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.

Inferring the private information of humans from their strategic behavioral data is crucial and challenging. The main approach is first obtaining human behavior functions (which map public information and human private information to behavior), enabling subsequent inference of private information from observed behavior. Most existing studies rely on strong equilibrium assumptions to obtain behavior functions. Our work focuses on continuous double auctions, where multiple traders with heterogeneous rationalities and beliefs dynamically trade commodities and deriving equilibria is generally intractable. We develop a knowledge-aware machine learning-based framework to infer each trader's private cost vectors for producing different units of its commodity. Our key idea is to learn behavior functions by incorporating the statistical knowledge about private costs given the observed trader asking behavior across the population. Specifically, we first use a neural network to characterize each trader's behavior function. Second, we leverage the statistical knowledge to derive the posterior distribution of each trader's private costs given its observed asks. Third, through designing a novel loss function, we utilize the knowledge-based posterior distributions to guide the learning of the neural network. We conduct extensive experiments on a large experimental dataset, and demonstrate the superior performance of our framework over baselines in inferring the private information of humans.

Inferring bargainers' private valuations on items from their decisions is crucial for analyzing their strategic behaviors in bilateral sequential bargaining. Most existing approaches that infer agents' private information from observable data either rely on strong equilibrium assumptions or require a careful design of agents' behavior models. To overcome these weaknesses, we propose a Bayesian Learning-based Valuation Inference (BLUE) framework. Our key idea is to derive feasible intervals of bargainers' private valuations from their behavior data, using the fact that most bargainers do not choose strictly dominated strategies. We leverage these feasible intervals to guide our inference. Specifically, we first model each bargainer's behavior function (which maps his valuation and bargaining history to decisions) via a recurrent neural network. Second, we learn these behavior functions by utilizing a novel loss function defined based on feasible intervals. Third, we derive the posterior distributions of bargainers' valuations according to their behavior data and learned behavior functions. Moreover, we account for the heterogeneity of bargainer behaviors, and propose a clustering algorithm (K-Loss) to improve the efficiency of learning these behaviors. Experiments on both synthetic and real bargaining data show that our inference approach outperforms baselines.

Kinship verification from facial images is a challenging task in computer vision. The majority of recent verification algorithms concatenate all features of patches in facial image to build the final feature representation, which implicitly takes every facial part into account for kinship verification. However, it is questionable by considering all face regions since certain facial parts such as the eyes of a child look like the other parent or someone else, which could decrease the verification performance of an algorithm. Motivated by this observation, we attempt to automatically single out the discriminative patches of face and discard interferential ones. Specifically, each weak classifier of AdaBoost is adaptively trained to select a feature composed of some crucial feature patches and various features can be obtained by different weak classifiers. In the stage of verification, a strong classifier constructed by these weak classifiers ensembling is utilized to merge the contributions of selected distinct face areas. Experimental results on KinfaceW-I and KinfaceW-II datasets demonstrate the efficacy of the proposed method compared with state-of-the-art kinship verification approaches.