Euler-Lagrange equations of stochastic differential games: application to a game of a productive asset Articles uri icon

publication date

  • May 2015

start page

  • 61

end page

  • 108


  • 1


  • 59

International Standard Serial Number (ISSN)

  • 0938-2259

Electronic International Standard Serial Number (EISSN)

  • 1432-0479


  • 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.


  • Economics


  • stochastic productive asset; markov perfect nash equilibrium; euler–lagrange equations