A payoff equality perspective for evolutionary games: Mental accounting and cooperation promotion

Abstract

The secret behind cooperation with the present profit-pursuing nature has been unveiled via the Evolutionary Game Theory and models. However, the payoff equality is not sufficiently explored. This paper proposes a simple but efficient way to focus on the synergetic behaviors of payoff equality and cooperation improvement. Herein, the classical Evolutional Game model is re-evaluated from the perspective of payoff equality. By assuming the similarity between the value function in “mental accounting effect” and the inverse of the Lorenz curve, the “rank strategy” is introduced in the form of a slightly alternated Fermi strategy which focuses on the rank difference on the wealth (payoff) distribution curve along the calculation of the Gini coefficient. Such introduction opens up a new perspective to the cross section between economics and the evolutionary game theory. Compared with the original Fermi strategy adoption (named payoff strategy), the rank strategy significantly aids the system to survive a higher benefit with a faster recovery after the enduring period. The reason behind this can be discussed from the formation of giant clusters, which also indicates a spillover effect in both cooperation and payoff equality improvement. A further breakdown in the population also suggests the leading role of rich players who help poor players in improving the payoff equality among them. The rank strategy is further evaluated in a broad parameter range with different combinations of the ratio of initial cooperators, the benefit (b) and the fitness (K). In most cases, the rank strategy shows a better performance in both the fraction of cooperators and the Gini coefficient, which concludes that the mental accounting effect could be the more realistic factor that may be critical to consider. The resolution in the cooperative mechanism may also be linked to wealth equality. Simulation results in this work suggest a close relationship between cooperation improvement and the payoff equality which is not extensively explored in earlier works. Simulations with Gini distribution explain “A good deed is never lost” in a numerical way.