Nash Equilibria and Absorbing Sets in Contribution Games with Inequality Aversion on Social Network

Abstract

The present study derives the Nash equilibrium and absorbing sets of the contribution game, which is an extension of the inequality aversion model, to build a model including parameters of unhappiness and guilty in the profit function of this game. Prior resarch of the contribution game on the social network assumes a circle network connected to two adjacent players. Each player’s strategy on this game is “Contribution” and “Defect” to the public goods. Each player’s profit function depends on the other player’s strategies. The present study shows that Nash equilibrium and absorbing sets, as many players choose “Contribution”, are realized under the interval by using parameters of unhappiness and guilty. This implies that, under some assumptions, many people collaborate in this game on the social network if their guilty is larger than their unhappiness.