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Endogenous timing game with non-monotonic reaction functions

Author

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  • Grégoire Rota-Graziosi

    (CERDI - Centre d'Études et de Recherches sur le Développement International - UdA - Université d'Auvergne - Clermont-Ferrand I - CNRS - Centre National de la Recherche Scientifique)

  • Magnus Hoffmann

    (Department of Economics - Department of Economics - OVGU - Otto-von-Guericke-Universität Magdeburg = Otto-von-Guericke University [Magdeburg])

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 first-mover advantage or a second-mover incentive only depending on the nature of cross-effects in players' payoff 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, 2011. "Endogenous timing game with non-monotonic reaction functions," CERDI Working papers halshs-00553130, HAL.
    • Handle: RePEc:hal:cdiwps:halshs-00553130
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00553130
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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.
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    5. Avinash Dixit, 2008. "Strategic Behavior in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 431-438, Springer.
    6. B. Curtis Eaton, 2004. "The elementary economics of social dilemmas," Canadian Journal of Economics, Canadian Economics Association, vol. 37(4), pages 805-829, November.
    7. Kyung H. Baik & Jason F. Shogren, 2008. "Strategic Behavior in Contests: Comment," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 439-442, Springer.
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    9. Ron Adner & Peter Zemsky, 2005. "Disruptive Technologies and the Emergence of Competition," RAND Journal of Economics, The RAND Corporation, vol. 36(2), pages 229-254, Summer.
    10. Sadanand, Asha & Sadanand, Venkatraman, 1996. "Firm Scale and the Endogenous Timing of Entry: a Choice between Commitment and Flexibility," Journal of Economic Theory, Elsevier, vol. 70(2), pages 516-530, August.
    11. Amir Rabah, 1995. "Endogenous Timing in Two-Player Games: A Counterexample," Games and Economic Behavior, Elsevier, vol. 9(2), pages 234-237, May.
    12. Constantinos Syropoulos, 1994. "Endogenous Timing in Games of Commercial Policy," Canadian Journal of Economics, Canadian Economics Association, vol. 27(4), pages 847-864, November.
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    Cited by:

    1. 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.
    2. 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.
    3. Carsten Eckel & Yutao Han & Kate Hynes & Jin Zhang, 2021. "Structural fund, endogenous move and commitment," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 28(2), pages 465-482, April.
    4. Ilkka Leppänen, 2020. "Partial commitment in an endogenous timing duopoly," Annals of Operations Research, Springer, vol. 287(2), pages 783-799, April.

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    More about this item

    Keywords

    first-mover advantage; endogenous timing game; second-mover incentive; Subgame Perfect Nash Equilibrium;
    All these keywords.

    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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