Lead, Follow or Cooperate? Endogenous Timing & Cooperation in Symmetric Duopoly Games
AbstractThe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper 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.
Length: 18 pages
Date of creation: 2011
Date of revision: 2011
Endogenous Timing; Cooperation;
Find related papers by JEL classification:
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D23 - Microeconomics - - Production and Organizations - - - Organizational Behavior; Transaction Costs; Property Rights
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-15 (All new papers)
- NEP-BEC-2011-08-15 (Business Economics)
- NEP-COM-2011-08-15 (Industrial Competition)
- NEP-EVO-2011-08-15 (Evolutionary Economics)
- NEP-GTH-2011-08-15 (Game Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- van Damme, Eric & Hurkens, Sjaak, 2004.
"Endogenous price leadership,"
Games and Economic Behavior,
Elsevier, vol. 47(2), pages 404-420, May.
- Damme, E.E.C. van & Hurkens, S., 2004. "Endogenous price leadership," Open Access publications from Tilburg University urn:nbn:nl:ui:12-129320, Tilburg University.
- Eric van Damme & Sjaak Hurkens, 1998. "Endogenous price leadership," Economics Working Papers 289, Department of Economics and Business, Universitat Pompeu Fabra.
- Eric van Damme & Sjaak Hurkens, 2001. "Endogenous price leadership," Economics Working Papers 581, Department of Economics and Business, Universitat Pompeu Fabra.
- Ray, Debraj & Vohra, Rajiv, 1997.
"Equilibrium Binding Agreements,"
Journal of Economic Theory,
Elsevier, vol. 73(1), pages 30-78, March.
- Amir Rabah, 1995. "Endogenous Timing in Two-Player Games: A Counterexample," Games and Economic Behavior, Elsevier, vol. 9(2), pages 234-237, May.
- Marco Marini & Sergio Currarini, 2004.
"Coalition Formation in Games without Synergies,"
2004.43, Fondazione Eni Enrico Mattei.
- Jim Jin & Rabah Amir & Madjid Amir, 2000.
"Sequencing R&D decisions in a two-period duopoly with spillovers,"
Springer, vol. 15(2), pages 297-317.
- 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.
- Currarini, Sergio & Marini, Marco, 2002.
"A conjectural cooperative equilibrium for strategic form games,"
33384, University Library of Munich, Germany.
- Currarini, Sergio & Marini, Marco, 2002. "A conjectural cooperative equilibrium for strategic form games," MPRA Paper 33381, University Library of Munich, Germany.
- 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.
- 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.
- Matthew O. Jackson & Asher Wolinsky, 1995.
"A Strategic Model of Social and Economic Networks,"
1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954.
- 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.
- Hamilton, J.H. & Slutsky, S.M., 1988. "Endogenous Timing In Duopoly Games: Stackelberg Or Cournot Equilibria," Papers 88-4, Florida - College of Business Administration.
- Amir, Rabah & Grilo, Isabel, 1999. "Stackelberg versus Cournot Equilibrium," Games and Economic Behavior, Elsevier, vol. 26(1), pages 1-21, January.
- von Stengel, Bernhard, 2010. "Follower payoffs in symmetric duopoly games," Games and Economic Behavior, Elsevier, vol. 69(2), pages 512-516, July.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Carmela Nicoletti).
If references are entirely missing, you can add them using this form.