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Abstract:
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"Our goal in this paper is methodological. We propose an abstract model where the compatibility of the RM axiom, the IR axiom, and Pareto Optimality can by systematically explored. This model encompasses all three examples above, and more. It consists of a surplus-sharing problem (an ordinal version of axiomatic bargaining) where both the feasible set and the vector of secure utility levels (disagreement point) depend upon a common parameter A (interpreted as the common property resource). The set of parameters is ordered in such a way that when A increases, the set of feasible (cooperative) utility vectors expands, and also the secure utility level of each agent rises. Thus when A increases cooperative opportunities are better but at the same time the individual rationality constraint is tighter. Does it exist, then, a solution of each surplus-sharing problem (Pareto optimal and individually rational) that is increasing with respect to the parameter A?"
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