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Continuous-time Games of Timing

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  • Rida Laraki
  • Eilon Solan
  • Nicolas Vieille

Abstract

We address the question of existence of equilibrium in general timing games of complete information. Under weak assumptions, any two-player timing game has a subgame perfect e-equilibrium, for each e > 0. This result is tight. For some classes of games (symmetric games, games with cumulative payoffs), stronger existence results are established.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1363.

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Date of creation: Feb 2003
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Handle: RePEc:nwu:cmsems:1363

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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. VIEILLE, Nicolas & SOLAN, Eilon, 2001. "Stopping games: recent results," Les Cahiers de Recherche 744, HEC Paris.
  2. Roger B. Myerson, 1984. "Multistage Games with Communication," Discussion Papers 590, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Fudenberg, Drew & Levine, David, 1986. "Limit games and limit equilibria," Journal of Economic Theory, Elsevier, vol. 38(2), pages 261-279, April.
  4. J. Maynard Smith, 2010. "The Theory of Games and Evolution of Animal Conflicts," Levine's Working Paper Archive 448, David K. Levine.
  5. Fudenberg, Drew & Tirole, Jean, 1985. "Preemption and Rent Equilization in the Adoption of New Technology," Review of Economic Studies, Wiley Blackwell, vol. 52(3), pages 383-401, July.
  6. BERGIN, James, 1990. "A model of strategic behaviour in repeated games," CORE Discussion Papers 1990032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Bulow, Jeremy I & Klemperer, Paul, 1997. "The Generalized War of Attrition," CEPR Discussion Papers 1564, C.E.P.R. Discussion Papers.
  8. Simon, Leo K. & Stinchcombe, Maxwell B., 1987. "Extensive From Games in Continuous Time: Pure Strategies," Department of Economics, Working Paper Series qt03x115sh, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  9. Bilodeau, Marc & Slivinski, Al, 1996. "Toilet cleaning and department chairing: Volunteering a public service," Journal of Public Economics, Elsevier, vol. 59(2), pages 299-308, February.
  10. Bergin, James & MacLeod, W Bentley, 1993. "Continuous Time Repeated Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 21-37, February.
  11. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
  12. Eric Maskin & Jean Tirole, 1997. "Markov Perfect Equilibrium, I: Observable Actions," Harvard Institute of Economic Research Working Papers 1799, Harvard - Institute of Economic Research.
  13. Hendricks, Ken & Weiss, Andrew & Wilson, Charles A, 1988. "The War of Attrition in Continuous Time with Complete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 663-80, November.
  14. Perry Motty & Reny Philip J., 1993. "A Non-cooperative Bargaining Model with Strategically Timed Offers," Journal of Economic Theory, Elsevier, vol. 59(1), pages 50-77, February.
  15. Fine, Charles H. & Li, Lode, 1989. "Equilibrium exit in stochastically declining industries," Games and Economic Behavior, Elsevier, vol. 1(1), pages 40-59, March.
  16. Stinchcombe, Maxwell B., 1992. "Maximal strategy sets for continuous-time game theory," Journal of Economic Theory, Elsevier, vol. 56(2), pages 235-265, April.
  17. Fudenberg, Drew & Tirole, Jean, 1986. "A Theory of Exit in Duopoly," Econometrica, Econometric Society, vol. 54(4), pages 943-60, July.
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Citations

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Cited by:
  1. Bobtcheff, Catherine & Mariotti, Thomas, 2012. "Potential competition in preemption games," Games and Economic Behavior, Elsevier, vol. 75(1), pages 53-66.
  2. repec:hal:journl:halshs-00717135 is not listed on IDEAS
  3. Andreas Park & Lones Smith, 2008. "Caller Number Five and Related Timing Games," Working Papers tecipa-317, University of Toronto, Department of Economics.
  4. Gonzalez-Diaz, Julio & Borm, Peter & Norde, Henk, 2007. "A silent battle over a cake," European Journal of Operational Research, Elsevier, vol. 177(1), pages 591-603, February.
  5. Philippe Bich & Rida Laraki, 2012. "A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games," Documents de travail du Centre d'Economie de la Sorbonne 12040, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  6. Michael Ludkovski, 2010. "Stochastic Switching Games and Duopolistic Competition in Emissions Markets," Papers 1001.3455, arXiv.org, revised Aug 2010.
  7. Philippe Bich & Rida Laraki, 2012. "A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00717135, HAL.
  8. Rida Laraki & Eilon Solan, 2012. "Equilibrium in Two-Player Nonzero-Sum Dynkin Games in Continuous Time," Working Papers hal-00753508, HAL.
  9. Wilko Bolt & Kimmo Soram�ki, 2008. "Competition, bargaining power and pricing in two-sided markets," DNB Working Papers 181, Netherlands Central Bank, Research Department.
  10. Azevedo, Alcino & Paxson, Dean, 2014. "Developing real option game models," European Journal of Operational Research, Elsevier, vol. 237(3), pages 909-920.
  11. Philippe Bich & Rida Laraki, 2013. "On the Existence of Approximated Equilibria and Sharing-Rule Equilibria in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00846143, HAL.
  12. Aureo de Paula, 2004. "Social Interactions in a Synchronization Game," Econometric Society 2004 Latin American Meetings 277, Econometric Society.
  13. repec:hal:wpaper:hal-00846143 is not listed on IDEAS

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