Safe Equilibrium
Abstract
The standard gametheoretic 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 worstcase 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 strategicform games (for all possible values of the rationality parameters), and prove that its computation is PPADhard. We present exact algorithms for computing a safe equilibrium in both 2 and $n$player games, as well as scalable approximation algorithms.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.04266
 Bibcode:
 2022arXiv220104266G
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Computer Science  Artificial Intelligence;
 Computer Science  Cryptography and Security;
 Computer Science  Multiagent Systems;
 Economics  Theoretical Economics