The Bargaining Problem Revisited: Minimum Utility Point, Restricted Monotonicity Axiom, and the Mean as an Estimate of Expected Utility

On the basis of the results obtained by different experiments testing two-person bargaining situations, it is reasonable to assume that under certain circumstances bargainers are more likely to refer to a “minimum utility point” in forming their strategies, and hence reach different agreements than as hitherto suggested in the literature, e.g., the Nash or the Kalai-Smorodinsky solution. The employment of such a minimum utility point is not merely descriptive, but normative, and should be viewed as a modification of the Pareto-optimum axiom, as well as other axioms, applicable in certain bargaining situations. It is also argued that such a modification is more reasonable than Kalai and Smorodinsky's axiom of monotonicity, which they suggested should replace Nash's axiom of independence of irrelevant alternatives. It is suggested that many real-life, as well as laboratory, two-person bargaining situations differ from the two-person bargaining problem characterized by Nash, and hence the employment of a probabilistic model is advocated in order to predict the bargainers' expected utility.