On the Nash bargaining solution with noise

Suppose two parties have to share a surplus of random size.Each of the two can either commit to a demand prior to the realization of the surplus - as in the Nash demand game with noise - or remain silent and wait until the surplus was publicly observed.Adding the strategy to wait to the noisy Nash demand game results in two strict equilibria, in each of which one player takes almost the whole surplus, provided uncertainty is small.If commitments concern only who makes the first offer, the more balanced Nash bargaining solution is approximately restored.In all cases commitment occurs in equilibrium, even though this entails the risk of breakdown of negotiations.

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