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Endogenous timing game with non-monotonic reaction functions

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  • Grégoire ROTA-GRAZIOSI

    () (Centre d'Etudes et de Recherches sur le Développement International(CERDI))

  • Magnus HOFFMANN

Abstract

The aim of this paper is to generalize the endogenous timing game proposed by Hamilton and Slutsky (1990) to cases where the reaction functions are non-motononic, as for instance in the literature on contest. Following the taxonomy of social dilemma provided by Eaton (2004) we consider several pos- sible situations depending on the nature of interactions (plain complementarity or plain substituability and strategic complementarity or strategic substitutability). Under the assumptions of the existence and the uniqueness of the Nash and Stackelberg equilibria, we highlight the presence of a ?rst-mover advantage or a second-mover incentive only depending on the nature of cross-e?ects in players’ payo? functions and the slopes of their reaction functions at the Nash equilibrium of the static game. These properties allow us to determine rigorously the Subgame Perfect Nash Equilibrium (SPNE) in the ten studied situations. We establish under which conditions on the nature of interactions a leader emerges at the SPNE

Suggested Citation

  • Grégoire ROTA-GRAZIOSI & Magnus HOFFMANN, 2010. "Endogenous timing game with non-monotonic reaction functions," Working Papers 201017, CERDI.
  • Handle: RePEc:cdi:wpaper:1167
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    References listed on IDEAS

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    1. B. C. Eaton, 2002. "Applied Microeconomic Theory," Books, Edward Elgar Publishing, number 1330.
    2. Amir, Rabah & Stepanova, Anna, 2006. "Second-mover advantage and price leadership in Bertrand duopoly," Games and Economic Behavior, Elsevier, vol. 55(1), pages 1-20, April.
    3. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
    4. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
    5. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
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    7. Amir Rabah, 1995. "Endogenous Timing in Two-Player Games: A Counterexample," Games and Economic Behavior, Elsevier, vol. 9(2), pages 234-237, May.
    8. Baik, Kyung H & Shogren, Jason F, 1992. "Strategic Behavior in Contests: Comment," American Economic Review, American Economic Association, vol. 82(1), pages 359-362, March.
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    Cited by:

    1. Eichner, Thomas, 2014. "Endogenizing leadership and tax competition: Externalities and public good provision," Regional Science and Urban Economics, Elsevier, vol. 46(C), pages 18-26.
    2. Hubert Kempf & Grégoire Rota-Graziosi, 2015. "Further analysis on leadership in tax competition: the role of capital ownership—a comment," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 22(6), pages 1028-1039, December.

    More about this item

    Keywords

    Endogenous timing game; ?rst-mover advantage; Second-mover incentive; Subgame Perfect Nash Equilibrium;

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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