Computation of Markov Perfect Nash Equilibria without Hamilton—Jacobi—Bellman Equations

  1. Martín-Herrán, Guiomar 1
  2. Rincón-Zapatero, Juan Pablo
  1. 1 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

Book:
Advances in Computational Management Science

ISSN: 1388-4301

ISBN: 9781461353683,  9781461510475

Year of publication: 2002

Pages: 135-151

Type: Book chapter

DOI: 10.1007/978-1-4615-1047-5_9 GOOGLE SCHOLAR lock_openOpen access editor

Abstract

In this paper we provide new insights on the method for computing Markov perfect Nash equilibria presented for the first time in [12]. This method does not use the Hamilton—Jacobi—Bellman equations, but characterizes Markov perfect equilibria by means of a system of quasilinear partial differential equations. A quasilinear system is much more amenable than a fully non-linear system of partial differential equations as the Hamilton—Jacobi—Bellman system usually is. This fact allows us to establish results on existence and uniqueness of solutions and also to derive its analytical expressions in some cases. Otherwise, this approach simplifies a qualitative analysis, making possible the application of well—known numerical routines to find an approximate Nash equilibrium. The main features of the method are shown in the analysis of some competitive resource games.

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