Cooperation between independent reinforcement learners under wealth inequality and collective risks

We study how wealth inequality influences behavioral dynamics in groups of independent reinforcement learners facing a threshold public goods dilemma with uncertain returns. The game allows individuals to contribute or not to a common pool to reduce their chances of future losses. The non-linearity introduced by the threshold, the stochasticity introduced by the risk and the wealth heterogeneity of players result in a game setting with multiple equilibria. We find that the learners’ dynamics in this case play a major role in determining the attained equilibrium point. Our results suggest that, under individual-based learning, wealth inequality can have sizable effects on the emerging collective behaviors, decreasing the overall chances of group success. Moreover, we compute the class-based Nash equilibria (i.e., where same wealth-class agents are assumed to play the same strategy) for this game and compare the performance of groups composed of independent learning agents with the performance obtained under the payoff maximizing class-based Nash equilibrium. We find that the learned strategies never really match optimal performance for all tested values of risk.