Characterization of Markovian equilibria in a class of differential games

We consider an alternative method to the classical one for the determination of Markov perfect Nash equilibria. The approach shown in the paper is based on the study of a quasi-linear system of partial differential equations instead of the Hamilton–Jacobi–Bellman system. The simpler structure of the...

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Bibliographic Details
Published in:Journal of economic dynamics & control 2004-04, Vol.28 (7), p.1243-1266
Main Author: Rincón-Zapatero, J.P
Format: Article
Language:English
Subjects:
Differential games
Economic models
Economic theory
Economics
Equilibrium
Game theory
Games
Markov analysis
Markovian equilibrium
Markovian processes
Mathematical analysis
Model testing
Non-renewable resource
Partial differential equations
Problem solving
Quasi-linear equation
Studies
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Summary:We consider an alternative method to the classical one for the determination of Markov perfect Nash equilibria. The approach shown in the paper is based on the study of a quasi-linear system of partial differential equations instead of the Hamilton–Jacobi–Bellman system. The simpler structure of the former allows us to determine existence and uniqueness of Nash equilibria in non-renewable resource games under some assumptions. When closed-form solutions are not available, we give a method to obtain numerical solutions.
ISSN:0165-1889
1879-1743
DOI:10.1016/S0165-1889(03)00118-0