Diverse roles of reduced learning ability of players in evolution of cooperation

Individual heterogeneity in reproductive rate is found to play an important role in the emergence and persistence of cooperation. Most existing literature focused mainly on the enhancement of cooperation by the introduction of inhomogeneous teaching capability of the individuals. It is far from clear how heterogeneous learning ability of the individuals affects the evolution of cooperation. To fill this research gap, we make comparative studies of the evolutionary spatial prisoner’s dilemma game with reduced learning or teaching ability of the players, under both synchronous and asynchronous strategy updating schemes. By carrying out extensive computer simulations, we show that cooperation can always be facilitated if inhomogeneous teaching ability of the players is considered, irrespective of the strategy updating manner. By contrast, cooperation is promoted (inhibited) in the case of synchronous (asynchronous) strategy updating, if heterogeneous learning ability is considered, which is attributed to the reduced ability of cooperators to expand their domains. Introduction. – Cooperation is ubiquitous in nature, ranging from biological, social, physical, to economical systems [1]. Understanding and searching for generic mechanisms that can foster and sustain cooperation among selfish, unrelated individuals still remains an interesting and challenging problem up to date [2–5]. Evolutionary game theory offers a powerful mathematical framework to address the conundrum of evolution of cooperation [2]. Particularly, the prisoner’s dilemma (PD) has long been considered the paradigm for studying the emergence of cooperation among selfish individuals. In a typical scenario of the PD game, two interacting individuals have to choose simultaneously whether they want to cooperate or defect. Being a cooperator will pay the cost c in order to provide a greater benefit b to the partner. Being a defector does not distribute any benefits and incur no cost. Under such circumstances, mutual cooperation will (a)corresponding author: [email protected] yield the highest collective benefit shared equally between the players, while a defector can have a higher individual payoff if the opponent decides to cooperate. Therefore, mutual cooperation can easily be crushed by any unilateral defection, which in turn drives both players to choosing defection, whereby they will end up with a lower payoff than if both would cooperate, leading to the deadlock and dilemma. In the past decades, many mechanisms supporting cooperation have been proposed to resolve the dilemma, such as kin selection [6], direct and indirect reciprocity [7, 8], spatial (or network) reciprocity [9, 10], multi-level (or group) selection [11], voluntary participation [12], nonlinear attractive effect [13], dynamical linking [14], migration [15], credit records [16], co-evolving networks [17], diversity of time scale [18, 19], heterogeneous interaction degree [20], interdependent interaction network [21], punishment [22, 23], wisdom of group [24], to name a few.