Evolutionary snowdrift game with an additional strategy in fully connected networks and regular lattices

The effects of an additional strategy or character in the evolutionary snowdrift game (SG) are studied in a well-mixed population or fully connected network and in a square lattice. The SG, 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). The additional L-strategy amounts to a strongly persuasive character that a fixed payoff is given to each player when a L-player is involved, regardless of the character of the opponent. In a fully connected network, it is found that either C lives with D or the L-players 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 L-players 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.