Some results on the Markov equilibria of a class of homogeneous differential games
AbstractWe consider the class of differential games with transition dynamics and constraints that are homogeneous of degree one. We show that if the integrand of the objective function is homogeneous of degree , then best replies to linear homogeneous Markov strategies are linear homogeneous, and the value function is homogeneous of degree . A parallel result holds when one applies logarithmic transformation to the integrand. Examples are provided. Nous Ã©tudions la classe de jeux diffÃ©rentiels dont l'Ã©quation de transition et les contraintes sont caractÃ©risÃ©es par l'homogÃ©nÃ©itÃ© du premier degrÃ©. Nous prouvons que si la fonction d'objectif possÃ¨de l'homogÃ©nÃ©itÃ© du degrÃ© , alors la meilleure rÃ©ponse aux stratÃ©gies markoviennes qui possÃ¨dent l'homogÃ©nÃ©itÃ© du premier degrÃ© doit avoir la mÃªme propriÃ©tÃ©, et la fonction de valeur est caractÃ©risÃ©e par l'homogÃ©nÃ©itÃ© du degrÃ© . On obtient un rÃ©sultat similaire dans le cas d'une transformation logarithmique de la fonction d'objectif. L'article contient trois exemples.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Behavior & Organization.
Volume (Year): 33 (1998)
Issue (Month): 3-4 (January)
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Other versions of this item:
- Ngo Van Long & Koji Shimomura, 1995. "Some Results on the Markov Equilibria of a Class of Homogeneous Differential Games," CIRANO Working Papers 95s-36, CIRANO.
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
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