Abstract
Free-riding produces inequality in the prisoners’ dilemma: cooperators suffer costs that defectors avoid, thus putting them at a material disadvantage to their anti-social peers. This inequality, accordingly, conveys information about a social partner’s choices in past game play and raises the possibility that agents can use the aggregation of past payoffs—i.e. wealth—to identify a social partner who uses their same strategy. Building on these insights, we study a computational model in which agents can employ a strategy—when playing multiple one-shot prisoners’ dilemma games per generation—in which they view other agents’ summed payoffs from previous games, choose to enter a PD game with the agent whose summed payoffs most-closely approximate their own, and then always cooperate. Here we show that this strategy of wealth homophily—labelled COEQUALS (“CO-operate with EQUALS”)—can both invade an incumbent population of defectors and resist invasion. The strategy succeeds because wealth homophily leads agents to direct cooperation disproportionately toward others of their own type—a phenomenon known as “positive assortment”. These findings illuminate empirical evidence indicating that viewable inequality degrades cooperation and they show how a standard feature of evolutionary game models—viz. the aggregation of payoffs during a generation—can double as an information mechanism that facilitates positive assortment.
Highlights
In a large population with parameters set to their median values, evolutionary dynamics under each value of b show consistent movement of the population from states of widespread defection to universal adoption of COEQUALS
In the presence of cooperators, the population gravitates toward defection when a small proportion of agents adopt COEQUALS, but this trajectory turns toward greater adoption of COEQUALS as defectors become more common, eventually leading to the replacement of defectors with adopters of the COEQUALS strategy (Panels (A–C), Fig. 1)
The phase diagrams suggest that COEQUALS performs better in a harsh environment brimming with defectors than a friendly population of cooperators
Summary
Examples of these population structures include network arrangements[22,23,24,25,26,27]; cf. and clustering patterns that facilitate group selection[29,30] Another category of mechanisms consists of behavioral programs that channel cooperation disproportionately to organisms of a cooperative persuasion[31,32,33,34,35]. Studied in an environment in which agents played multiple one-shot PD games per generation in a well-mixed population, the original version of COEQUALS stipulated that agents compare the sum of their past payoffs with those of their social partner and cooperate with partners who possess summed payoffs equal to their own, defecting otherwise This strategy flourishes in environments in which a correlation exists between the strategy agents implement and the sum total of payoffs they possess at any point in a generation. Total payoffs serve as a valid cue of the strategy an agent adopts; cooperating with partners who possess equal payoffs from past play amounts to cooperating disproportionately with agents of one’s own type—i.e. positive assortment[9]
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