The cutting power of preparation

Olivier Tercieux () and Mark Voorneveld
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Olivier Tercieux: PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Mark Voorneveld: Tilburg University - Department of Econometrics and Operations Research - Tilburg University [Netherlands], SSE - Stockholm School of Economics

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Abstract: In a strategic game, a curb set (Basu and Weibull, Econ Lett 36:141-146, 1991) is a product set of pure strategies containing all best responses to every possible belief restricted to this set. Prep sets (Voorneveld, Games Econ Behav 48:403-414, 2004) relax this condition by only requiring the presence of at least one best response to such a belief. The purpose of this paper is to provide sufficient conditions under which minimal prep sets give sharp predictions. These conditions are satisfied in many economically relevant classes of games, including supermodular games, potential games, and congestion games with player-specific payoffs. In these classes, minimal curb sets generically have a large cutting power as well, although it is shown that there are relevant subclasses of coordination games and congestion games where minimal curb sets have no cutting power at all and simply consist of the entire strategy space.

Keywords: Curb sets; Prep sets; Supermodular games; Potential games; Congestion games (search for similar items in EconPapers)
Date: 2010-03
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Citations: View citations in EconPapers (2)

Published in Mathematical Methods of Operations Research, 2010, 71 (1), pp.85-101. ⟨10.1007/s00186-009-0286-5⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-00754467

DOI: 10.1007/s00186-009-0286-5

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