loners take over the whole population. In a square lattice, three possible situations are found: a uniform C-population, C lives with D, and the coexistence of all three characters. The presence of loners is found to enhance cooperation in a square lattice by enhancing the payoff of cooperators. The results are discussed in terms of the effects in restricting a player to compete only with his nearest neighbors in a square lattice, as opposed to competing with all players in a fully-connected network.