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 $\psi$-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.
From: Anne Reulke [view email] [via CCSD proxy]
[v1]
Wed, 24 Jun 2026 11:19:44 UTC (763 KB)
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