Uniqueness of equilibrium payoffs in the stochastic model of bargaining

I provide a sufficient condition for the uniqueness of equilibrium payoffs in a model of stochastic bargaining with unanimity rule and risk-averse players. My Condition (S) implies Condition (C) of Merlo and Wilson (1995) and is easy to verify in applications. •Unanimity bargaining with stochastic surplus and risk-averse players is considered.•A known condition for the uniqueness of equilibrium payoffs is difficult to verify.•I provide a new sufficient condition which is easy to check in applications.•The new sufficient condition requires that players are “not too risk-averse”.