# Safe Equilibrium

arXiv: https://arxiv.org/abs/2201.04266 · HTML: https://mlsanity.com/paper/2201.04266/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 15 references that are in the map.
- First posted on arXiv 12 Jan 2022.

## Builds on (most cited first, 1 of 1)

- [Fast Complete Algorithm for Multiplayer Nash Equilibrium](https://mlsanity.com/paper/2002.04734/) (2020)

## Built on by (most cited first, 2 of 2)

- [A Survey of Safe Reinforcement Learning and Constrained MDPs: A Technical Survey on Single-Agent and Multi-Agent Safety](https://mlsanity.com/paper/2505.17342/) (2025)
- [(Ir)rationality in AI: State of the Art, Research Challenges and Open Questions](https://mlsanity.com/paper/2311.17165/) (2023)

## Abstract (arXiv)

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. We present exact algorithms for computing a safe equilibrium in both 2 and n-player games, as well as scalable approximation algorithms.