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Collective choice functions on non-convex problems

Author

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  • Marco Mariotti

Abstract

Collective choice problems on sets in ${\frak R}_+^n$ arise naturally in economics. Such problems have been extensively studied both in the theory of revealed preferences (Peters and Wakker, 1991) and in axiomatic bargaining theory under the assumption of convexity. However, our knowledge of collective choice functions on non-convex problems is still patchy. In this paper I study the existence and characterisation of continuous choice functions on the domain $\Gamma$ of comprehensive problems. The main result completely characterises rational choice functions that are continuous and satisfy Weak Pareto Optimality: they form the class of Monotone Path Choice Functions on $\Gamma$ . I also show that any discontinuous rational and weakly Pareto optimal choice function must be non- anonymous. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Marco Mariotti, 2000. "Collective choice functions on non-convex problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(2), pages 457-463, September.
    • Handle: RePEc:spr:joecth:v:16:y:2000:i:2:p:457-463
    DOI: 10.1007/PL00020951
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    Cited by:

    1. Stan Cheung & Marco Mariotti & Roberto Veneziani, 2024. "The Hard Problem and the Tyranny of the Loser," Working Papers 971, Queen Mary University of London, School of Economics and Finance.
    2. Vincent Martinet & Pedro Gajardo & Michel De Lara & Héctor Ramírez Cabrera, 2011. "Bargaining with intertemporal maximin payoffs," EconomiX Working Papers 2011-7, University of Paris Nanterre, EconomiX.

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