# Online Parameter Identification of Generalized Non-cooperative Game

arXiv: https://arxiv.org/abs/2310.09511 · HTML: https://mlsanity.com/paper/2310.09511/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 35 references that are in the map.
- First posted on arXiv 14 Oct 2023.

## Builds on (most cited first, 8 of 8)

- [Game-Theoretic Modeling of Driver and Vehicle Interactions for Verification and Validation of Autonomous Vehicle Control Systems](https://mlsanity.com/paper/1608.08589/) (2016)
- [Multi-agent Inverse Reinforcement Learning for Two-person Zero-sum Games](https://mlsanity.com/paper/1403.6508/) (2014)
- [LUCIDGames: Online Unscented Inverse Dynamic Games for Adaptive Trajectory Prediction and Planning](https://mlsanity.com/paper/2011.08152/) (2020)
- [Online Market Equilibrium with Application to Fair Division](https://mlsanity.com/paper/2103.12936/) (2021)
- [Distributed Learning for Stochastic Generalized Nash Equilibrium Problems](https://mlsanity.com/paper/1608.00039/) (2016)
- [Inverse Game Theory for Stackelberg Games: the Blessing of Bounded Rationality](https://mlsanity.com/paper/2210.01380/) (2022)
- [Using Inverse Optimization to Learn Cost Functions in Generalized Nash Games](https://mlsanity.com/paper/2102.12415/) (2021)
- [Inverse Matrix Games with Unique Quantal Response Equilibrium](https://mlsanity.com/paper/2207.08275/) (2022)

## Abstract (arXiv)

This work studies the parameter identification problem of a generalized non-cooperative game, where each player's cost function is influenced by an observable signal and some unknown parameters. We consider the scenario where equilibrium of the game at some observable signals can be observed with noises, whereas our goal is to identify the unknown parameters with the observed data. Assuming that the observable signals and the corresponding noise-corrupted equilibriums are acquired sequentially, we construct this parameter identification problem as online optimization and introduce a novel online parameter identification algorithm. To be specific, we construct a regularized loss function that balances conservativeness and correctiveness, where the conservativeness term ensures that the new estimates do not deviate significantly from the current estimates, while the correctiveness term is captured by the Karush-Kuhn-Tucker conditions. We then prove that when the players' cost functions are linear with respect to the unknown parameters and the learning rate of the online parameter identification algorithm satisfies μk propto 1/√k, along with other assumptions, the regret bound of the proposed algorithm is O(√K). Finally, we conduct numerical simulations on a Nash-Cournot problem to demonstrate that the performance of the online identification algorithm is comparable to that of the offline setting.