Inverse Game Theory: An Incenter-Based Approach

Estimating player utilities from observed equilibria is crucial for many applications. Existing approaches to tackle this problem are either limited to specific games or do not scale well with the number of players. Our work addresses these issues by proposing a novel utility estimation method for general multi-player non-cooperative games. Our main idea consists in reformulating the inverse game problem as an inverse variational inequality problem and in selecting among all utility parameters consistent with the data, the so-called incenter. We show that the choice of the incenter can produce parameters that are most robust to the observed equilibrium behaviors. However, its computation is challenging, as the number of constraints in the corresponding optimization problem increases with the number of players and the behavior space size. To tackle this challenge, we propose a loss function-based algorithm, making our method scalable to games with many players or a continuous action space. Furthermore, we show that our method can be extended to incorporate prior knowledge of player utilities, and that it can handle inconsistent data, i.e., data where players do not play exact equilibria. Numerical experiments on three game applications demonstrate that our methods outperform the state of the art. The code, datasets, and supplementary material are available at https://github.com/cuilvye/Incenter-Project.