Equilibrium and Infeasibility: A new solution concept for games
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.
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BibTeX
@misc{reulke2026equilibrium,
title = {{Equilibrium and Infeasibility: A new solution concept for games}},
author = {Anne Reulke and Mikaël Touati and Rachid El-Azouzi},
howpublished = {HAL},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.25707},
eprint = {2606.25707},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05668026v2},
}
RIS
TY - UNPB
TI - Equilibrium and Infeasibility: A new solution concept for games
AU - Anne Reulke
AU - Mikaël Touati
AU - Rachid El-Azouzi
PY - 2026
DA - 2026/06/24
PB - HAL
DO - 10.48550/arxiv.2606.25707
UR - https://hal.science/hal-05668026v2
AB - 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.
ER -