Approximating Nash Equilibria in Nonzero-Sum Games

Abstract

This paper deals with the approximation of Nash equilibria in m-player games. We present conditions under which an approximating sequence of games admits nearequilibria that approximate near-equilibria in the limit game. We apply the results to two classes of games: (i) a duopoly game approximated by a sequence of matrix games, and (ii) a stochastic game played under the S-adapted information structure approximated by games played over a sampled event tree. Numerical illustrations show the usefulness of this approximation theory.

Generalized Nash equilibrium problems

“…This issue has been analyzed in some detail for NEPs, see for example Altman et al 2000;Cavazzuti and Pacchiarotti 1986;Dafermos 1990;Flåm 1994;Margiocco et al 1997Margiocco et al , 1999Margiocco et al , 2002 Obviously, for NEPs one can use its reduction to VI and then apply the well-developed sensitivity theory existing for the latter class of problems (Facchinei and Pang 2003).…”

Generalized Nash Equilibrium Problems

“…This issue has been analyzed in some detail for NEPs, see for example (Altman et al 2000;Cavazzuti and Pacchiarotti 1986;Dafermos 1990;Flåm 1994;Margiocco et al 1997Margiocco et al , 1999Margiocco et al , 2002. Obviously, for NEPs one can use its reduction to VI and then apply the well-developed sensitivity theory existing for the latter class of problems (Facchinei and Pang 2003).…”

Routing Games in the many players regime

“…We can then conclude from [2] that the equilibrium converges to the Wardrop one. The three assertions of the theorem are proven by applying [2][Theorem 3.1].…”