Chapter 1 The Social Ultimatum Game

Abstract The Ultimatum Game is a key exemplar that shows how human play often deviates from “rational ” strategies suggested by game-theoretic analysis. One explanation is that humans cannot put aside the assumption of being in a multi-player multi-round environment that they are accustomed to in the real world. In this paper, we introduce the Social Ultimatum Game, where players can choose their partner among a society of agents, and engage in repeated interactions of the Ultimatum Game. We provide theoretical results that show the equilibrium strategies under rational actor models for the Social Ultimatum Game, which predict “unfair” offers as the stable solution. We develop mathematical models of human play that include “irrational ” concepts such as fairness, reciprocity, and adaptation to social norms. We investigate the stability of maintaining a society of “fair ” agents under these conditions. Finally, we discuss experimental data from initial human trials of the Social Ultimatum Game. 1.