Equilibrium and Infeasibility: A new solution concept for games

2026-06-24

AI Summary

This study addresses the issue of potentially infeasible individual constraints in non-cooperative generalized games by proposing a novel solution concept that integrates the generalized Nash equilibrium with the Nash bargaining solution. The approach introduces a sequence of penalized generalized Nash equilibria, whose limit defines a feasible solution. By combining penalty function techniques, generalized Nash equilibrium theory, and limit analysis of strategy profiles, the work establishes existence conditions and characterizations for this new solution across a broad class of games. The theoretical findings are validated through a variant of the classic “Divide-the-Dollar” game, demonstrating the framework’s effectiveness and applicability in handling scenarios with infeasible constraints.

Abstract

Addressing infeasibility in non-cooperative games has become an important topic, as many problems across different applications face this issue. In this paper, we propose a new solution concept for generalized games with possibly infeasible individual constraints. A solution is defined as the limit of a sequence of generalized Nash equilibria induced by games with penalty terms relaxing the individual constraints. Existence is established for a broad range of games and we provide conditions allowing to characterize a $ψ$-penalized solution as a strategy profile maximizing every player's utility over all her penalty minimizing strategies. A variation of Divide-the-Dollar serves as an illustrative example. We further establish the compatibility with the GNE and the solution to the Nash bargaining.

Problem

• infeasibility
• non-cooperative games
• generalized Nash equilibrium
• individual constraints
• solution concept

Innovation

• generalized Nash equilibrium
• infeasibility
• penalty method
• solution concept
• non-cooperative games