Evolutionary Bargaining with Cooperative Investments

Abstract

This paper explores the set of stochastically stable equilibria in a model in which individuals first decide to make a high or low investment, and then are matched to play a Nash demand game. If an agreement is not reached, then they are re-matched in the next period, and obtain a payoff discounted by d. We identify a condition under which stochastically stable bargaining conventions exist and find, that the stochastically stable division rule is independent of the long run investment strategy. In these conventions the potential to trade in subsequent periods always has an effect on the bargain, and the market acts more like a threat point, than an outside option. If investments are substitutes stochastically stable bargaining conventions imply larger investment incentives than the Nash bargaining solution whereas the opposite is true if investments are complements. Finally, if it is not efficient for trade to occur as a result of the outside option, and investments are complements, then no bargaining convention can develop, and investment levels are typically inefficient.