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WPO, COV and IIA bargaining solutions

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Author Info
Peters, Hans
Vermeulen, Dries (METEOR)
Abstract

The class of bargaining solutions that are defined on the domain of finite sets of alternatives and satisfy Weak Pareto Optimality (WPO), Independence of Irrelevant Alternatives (IIA) and Covariance (COV), is characterized. These solutions select from the set of maximizers of a nonsymmetric Nash product -- i.e., from a nonsymmetric (multi-valued) Nash bargaining solution -- according to a specific decomposition of the indifference curves of this Nash product. We use this characterization in two ways. First, we derive consequences on this domain and on larger domains of compact (non-convex) bargaining problems, and show that most results in the literature are special cases and consequences of our central results -- in particular by adding continuity or symmetry axioms. Second, since the continuity axiom prevents nontrivial selections from the Nash bargaining solutions, we use the Axiom of choice to construct for example non-single-valued discontinuous WPO, IIA and COV bargaining solutions. It is conjectured that, in the case of two-person bargaining problems,the existence of such discontinuous bargaining solutions cannot be shown from the Zermelo-Fraenkel axioms for set theory without using the Axiom of Choice.

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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 021.

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Date of creation: 2006
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Handle: RePEc:dgr:umamet:2006021

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Keywords: mathematical economics;

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  1. Peter Cramton & Yoav Shoham & Richard Steinberg, 2004. "Combinatorial Auctions," Papers of Peter Cramton 04mit, University of Maryland, Department of Economics - Peter Cramton, revised 2004. [Downloadable!]
  2. Sushil Bikhchandani & Shurojit Chatterjee & Arunava Sen, 2004. "Incentive Compatibility in Multi-unit Auctions," Levine's Bibliography 122247000000000750, UCLA Department of Economics. [Downloadable!]
  3. Gui,Hongwei & Müller,Rudolf & Vohra,Rakesh, 2004. "Dominant Strategy Mechanisms with Multidimensional Types," Research Memoranda 047, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
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  4. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July. [Downloadable!] (restricted)
  5. Raabe Katharina & Arnold, Ivo J.M. & Kool, Clemens J.M., 2006. "Industries and the Bank Lending Effects of Bank Credit Demand and Monetary Policy in Germany," Research Memoranda 006, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
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  6. Heydenreich Birgit & Müller, Rudolf & Uetz, Marc, 2006. "Decentralization and Mechanism Design for Online Machine Scheduling," Research Memoranda 007, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  7. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May. [Downloadable!] (restricted)
  8. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April. [Downloadable!] (restricted)
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