We propose a new non-cooperative approach to implement a cooperative bargaining solution. This approach relies on a mechanism which specifies what happens when, at the end of the bargaining phase, players' propositions are still not compatible. The mechanism uses a random lottery and the history of proposals. At equilibrium, under the threat of this mechanism, provided that the use of it carries a small cost, players reach consensus after a finite number of proposals. No discounting is needed. The equilibrium strategies implement the full Raiffa bargaining process and players agree on a solution arbitrarily close to the Raiffa solution.