Markov Perfect Nash Equilibria in a Class of Resource Games

Gerhard Sorger

CIRANO Working Papers from CIRANO

Abstract: A standard model of the exploitation of a renewable resource by non-cooperating agents is considered. Under the assumption that the resource is sufficiently productive we prove that there exist infinitely many Markov-perfect Nash equilibria (MPNE). Although these equilibria lead to overexploitation of the resource (tragedy of the commons) it is shown that for any T > 0 there exist MPNE with the property that the resource stock stays in an arbitrary small neighborhood of the efficient steady state for at least T time periods. Furthermore, we derive a necessary and sufficient condition for maximal exploitation of the resource to qualify as a MPNE and show that this condition is satisfied if there are sufficiently many players, or if the players are sufficiently impatient, or if the capacity of each player is sufficiently high. On analyse un modèle standard de l'exploitation des ressources renouvelables par des agents non-coopératifs. Dans le cas où les ressources sont suffisamment productives, on démontre l'existence d'un continuum d'équilibres Markov-parfaits de Nasch (EMPN). Quoique ces équilibres entrainent la surconsommation des ressources, on peut prouver que pour chaque T > 0, il y a des EMPN ayant la propriété que le stock de ressources demeure dans un voisinage arbitrairement petit de l'état stationnaire optimal pendant au moins T périodes. De plus, on obtient une condition nécessaire et suffisante pour que l'exploitation maximale des ressources soit un EMPN. On démontre que cette condition est vérifiée dans le cas où soit il y a beaucoup d'agents, soit les agents sont impatients, soit la capacité de chaque agent est grande.

Keywords: Renewable resources; differential game; Markov perfect equilibria; multiple equilibria; Ressources renouvelables; jeu différentiel; équilibres Markov-parfaits; équilibres multiples (search for similar items in EconPapers)
Date: 1996-04-01
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Citations: View citations in EconPapers (19)

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Journal Article: Markov-perfect Nash equilibria in a class of resource games (1997)
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Persistent link: https://EconPapers.repec.org/RePEc:cir:cirwor:96s-15

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