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.
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Acknowledgements
Most of this research was carried out while Olivier Tercieux was at Tilburg University. Mark Voorneveld thanks the Netherlands Organization for Scientific Research (NWO) and the Wallander/Hedelius Foundation for financial support during parts of the research. Olivier Tercieux gratefully acknowledges financial support from the French Ministry of Research (Action Concertee Incitative). We thank Henk Norde, Willemien Kets, and two anonymous referees for valuable comments.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Tercieux, O., Voorneveld, M. The cutting power of preparation. Math Meth Oper Res 71, 85–101 (2010). https://doi.org/10.1007/s00186-009-0286-5
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DOI: https://doi.org/10.1007/s00186-009-0286-5