Memory Retrieval in the Demand Game With a Few Possible Splits : Unfair Conventions Emerge in Fair Settings

We study the long-run evolutionary outcome emerging when two populations of agents play the demand game with three (or a few) possible splits, with the two populations differing in the sample sizes used when best responding to retrieved information from the past. We focus on the relation between the fairness of the emerging convention and the fairness of the setting, interpreted as the degree of inequality of the unfair splits of the resources. We find that there exists a threshold for the fairness of the setting such that, below the threshold (i.e., in an unfair setting), the emerging convention is the fair one, while above the threshold (i.e., in a fair setting), the emerging convention is unfair, favoring the agents with the longer sample size. Moreover, such a threshold gets lower (restricting the parameters for which the fair convention emerges) as the difference in the sample sizes between the two populations increases