Wealth-relative effects in cooperation games

This paper investigates cooperation games in which poor agents do not benefit from cooperation with wealthy agents. They instead benefit from considering wealth relative to decision payoffs of fitness or wealth. Of concern is the effect of cooperation on participants, their rational self-interest and choices, and not the evolution of cooperation directly. The accumulation of fitness or wealth has been shown in the literature to lead to different optimal strategies for wealthy and poor players in Chicken games. The effect could have important explanatory power if it were more broadly applicable. First we empirically compare two published results, one involving the temptation parameter vs. degree of cooperation in Prisoner's Dilemma, and the other a surprising result from a public goods game with participants from different cultures, networks and wealth in which a fixed rather than relative payoff scheme was used. Using the temptation data to calibrate the public goods behavior suggests wealth factors can provide an explanation for the results. Second we show using simulation that adding a survival threshold to a wealth or fitness accumulating Iterated Prisoner's Dilemma produces a wealth relative effect. We clarify previous results to show the poor must avoid survival risk, regardless of whether this is associated with cooperation or defection. We do this by introducing the Farmer's Game, a simulation of Iterated Prisoner's Dilemma with wealth accumulation and a survival threshold. This is used to evaluate the Tit-for-Tat strategy and four variants. Equilibrium payoffs keep the game scaled to social relevance, with a fraction of all payoffs externalized as a turn cost parameter. Findings include poor performance of Tit-for-Tat near the survival threshold, superior performance of low risk strategies for both poor and wealthy players, dependence of survival of the poor near the threshold on Tit-for-Tat forgiveness, unexpected optimization of forgiveness without encountering a social dilemma, improved performance of a diverse mix of strategies, and a more abrupt threshold of social catastrophe for the better performing mix. Lastly we compare cooperating and non-cooperating societies using the simulation and discover disturbing connections between cooperation and familiar non-egalitarian wealth distribution patterns.