Fairness in Multiplayer Ultimatum Games Through Moderate Responder Selection

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.