Generalized Nash Equilibrium Solutions in Dynamic Games With Shared Constraints

TL;DR

This paper introduces a new method for computing non-normalized Generalized Nash Equilibria in dynamic games with shared constraints using MCP formulation, broadening the solution options beyond traditional normalized approaches.

Contribution

It presents a novel MCP-based approach for non-normalized GNE computation and a systematic method for selecting optimal GNEs based on specific criteria.

Findings

MCP formulation effectively computes non-normalized GNEs.

The proposed method offers greater flexibility in solution selection.

Numerical examples demonstrate the approach's practicality.

Abstract

In dynamic games with shared constraints, Generalized Nash Equilibria (GNE) are often computed using the normalized solution concept, which assumes identical Lagrange multipliers for shared constraints across all players. While widely used, this approach excludes other potentially valuable GNE. This paper presents a novel method based on the Mixed Complementarity Problem (MCP) formulation to compute non-normalized GNE, expanding the solution space. We also propose a systematic approach for selecting the optimal GNE based on predefined criteria, enhancing practical flexibility. Numerical examples illustrate the methods effectiveness, offering an alternative to traditional normalized solutions.