The probability to reach an agreement as a foundation for axiomatic bargaining

We revisit the Nash bargaining model and axiomatize a procedural solution that maximizes the probability of successful bargaining. Our characterization spans several known solution concepts, including the special cases of the Nash, egalitarian, and utilitarian solutions. Using a probability-based language, we offer a natural interpretation for the product operator underlying the Nash solution: when the bargainers’ individual acceptance probabilities are independent, their product recovers the joint acceptance probability