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Euler–Lagrange equations of stochastic differential games: application to a game of a productive asset

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  • Ricardo Josa-Fombellida
  • Juan Rincón-Zapatero

Abstract

This paper analyzes a noncooperative and symmetric dynamic game where players have free access to a productive asset whose evolution is a diffusion process with Brownian uncertainty. A Euler–Lagrange equation is found and used to provide necessary and sufficient conditions for the existence and uniqueness of a smooth Markov Perfect Nash Equilibrium. The Euler–Lagrange equation also provides a stochastic Keynes–Ramsey rule, which has the form of a forward–backward stochastic differential equation. It is used to study the properties of the equilibrium and to make some comparative statics exercises. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Ricardo Josa-Fombellida & Juan Rincón-Zapatero, 2015. "Euler–Lagrange equations of stochastic differential games: application to a game of a productive asset," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 61-108, May.
    • Handle: RePEc:spr:joecth:v:59:y:2015:i:1:p:61-108
    DOI: 10.1007/s00199-015-0873-z
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    More about this item

    Keywords

    Stochastic productive asset; Markov Perfect Nash Equilibrium; Euler–Lagrange equations; C73; C61;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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