Strategic bargaining and difference games

In this paper difference games are considered in which two players bargain over a joint strategy in order to try to exploit the feasible outcomes which are individually rational with respect to the non-cooperative Nash equilibrium. Rubinstein's alternating bid model is used. As long as the players disagree they play their Nash strategy. The perfect equilibrium proposals for this bargaining game are derived. In the context of difference games these proposals are not necessarily Pareto efficient. A specific linear-quadratic difference game and a specific tree game serve as an illustration and show the meaning of cheating-proofness and time-consistency in this context. It is shown that when the Pareto efficient frontier lies 'close' to the Pareto efficient frontier of the next period it is better to have the other player propose first.