We study the evolution of fairness in a multiplayer version of the classical Ultimatum Game in which a group of N Proposers offers a division of resources to M Responders. In general, the proposal is rejected if the (average) proposed offer is lower than the (average) response threshold in the Responders group. A motivation for our work is the exchange of flexibilities between smart energy communities, where the surplus of one community can be offered to meet the demand of a second community. In the absence of any Responder selection criteria, the co-evolving populations of Proposers and Responders converge to a state in which proposals and acceptance thresholds are low, implying an unfair exchange that favors Proposers. To circumvent this, we test different rules which determine how Responders should be selected, contingent on their declared acceptance thresholds. We find that selecting moderate Responders optimizes overall fairness. Selecting the lowest-demanding Responders maintains unfairness, while selecting the highest-demanding individuals yields a worse outcome for all due to frequent rejected proposals. These results provide a practical message for institutional design and the proposed model allows testing policies and emergent behaviors on the intersection between social choice theory, group bargaining, competition, and fairness elicitation.

Indirect Reciprocity (IR) is possibly the most elaborated and cognitively demanding mechanism of cooperation discovered so far. It involves status and reputations and has been heralded as providing the biological basis of our morality. Most theoretical models employed to date have studied how IR can lead to the emergence and sustainability of cooperation in infinite populations. However, it is known that cooperation, norms, reciprocity and the art of managing reputations, are features that date back to primitive, small-scale societies, when interactions mostly occurred within tribes. In small populations, stochastic finite size effects are not only important, but may even render infinite populations analyses misleading. Thus, it remains an open question which norms prevail in small-scale societies and their influence in the evolutionary dynamics of IR. With the current extended abstract, we would like to offer a new analysis of this problem. In Santos et al. (2016) we show that population size strongly influences the merits of each social norm, while proposing a new formal tool to assess the evolutionary dynamics of reputation-based systems in finite populations. We show that a single social norm (Stern-Judging) emerges as the leading norm in small-scale societies. That simple norm dictates that only whoever cooperates with good individuals, and defects against bad ones, deserves a good reputation.