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This paper introduces two-player bargaining problems allowing for asymmetric subjective uncertainty about factors that determine whether agreement is achieved, focusing on surprising events, i.e. events believed possible by only one player. A ‘subjective Nash’ solution is proposed, in which a bargaining outcome is defined as immune to all possible appeals given the subjective uncertainty of disagreement. In addition to Pareto optimality and independence of irrelevant alternatives, the main axiom in the solution characterization is ‘subjective symmetry’. The solution is shown to be equivalent to a specific, non-symmetric, Nash solution, with preference dependent weights that equal the subjective probability players assign to the intersection of their belief supports. [ABSTRACT FROM AUTHOR]