Optional games on cycles and complete graphs

Hyeong-Chai Jeong; Seung-Yoon Oh; Benjamin Allen; Martin A Nowak

doi:10.1016/j.jtbi.2014.04.025

Optional games on cycles and complete graphs

J Theor Biol. 2014 Sep 7:356:98-112. doi: 10.1016/j.jtbi.2014.04.025. Epub 2014 Apr 26.

Authors

Hyeong-Chai Jeong¹, Seung-Yoon Oh², Benjamin Allen³, Martin A Nowak⁴

Affiliations

¹ Department of Physics, Sejong University, Gangjingu, Seoul 143-747, Republic of Korea; Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 20138, USA.
² Department of Physics, Sejong University, Gangjingu, Seoul 143-747, Republic of Korea.
³ Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 20138, USA; Department of Mathematics, Emmanuel College, Boston, MA 02115, USA.
⁴ 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.

PMID: 24780293
DOI: 10.1016/j.jtbi.2014.04.025

Abstract

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.

Keywords: Evolution of cooperation; Evolutionary game theory; Evolutionary graph theory; Spatial games.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Game Theory*
Humans
Models, Theoretical*
Social Behavior*
Stochastic Processes