A Non-cooperative Approach to Dynamic Bargaining

Many negotiations (for instance, among political parties or partners in a business) are characterised by dynamic bargain- ing: current agreements affect future bargaining possibilities. We study such situations using bargaining games á la Rubinstein (1982), with the novelty that players can decide how much to invest, as well as how to share the residual surplus for their own consumption. We show that under certain conditions, there is a unique (stationary) Markov Perfect Equilibrium characterised by immediate agreement. Moreover, standard results in bargaining theory can be overturned. For instance, despite the complexity of the bargaining game, there are equilibrium strategies as in an ul- timatum, where the responder does not consume anything. Also, a more patient proposer may consumes less than his opponent. Additionally, a higher discount factor for one player may decrease the MPE investment rates for both players. We study the effect of different rates of time preferences, intertemporal elasticities of substitution and rates of return on the equilibrium demands.