Aspiration adaptation in the ultimatum minigame

Abstract

Two agents recurrently play a 2×2 version of the ultimatum game. Each player sticks to his past action if it was satisfactory relative to an endogenous aspiration level and otherwise abandons it with positive probability. This type of satisficing behavior is shown to yield efficiency in the limit. It does not favor a specific distribution of surplus and can give an explanation for the incidence of equitable offers in practice. Numerical investigations link a player's character as captured by the model parameters to his average bargaining success. Results indicate that it is beneficial to be persistent and stubborn, i.e., slow in adapting aspirations and switching actions in response to major dissatisfaction. Also, it is an advantage to be capricious, i.e., to experience large and frequent perturbations of aspiration level and to discriminate only little between minor and major dissatisfaction.