# Risk-Averse Equilibrium for Games

arXiv: https://arxiv.org/abs/2002.08414 · HTML: https://mlsanity.com/paper/2002.08414/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2020.

## Built on by (most cited first, 4 of 4)

- [A Game-Theoretic Framework for Managing Risk in Multi-Agent Systems](https://mlsanity.com/paper/2205.15434/) (2022)
- [Tractable Equilibrium Computation in Markov Games through Risk Aversion](https://mlsanity.com/paper/2406.14156/) (2024)
- [Training Generalizable Collaborative Agents via Strategic Risk Aversion](https://mlsanity.com/paper/2602.21515/) (2026)
- [Strategically Robust Multi-Agent Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2603.09208/) (2026)

## Abstract (arXiv)

The term rational has become synonymous with maximizing expected payoff in the definition of the best response in Nash setting. In this work, we consider stochastic games in which players engage only once, or at most a limited number of times. In such games, it may not be rational for players to maximize their expected payoff as they cannot wait for the Law of Large Numbers to take effect. We instead define a new notion of a risk-averse best response, that results in a risk-averse equilibrium (RAE) in which players choose to play the strategy that maximizes the probability of them being rewarded the most in a single round of the game rather than maximizing the expected received reward, subject to the actions of other players. We prove the risk-averse equilibrium to exist in all finite games and numerically compare its performance to Nash equilibrium in finite-time stochastic games.