Comparing Open-loop With Markov Equilibria in a Class of Differential Games
AbstractWe consider a class of differential games with transition equations that are homogeneous of degree one. For any game G with a discount rate r, consider a Markov perfect equilibrium (MPE) with strategies that are linear in the state variables. We show that the time paths of the control variables of this equilibrium constitute an open-loop equilibrium of a corresponding game that differs from G only in that its rate of discount is equal to r plus a suitably chosen constant. In the context of a resource depletion game, this implies that the open-loop solution is more conservationist. In an alternative formulation, we consider a game G with a rate of stock depreciation and a Markov perfect equilibrium with strategies that are linear in the state variable. Then the resulting equilibrium time paths of the control variables can be used to form an open-loop equilibrium of a corresponding game with a rate of depreciation that is equal to plus a suitably chosen constant. The interpretation for the case of a resource game is similar. We also prove a converse result: under certain assumptions, an open loop equilibrium of a differential game G can be used to construct a MPE of a modified game . This result is useful because it means a MPE can be found by first solving for an open loop equilibrium. On considÃ¨re une classe de jeux dynamiques oÃ¹ l'Ã©volution du stock est une fonction homogÃ¨ne du premier degrÃ©. Ãtant donnÃ© un jeu G avec le taux d'actualisation r , on considÃ¨re un Ã©quilibre Markov-parfait dont les stratÃ©gies sont linÃ©aires par rapport aux variables d'Ã©tat. On montre que les sentiers des variables de contrÃ´le de cet Ã©quilibre constituent un Ã©quilibre en boucle ouverte d'un jeu qui correspond Ã , et qui a un taux d'actualisation ( . Dans le contexte d'un jeu d'exploitation de ressources naturelles, celÃ implique que l'Ã©quilibre en boucle ouverte tends Ã conserver les ressources. Alternativement, on considÃ¨re un jeu G oÃ¹ le taux de dÃ©prÃ©cia
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Bibliographic InfoArticle provided by Japanese Economic Association in its journal Japanese Economic Review.
Volume (Year): 50 (1999)
Issue (Month): 4 (December)
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Web page: http://www.blackwellpublishing.com/journal.asp?ref=1352-4739
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Other versions of this item:
- Ngo Van Long & Koji Shimomura & Harutaka Takahashi, 1997. "Comparing Open-Loop with Markov Equilibria in a Class of Differential Games," CIRANO Working Papers 97s-22, CIRANO.
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General
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.:
- Ngo Van Long & Koji Shimomura, 1995.
"Some Results on the Markov Equilibria of a Class of Homogeneous Differential Games,"
CIRANO Working Papers
- Van Long, Ngo & Shimomura, Koji, 1998. "Some results on the Markov equilibria of a class of homogeneous differential games," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 557-566, January.
- Talat S. Genc & Georges Zaccour, 2010. "Investment Dynamics: Good News Principle," Working Papers 1006, University of Guelph, Department of Economics and Finance.
- Ngo Long, 2011. "Dynamic Games in the Economics of Natural Resources: A Survey," Dynamic Games and Applications, Springer, vol. 1(1), pages 115-148, March.
- Charles Figuières, 2009. "Markov interactions in a class of dynamic games," Theory and Decision, Springer, vol. 66(1), pages 39-68, January.
- Murray C. Kemp & Ngo Van Long, 2007. "Development Aid in the Presence of Corruption: Differential Games among Donors," CIRANO Working Papers 2007s-23, CIRANO.
- Sébastien Rouillon, 2014. "Do Social Status Seeking Behaviors Worsen the Tragedy of the Commons?," Dynamic Games and Applications, Springer, vol. 4(1), pages 73-94, March.
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