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The cutting power of preparation

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  • Olivier Tercieux
  • Mark Voorneveld

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. Copyright The Author(s) 2010

Suggested Citation

  • Olivier Tercieux & Mark Voorneveld, 2010. "The cutting power of preparation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 85-101, February.
    • Handle: RePEc:spr:mathme:v:71:y:2010:i:1:p:85-101
    DOI: 10.1007/s00186-009-0286-5
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    1. Mark Voorneveld & Willemien Kets & Henk Norde, 2006. "An Axiomatization of Minimal Curb Sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 153-153, April.
    2. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    4. Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August.
    5. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    6. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
    7. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    8. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-411, May.
    9. Mark Voorneveld & Peter Borm & Freek Van Megen & Stef Tijs & Giovanni Facchini, 1999. "Congestion Games And Potentials Reconsidered," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 283-299.
    10. Kosfeld, Michael & Droste, Edward & Voorneveld, Mark, 2002. "A myopic adjustment process leading to best-reply matching," Games and Economic Behavior, Elsevier, vol. 40(2), pages 270-298, August.
    11. Hurkens, Sjaak, 1996. "Multi-sided Pre-play Communication by Burning Money," Journal of Economic Theory, Elsevier, vol. 69(1), pages 186-197, April.
    12. Kets, Willemien & Voorneveld, Mark, 2005. "Learning to be prepared," SSE/EFI Working Paper Series in Economics and Finance 590, Stockholm School of Economics.
    13. Slikker, Marco, 2001. "Coalition Formation and Potential Games," Games and Economic Behavior, Elsevier, vol. 37(2), pages 436-448, November.
    14. Voorneveld, Mark, 1997. "Equilibria and approximate equilibria in infinite potential games," Economics Letters, Elsevier, vol. 56(2), pages 163-169, October.
    15. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    16. Slade, Margaret E, 1994. "What Does an Oligopoly Maximize?," Journal of Industrial Economics, Wiley Blackwell, vol. 42(1), pages 45-61, March.
    17. Challet, Damien & Marsili, Matteo & Zhang, Yi-Cheng, 2013. "Minority Games: Interacting agents in financial markets," OUP Catalogue, Oxford University Press, number 9780199686698.
    18. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.
    19. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
    20. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    21. Thomas Quint & Martin Shubik, 1994. "A Model of Migration," Cowles Foundation Discussion Papers 1088, Cowles Foundation for Research in Economics, Yale University.
    22. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
    23. W. Brian Arthur, 1994. "Inductive Reasoning, Bounded Rationality and the Bar Problem," Working Papers 94-03-014, Santa Fe Institute.
    24. M. Koster & H. Reijnierse & M. Voorneveld, 2003. "Voluntary Contributions to Multiple Public Projects," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 5(1), pages 25-50, January.
    25. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
    26. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
    27. Vitaly Pruzhansky, 2003. "On Finding Curb Sets in Extensive Games," Tinbergen Institute Discussion Papers 03-098/1, Tinbergen Institute.
    28. Voorneveld, Mark, 2005. "Persistent retracts and preparation," Games and Economic Behavior, Elsevier, vol. 51(1), pages 228-232, April.
    29. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    30. Vitaly Pruzhansky, 2003. "On finding curb sets in extensive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 205-210, December.
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    Cited by:

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    3. Kets, W. & Voorneveld, M., 2007. "Congestion, Equilibrium and Learning : The Minority Game," Discussion Paper 2007-61, Tilburg University, Center for Economic Research.
    4. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    5. Kets, W. & Voorneveld, M., 2005. "Learning to be Prepared," Discussion Paper 2005-117, Tilburg University, Center for Economic Research.

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    More about this item

    Keywords

    Curb sets; Prep sets; Supermodular games; Potential games; Congestion games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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