Wealth-relative effects in cooperation games

Abstract

This paper investigates conditions under which game agents benefit from considering wealth relative to decision payoff, presents simulation analysis of these effects, and explains why they often do not show up but it is realistic that they should. We extend the known categories of games reported to exhibit wealth relative effects (chicken games) to many others (including Prisoners Dilemma) while clarifying that the poor must avoid survival risk, regardless of whether this is associated with cooperation or defection. A simulation of iterated Prisoners Dilemma with wealth accumulation and a survival threshold (which we call the Farmers Game) is used to evaluate tit-for-tat and four variants, including Subsist, Thief, Exploit and Middle (even lower risk than Subsist). Equilibrium payoffs are used to 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 Subsist and Middle 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. Additionally we find that experimental results which appear to be at odds with conventional findings of cooperation vs. network size can be reconciled with theory and simulation via wealth-relative weighting, which opens the door to practical application of cooperation theory.\n\nSignificance StatementEnabling comparison of theoretical and simulated game cooperation theory results to controlled experiments with live subjects and in-situ data from field surveys will enable application of scientifically verified results to societal and policy problems, and will generate new and unexpected insights through clearer interpretation of data. Extension of wealth-relative effects to a broader range of games also allows analysis of real life situations with greater confidence.