How Best to Disagree in Order to Agree?

We follow a new approach for the implementation of cooperative bargaining solutions in a non-cooperative framework. We model what happens in case of disagreement in order to give players the incentive to reach an agreement which coincides with a cooperative solution. Our model consist of two phases. Many of the standard bargaining procedures can constitute the first phase. The second mechanism phase is only triggered in case of disagreement and relies on the proposals made during the negotiation phase. The mechanism works back through the history of proposals as long as the players reject them. At the sub game perfect equilibrium, when the parties are risk averse, they negotiate by making gradual concessions leading to a final agreement which turns out to be the Raiffa solution.