@inproceedings{
ganzfried2023safe,
title={Safe Equilibrium},
author={Sam Ganzfried},
booktitle={Multi-Agent Security Workshop @ NeurIPS'23},
year={2023},
url={https://openreview.net/forum?id=4831vtb6Bp}
}
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may obtain an extremely low payoff. On the other hand, a maximin strategy assumes that all opposing agents are playing to minimize our payoff (even if it is not in their best interest), and ensures the maximal possible worst-case payoff, but results in exceedingly conservative play. We propose a new solution concept called safe equilibrium that models opponents as behaving rationally with a specified probability and behaving potentially arbitrarily with the remaining probability.  We prove that a safe equilibrium exists in all strategic-form games (for all possible values of the rationality parameters), and prove that its computation is PPAD-hard.
Safe Equilibrium
Sam Ganzfried