Equilibrium and Infeasibility: A new solution concept for games
For game theorists and applied researchers, this provides a way to handle infeasibility in non-cooperative games, but the contribution is incremental as it builds on penalty methods.
The paper introduces a new solution concept for generalized games with infeasible individual constraints, defined as the limit of penalty-based Nash equilibria. Existence is proven for a broad class of games, and the solution is characterized as a strategy profile maximizing each player's utility over penalty-minimizing strategies.
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.