Spatial evolution of cooperation with variable payoffs

Abstract

In the evolution of cooperation, the individuals’ payoffs are commonly random in real situations, e.g., the social networks and the economic regions, leading to unpredictable factors. Therefore, there are chances for each individual to obtain the exceeding payoff and risks to get the low payoff. In this paper, we consider that each individual’s payoff follows a specific probability distribution with a fixed expectation, where the normal distribution and the exponential distribution are employed in our model. In the simulations, we perform the models on the weak prisoner’s dilemmas (WPDs) and the snowdrift games (SDGs), and four types of networks, including the hexagon lattice, the square lattice, the small-world network, and the triangular lattice are considered. For the individuals’ normally distributed payoff, we find that the higher standard deviation usually inhibits the cooperation for the WPDs but promotes the cooperation for the SDGs. Besides, with a higher standard deviation, the cooperation clusters are usually split for the WPDs but constructed for the SDGs. For the individuals’ exponentially distributed payoff, we find that the small-world network provides the best condition for the emergence of cooperators in WPDs and SDGs. However, when playing SDGs, the small-world network allows the smallest space for the pure cooperative state while the hexagon lattice allows the largest.

Small group size promotes more egalitarian societies as modeled by the hawk-dove game

“…In the future, the effect of group size on social systems can be investigated in other evolutionary games to examine if group size is a general mechanism for the biological or cultural evolution of cooperative behavior across different types of cooperative games. Another interesting direction for research would be varying payoffs in the HDG, which would introduce greater biological realism [ 63 ].…”

Information Dynamics in Evolving Networks Based on the Birth-Death Process: Random Drift and Natural Selection Perspective

“…The dynamic process of network population has been widely studied during the past two decades. Most dynamic studies in evolving or temporal networks focus on the proportion of a specific behavior [45], [12], [46], which neglects the fixation probability of the behavior in a finite population. Here, we analyze the collective behavior by fixation probability of the evolving network from two perspectives, including random drift and natural selection.…”

Research on multi-layer network routing selection strategy based on cooperative evolutionary game in IoT environment

“…Pi et al introduced the similarity between players into the strategy updating rules [32] to explore the evolutionary game process, including strategy updating, player type transformation, and dynamic evolution of network structure, and explored the influence of conformists and profiteers on the evolution of cooperation in multiple games. Zeng et al assumed that individuals follow a probability distribution of normal distribution and exponential distribution and found that a higher standard deviation usually inhibits cooperation in WPDs but promotes cooperation in SDGs [33]. Rationality can survive and make profits through cooperation, which naturally solves the social dilemma of profit and cooperation.…”