Complexity of the Existence of Constrained Secure Equilibria in Multi-Player Games
Abstract
We consider a multi-player non-zero-sum turn-based game (abbreviated as multi-player game) on a finite directed graph. A secure equilibrium (SE) is a strategy profile in which no player has the incentive to deviate from the strategy because no player can increase her own payoff or lower the payoff of another player. SE is a promising refinement of Nash equilibrium in which a player does not care the payoff of another player. In this paper, we discuss the decidability and complexity of the problem of deciding whether a secure equilibrium with constraints (a payoff profile specifying which players must win) exists for a given multi-player game.
Cite
@article{arxiv.2509.01870,
title = {Complexity of the Existence of Constrained Secure Equilibria in Multi-Player Games},
author = {Hiroki Mizuno and Yoshiaki Takata and Hiroyuki Seki},
journal= {arXiv preprint arXiv:2509.01870},
year = {2025}
}
Comments
5 pages, 1 figure, this is a longer version of a short paper submitted to IEICE Transactions on Information and Systems