# Learning of Nash Equilibria in Risk-Averse Games

arXiv: https://arxiv.org/abs/2403.10399 · HTML: https://mlsanity.com/paper/2403.10399/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2024.

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

- [Tractable Equilibrium Computation in Markov Games through Risk Aversion](https://mlsanity.com/paper/2406.14156/) (2024)
- [Wasserstein Distributionally Robust Nash Equilibrium Seeking with Heterogeneous Data: A Lagrangian Approach](https://mlsanity.com/paper/2511.14048/) (2025)
- [Risk-Averse Learning with Varying Risk Levels](https://mlsanity.com/paper/2512.22986/) (2025)
- [Strategically Robust Multi-Agent Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2603.09208/) (2026)

## Abstract (arXiv)

This paper considers risk-averse learning in convex games involving multiple agents that aim to minimize their individual risk of incurring significantly high costs. Specifically, the agents adopt the conditional value at risk (CVaR) as a risk measure with possibly different risk levels. To solve this problem, we propose a first-order risk-averse leaning algorithm, in which the CVaR gradient estimate depends on an estimate of the Value at Risk (VaR) value combined with the gradient of the stochastic cost function. Although estimation of the CVaR gradients using finitely many samples is generally biased, we show that the accumulated error of the CVaR gradient estimates is bounded with high probability. Moreover, assuming that the risk-averse game is strongly monotone, we show that the proposed algorithm converges to the risk-averse Nash equilibrium. We present numerical experiments on a Cournot game example to illustrate the performance of the proposed method.