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
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 InfoArticle provided by Japanese Economic Association in its journal Japanese Economic Review.
Volume (Year): 50 (1999)
Issue (Month): 4 (December)
Contact details of provider:
Web page: http://www.blackwellpublishing.com/journal.asp?ref=1352-4739
More information through EDIRC
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.
- 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.
- Talat S. Genc & Georges Zaccour, 2010. "Investment Dynamics: Good News Principle," Working Papers 1006, University of Guelph, Department of Economics and Finance.
- Charles Figuières, 2009. "Markov interactions in a class of dynamic games," Theory and Decision, Springer, vol. 66(1), pages 39-68, January.
- 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.
- Murray C. Kemp & Ngo Van Long, 2007. "Development Aid in the Presence of Corruption: Differential Games among Donors," CIRANO Working Papers 2007s-23, CIRANO.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If references are entirely missing, you can add them using this form.