Abstract
Cooperation is widely recognized to be fundamental for the well-balanced development of human societies. Several different approaches have been proposed to explain the emergence of cooperation in populations of individuals playing the Prisoner’s Dilemma game, characterized by two concurrent natural mechanisms: the temptation to defect and the fear to be betrayed by others. Few results are available for analyzing situations where only the temptation to defect (Chicken game) or the fear to be betrayed (Stag-Hunt game) is present. In this paper, we analyze the emergence of full and partial cooperation for these classes of games. We find the conditions for which these Nash equilibria are asymptotically stable, and we show that the partial one is also globally stable. Furthermore, in the Chicken and Stag-Hunt games, partial cooperation has been found to be more rewarding than the full one of the Prisoner’s Dilemma game. This result highlights the importance of such games for understanding and sustaining different levels of cooperation in social networks.
Highlights
Cooperation in a population is a key emerging phenomenon, which has fascinated many scientists in several fields, ranging from biology to social and economics science [1,2,3,4,5,6,7], and recently considered in technological applications [8,9]
A steady state x∗ is a solution of Equation (8) satisfying ẋv = 0 ∀v ∈ V
The emergence of cooperative consensus for SH and CH games has been tackled in the framework of the Self-Regulated Evolutionary Game on Network Equation (SR-EGN) equation, which describes the behavior of a population of randomly interconnected individuals, driven by game theoretic mechanisms, jointly with internal self-regulating factors
Summary
Cooperation in a population is a key emerging phenomenon, which has fascinated many scientists in several fields, ranging from biology to social and economics science [1,2,3,4,5,6,7], and recently considered in technological applications [8,9]. Cooperation has been sometimes seen to contrast with the Darwinian concept of natural selection, it emerges in many complex systems providing substantial benefits for all members of groups and organizations [10,11,12,13,14,15,16,17]. This topic is tackled using the tools of evolutionary game theory, which constitute the mathematical foundations for modeling the decision making process of players taking part in a replicator/selection competition. As part of a society, individuals often use punishment mechanisms which limit the detrimental behavior of free riders or they can be awarded if they prefer cooperative behaviors [10,17,30,31,32,33]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
