Stationary distributions of noisy replicator dynamics in the ultimatum game

The Ultimatum game has aquired an iconic status in that a rational expectat ions analysis, which concludes that the unique subgame-perfect equilibrium should be played, is not borne out in laboratory experiments. This paper pr esents an analytical study of the infinite-dimensional replicator dynamics with mutational noise, which models an adaptive learning process for a vers ion of the Ultimatum Game in which the stake is infinitely divisible. The m utational noise represents the influence of behavioural dispositions derive d from prior social experience in bargaining situations. We find that the s ubgame-perfect equilibrium is selected in the most naive low-noise limit. H owever, we also show that the long run behaviour of the dynamics can settle on an equilibrium far from the subgame-perfect equilibrium when other limi ts involving the two noise parameters are taken.