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A logic-based axiomatic model of bargaining. (English) Zbl 1237.91122

Summary: This paper introduces an axiomatic model for bargaining analysis. We describe a bargaining situation in propositional logic and represent bargainers’ preferences in total pre-orders. Based on the concept of minimal simultaneous concessions, we propose a solution to \(n\)-person bargaining problems and prove that the solution is uniquely characterized by five logical axioms: consistency, comprehensiveness, collective rationality, disagreement, and contraction independence. This framework provides a naive solution to multi-person, multi-issue bargaining problems in discrete domains. Although the solution is purely qualitative, it can also be applied to continuous bargaining problems through a procedure of discretization, in which case the solution coincides with the Kalai-Smorodinsky solution.

MSC:

91B26 Auctions, bargaining, bidding and selling, and other market models
03B80 Other applications of logic
91A06 \(n\)-person games, \(n>2\)
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