Conventions and Social Mobility in Bargaining Situations

This paper studies the evolution of a population whose members use their social class to coor-dinate their actions in a simple tacit bargaining game. In the spirit of Rosenthal and Landau [1979], we interpret the equilibrium behaviours that the players may adopt, as a function of their class, as customs. Players may change their class depending on the outcome of the game, and may also change their custom, as a result of some learning process. We are interested in the characterization of the fixed points of the adjustment process over the space of classes and customs from a distributional point of view. Wefind that, although any custom (when it operates alone) generates the same limiting class distribution as any other, these limiting distrbutions can be ranked with respect of their mobility. If players are allowed to change their custom when they find it unsatisfactory, then social mobility appears to be the key variable to predict the type of custom which will predominate in the long run even though, in general, no one custom is dominant. In particular, customs which promote social mobility appear to exhibit, in all the cases we have analysed, stronger stability properties.