Markov perfect Nash equilibria in models with a single capital stock

Many economic problems can be formulated as dynamic games in which strategically interacting agents choose actions that determine the current and future levels of a single capital stock. We study necessary as well as sufficient conditions that allow us to characterise Markov perfect Nash equilibria...

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Bibliographic Details
Published in:Economic theory 2014-08, Vol.56 (3), p.585-625
Main Authors: Dockner, Engelbert, Wagener, Florian
Format: Article
Language:English
Subjects:
Analysis
Capital stock
Capital stocks
Consumption
Consumption functions
Differential games
Economic status
Economic systems
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Equilibrium
Game Theory
Games
Hamilton Jacobi equation
Investment
Markov models
Markov processes
Markovian processes
Microeconomics
Nash equilibrium
Ordinary differential equations
Partial differential equations
Public Finance
Representative agent
Research Article
Shadow prices
Social and Behav. Sciences
Studies
Trajectories
Variables
Viscosity
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Summary:Many economic problems can be formulated as dynamic games in which strategically interacting agents choose actions that determine the current and future levels of a single capital stock. We study necessary as well as sufficient conditions that allow us to characterise Markov perfect Nash equilibria for these games. These conditions can be translated into an auxiliary system of ordinary differential equations that helps us to explore stability, continuity and differentiability of these equilibria. The techniques are used to derive detailed properties of Markov perfect Nash equilibria for several games including voluntary investment in a public capital stock, the intertemporal consumption of a reproductive asset and the pollution of a shallow lake.
ISSN:0938-2259
1432-0479
DOI:10.1007/s00199-014-0805-3