Continuous time approximation of Nash equilibria in monotone games
Roméo Awi, Ryan Hynd, Henok Mawi · Communications in Contemporary Mathematics · 2023
We consider the problem of approximating Nash equilibria of [Formula: see text] functions [Formula: see text] of [Formula: see text] variables. In particular, we show systems of the form [Formula: see text] [Formula: see text] are well-posed and the large time limits of their solutions [Formula: see text] are Nash equilibria for [Formula: see text] provided that these functions satisfy an appropriate monotonicity condition. To this end, we will invoke the theory of maximal monotone operators on a Hilbert space. We will also identify an application of these ideas in game theory and show how to approximate equilibria in some game theoretic problems in function spaces.