Optional games on cycles and complete graphs

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.

References in corpus (5)

• Evolutionary games on graphs
• Social dilemmas in an online social network: the structure and evolution of cooperation
• Stochasticity and evolutionary stability
• Promotion of cooperation induced by the interplay between structure and game dynamics
• Strategy abundance in evolutionary many-player games with multiple strategies

Cited by in corpus (5)

• Duality between cooperation and defection in the presence of tit-for-tat in replicator dynamics
• Simulation of an Optional Strategy in the Prisoner's Dilemma in Spatial and Non-spatial Environments
• Long-range prisoner's dilemma game on a cycle
• Nash equilibrium and evolutionary dynamics in semifinalists' dilemma
• Assortative clustering in a one-dimensional population with replication strategies