Direct Sum Matrix Game with Prisoner's Dilemma and Snowdrift Game

Abstract

A direct sum form is proposed for constructing a composite game from two games, prisoner's dilemma and snowdrift game. This kind of direct sum form game is called a multiple roles game. The replicator dynamics of the multiple roles game with will-mixed populations is explored. The dynamical behaviors on square lattice are investigated by numerical simulation. It is found that the dynamical behaviors of population on square lattice depend on the mixing proportion of the two simple games. Mixing SD activities to pure PD population inhibits the proportion of cooperators in PD, and mixing PD activities to pure SD population stimulates the proportion of cooperators in SD. Besides spatial reciprocity, our results show that there are roles reciprocities between different types of individuals.

Evolutionary dynamics of cooperation on interdependent networks with the Prisoner's Dilemma and Snowdrift Game

“…Instead, strategic information is transmitted between interdependent networks to affect the evolution of cooperation on both of them. Ma et al showed that there are roles reciprocities between different types of individuals, where mixing SG activities to pure PD population inhibits the proportion of cooperators in PD, and mixing PD activities to pure SG population stimulates the proportion of cooperators in SG [39]. While on interdependent networks, the evolution of cooperation is promoted dramatically by the network interdependence on the network playing PD, but inhibited marginally on the network playing SG, respectively.…”

A generalized public goods game with coupling of individual ability and project benefit

“…The payoff functions in the original PGG accompanied with the payoff functions in the NSG determine the evolutionary dynamics in the present model. The coupling model of the PD and the SG is also presented in ref [54,55]…”