# Inverse Matrix Games with Unique Quantal Response Equilibrium

arXiv: https://arxiv.org/abs/2207.08275 · HTML: https://mlsanity.com/paper/2207.08275/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2022.

## Built on by (most cited first, 3 of 3)

- [Soft-Bellman Equilibrium in Affine Markov Games: Forward Solutions and Inverse Learning](https://mlsanity.com/paper/2304.00163/) (2023)
- [Active Inverse Learning in Stackelberg Trajectory Games](https://mlsanity.com/paper/2308.08017/) (2023)
- [Online Parameter Identification of Generalized Non-cooperative Game](https://mlsanity.com/paper/2310.09511/) (2023)

## Abstract (arXiv)

In an inverse game problem, one needs to infer the cost function of the players in a game such that a desired joint strategy is a Nash equilibrium. We study the inverse game problem for a class of multiplayer matrix games, where the cost perceived by each player is corrupted by random noise. We provide sufficient conditions for the players' quantal response equilibrium -- a generalization of the Nash equilibrium to games with perception noise -- to be unique. We develop efficient optimization algorithms for inferring the cost matrix based on semidefinite programs and bilevel optimization. We demonstrate the application of these methods in encouraging collision avoidance and fair resource allocation.