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

Ricardo Josa-Fombellida () and Juan Pablo Rincón-Zapatero

Economic Theory, 2015, vol. 59, issue 1, 108 pages

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

Keywords: Stochastic productive asset; Markov Perfect Nash Equilibrium; Euler–Lagrange equations; C73; C61 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s00199-015-0873-z

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