Abstract
A reformation of Nash's axiom of Independence of Irrelevant Alternatives is proposed, generalizing an idea due to Roth. It involves the concept of a reference function g, whose purpose is to summarize the main features of the bargaining problem and so facilitate the evaluation of the relative bargaining positions of the players. It is with respect to g that the Independence condition is reformulated. In conjunction with the other axioms used by Nash, it is shown that if g satisfies certain natural properties, the bargaining problem admits of a unique solution. Several examples of reference functions are shown to satisfy these conditions. An existence problem discovered by Roth for a particular choice of g is shown to be resolved if solutions are permitted to be multi-valued, the axioms being correspondingly reformulated.
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