Instability in Evolutionary Games

Abstract

Background: Phenomena of instability are widely observed in many dissimilar systems, with punctuated equilibrium in biological evolution and economic crises being noticeable examples. Recent studies suggested that such instabilities, quantified by the abrupt changes of the composition of individuals, could result within the framework of a collection of individuals interacting through the prisoner's dilemma and incorporating three mechanisms: (i) imitation and mutation, (ii) preferred selection on successful individuals, and (iii) networking effects. Methodology/Principal Findings: We study the importance of each mechanism using simplified models. The models are studied numerically and analytically via rate equations and mean-field approximation. It is shown that imitation and mutation alone can lead to the instability on the number of cooperators, and preferred selection modifies the instability in an asymmetric way. The co-evolution of network topology and game dynamics is not necessary to the occurrence of instability and the network topology is found to have almost no impact on instability if new links are added in a global manner. The results are valid in both the contexts of the snowdrift game and prisoner's dilemma. Conclusions/Significance: The imitation and mutation mechanism, which gives a heterogeneous rate of change in the system's composition, is the dominating reason of the instability on the number of cooperators. The effects of payoffs and network topology are relatively insignificant. Our work refines the understanding on the driving forces of system instability. © 2012 Yang et al.