WPO, COV and IIA bargaining solutions for non-convex bargaining problems

H.J.M. Peters, A.J. Vermeulen*

*Corresponding author for this work

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12 Citations (Web of Science)


We characterize all n-person multi-valued bargaining solutions, defined on the domain of all finite bargaining problems, and satisfying Weak Pareto Optimality (WPO), Covariance (COV), and Independence of Irrelevant Alternatives (IIA). We show that these solutions are obtained by iteratively maximizing nonsymmetric Nash products and determining the final set of points by so-called LDR decompositions. If, next, we assume the (set-theoretic) Axiom of Determinacy, then this class coincides with the class of iterated Nash bargaining solutions; but if we assume the Axiom of Choice then we are able to construct an additional large set of discontinuous and even nonmeasurable solutions. We show however that none of these nonmeasurable solutions can be defined in terms of set theoretic formulae. We next show that a number of existing results in the literature as well as some new results are implied by our approach. These include a characterization of all WPO, COV and IIA solutions-including single-valued ones-on the domain of all compact bargaining problems, and an extension of a theorem of Birkhoff characterizing translation invariant and homogeneous orderings.

Original languageEnglish
Pages (from-to)851-884
Number of pages34
JournalInternational Journal of Game Theory
Issue number4
Publication statusPublished - Nov 2012


  • Nash bargaining solutions
  • Non-convex bargaining problems
  • RISK

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