Optional games on cycles and complete graphs.
We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition, there are one or several possibilities to opt out from the game by adopting loner strategies. Optional games lead to relaxed social dilemmas. Here we explore the interaction between spatial structure and optional games. We find that increasing the number of loner strategies (or equivalently increasing mutational bias toward loner strategies) facilitates evolution of cooperation both in well-mixed and in structured populations. We derive various limits for weak selection and large population size. For some cases we derive analytic results for strong selection. We also analyze strategy selection numerically for finite selection intensity and discuss combined effects of optionality and spatial structure.
Department of Physics, Sejong University, Gangjingu, Seoul 143-747, Republic of Korea; Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 20138, USA.
Hyeong-Chai
HC
Jeong
Department of Physics, Sejong University, Gangjingu, Seoul 143-747, Republic of Korea.
Seung-Yoon
SY
Oh
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 20138, USA; Department of Mathematics, Emmanuel College, Boston, MA 02115, USA.
Benjamin
B
Allen
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 20138, USA; Department of Mathematics, Harvard University, Cambridge, MA 20138, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 20138, USA.
Martin A
MA
Nowak
D005716:Game Theory; D006801:Humans; D008962:Models, Theoretical; D012919:Social Behavior; D013269:Stochastic Processes
Evolution of cooperation; Evolutionary game theory; Evolutionary graph theory; Spatial games