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Lead, Follow or Cooperate? Endogenous Timing & Cooperation in Symmetric Duopoly Games

  • Marco Marini

    ()

    (Department of Economics, Society & Politics, Università di Urbino "Carlo Bo" and CREI, Università di Roma III)

  • Giorgio Rodano

    ()

    (Dipartimento di Informatica e Sistemistica "Antonio Ruberti", Università di Roma "La Sapienza")

The aim of this paper is to extend Hamilton and Slutsky's (1990) endogenous timing game by including the possibility for players to cooperate. At an initial stage players are assumed to announce both their purpose to play early or late a given duopoly game as well as their intention to cooperate or not with their rival. The cooperation and timing formation rule is rather simple: when both players agree to cooperate and play with a given timing, they end up playing their actions coordinately and simultaneously. Otherwise, they play as singletons with the timing as prescribed by their own announcement. We check for the existence of a subgame perfect Nash equilibrium (in pure strategies) of such a cooperation-timing duopoly game. Two main results on the emergence of cooperation are provided. If players' actions in the symmetric duopoly game are strategic substitutes and there is no discount, cooperating early is a subgame perfect equilibrium of the extended timing-cooperation game. Conversely, cooperating late (at period two) represents an equilibrium when players' strategies are strategic complements. Other equilibria are also possible. Most importantly, our model shows that, in general, the success of cooperation is a¤ected by the endogenous timing of the game. Moreover, the slope of players' best-replies appears crucial both for the success of cooperation as well as for the players' choice of sequencing their market actions.

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File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_11_12.pdf
File Function: First version, 2011
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Paper provided by University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini in its series Working Papers with number 1112.

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Length: 18 pages
Date of creation: 2011
Date of revision: 2011
Handle: RePEc:urb:wpaper:11_12
Contact details of provider: Web page: http://www.econ.uniurb.it/

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  1. Ray, D. & Vohra, R., 1993. "Equilibrium Binding Agreements," Papers 21, Boston University - Department of Economics.
  2. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
  3. Amir Rabah, 1995. "Endogenous Timing in Two-Player Games: A Counterexample," Games and Economic Behavior, Elsevier, vol. 9(2), pages 234-237, May.
  4. Eric van Damme & Sjaak Hurkens, 2001. "Endogenous price leadership," Economics Working Papers 581, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Madjid Amir & Rabah Amir & Jim Jin, 1999. "Sequencing R&D Decisions in a Two-period Duopoly with Spillovers," CIE Discussion Papers 1999-06, University of Copenhagen. Department of Economics. Centre for Industrial Economics.
  6. Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
  7. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954, March.
  8. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Currarini, Sergio & Marini, Marco, 2002. "A conjectural cooperative equilibrium for strategic form games," MPRA Paper 33384, University Library of Munich, Germany.
  10. Sergio Currarini & Marco A. Marini, 2006. "Coalition Formation In Games Without Synergies," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 111-126.
  11. Hamilton, J.H. & Slutsky, S.M., 1988. "Endogenous Timing In Duopoly Games: Stackelberg Or Cournot Equilibria," Papers 88-4, Florida - College of Business Administration.
  12. von Stengel, Bernhard, 2010. "Follower payoffs in symmetric duopoly games," Games and Economic Behavior, Elsevier, vol. 69(2), pages 512-516, July.
  13. Marini, Marco A. & Currarini, Sergio, 2003. "A sequential approach to the characteristic function and the core in games with externalities," MPRA Paper 1689, University Library of Munich, Germany, revised 2003.
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