Abstract. We demonstrate that one should not expect convergence of the proposals to the subgame perfect Nash equilibrium offer in standard ultimatum games. First, imposing strict experimental control of the behavior of the receiving players and focusing on the behavior of the proposers, we show experimentally that proposers do not learn to make the expected-payoff-maximizing offer. Second, we put the experimental data into perspective by considering a range of learning theories (from approximately optimal to boundedly rational). These theoretical benchmarks explain that the lack of convergence to the minimal offer is an inherent feature of the learning task faced by the proposers.

J.E.L. classification codes. C72, C91, D81, D83

Keywords. Ultimatum game, Non-equilibrium behavior, Laboratory experiment, Multi-armed bandit, Optimal learning, Gittins index, Bounded rationality