On the co-evolution of investment and bargaining norms

Two parties bargaining over a pie, the size of which is determined by their previous investment decisions. The bargaining rule is sensitive to investment behavior. Two games are considered. In both, bargaining proceeds according to the Nash Demand Game when a symmetric investments profile is observed. When, on the other hand, an asymmetric investments profile is observed, we assume that bargaining proceeds according to the Ultimatum Game in one case and according to a Dictator Game in the other. We hereby show that in both games when a unique stochastically stable outcome exists it supports an homogeneous behavior in the whole population both at the investment stage and at the distribution stage. A norm of investment and a norm of division must therefore coevolve in the two games, supporting both the efficient investment profile and the egalitarian distribution of the surplus, respectively. The two games differ depending on the conditions needed for the two norms to coevolve. The games are proposed to explain the social norms used in modern hunter-gatherer societies.