Finding Equilibria in Large (Generalized) Nash Games Using (Quasi) Variational Inequalities
Nash equilibrium (NE) is one of the most important concepts in game theory that captures a wide range of phenomena in engineering, economics, and finance. An NE is characterized by observing that in a stable game, no player can lower their cost by changing their action within their designated strategy. An equilibrium in the Nash game can be found by solving a variational inequality (VI) problem. Solving VI and stochastic VI (SVI) problems become more difficult if we consider that the players interact also at the level of the feasible sets. This situation arises naturally if the players share some common resource. This problem is modeled as Generalized NE (GNE) which can be formulated as Quasi VI (QVI) or Stochastic QVI (SQVI). In this talk, we present efficient iterative schemes to solve SVI and SQVI problems and present their convergence guarantees. To validate our theoretical findings, we provide some preliminary simulation results on different problems such as stochastic Nash Cournot competition over a network.
March 13, 2023 2:30pm