title: 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 2 x 2 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.
authors.affiliation: Department of Physics and Institute of Biophysics, Huazhong Normal University, Wuhan, China ; Department of Applied Physics, College of Science, Huazhong Agricultural University, Wuhan, China.
authors.forename: Chengzhang
authors.initials: C
authors.lastname: Ma
authors.affiliation: Department of Physics and Institute of Biophysics, Huazhong Normal University, Wuhan, China ; Department of Applied Physics, College of Science, Huazhong Agricultural University, Wuhan, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Cao
authors.affiliation: Department of Physics and Institute of Biophysics, Huazhong Normal University, Wuhan, China.
authors.forename: Wangheng
authors.initials: W
authors.lastname: Liu
authors.affiliation: Department of Physics and Institute of Biophysics, Huazhong Normal University, Wuhan, China ; Department of Applied Physics, College of Science, Huazhong Agricultural University, Wuhan, China.
authors.forename: Rong
authors.initials: R
authors.lastname: Gui
authors.affiliation: Department of Physics and Institute of Biophysics, Huazhong Normal University, Wuhan, China.
authors.forename: Ya
authors.initials: Y
authors.lastname: Jia
mesh_terms: D005716:Game Theory; D006801:Humans; D008962:Models, Theoretical; D011336:Probability