Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data

We consider learning, from strictly behavioral data, the structure and parameters of linear influence games (LIGs), a class of parametric graphical games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic inference (CSI): Making inferences from causal interventions on stable behavior in strategic settings. Applications include the identification of the most influential individuals in large (social) networks. Such tasks can also support policy-making analysis. Motivated by the computational work on LIGs, we cast the learning problem as maximum-likelihood estimation (MLE) of a generative model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation uncovers the fundamental interplay between goodness-of-fit and model complexity: good models capture equilibrium behavior within the data while controlling the true number of equilibria, including those unobserved. We provide a generalization bound establishing the sample complexity for MLE in our framework. We propose several algorithms including convex loss minimization (CLM) and sigmoidal approximations. We prove that the number of exact PSNE in LIGs is small, with high probability; thus, CLM is sound. We illustrate our approach on synthetic data and real-world U.S. congressional voting records. We briefly discuss our learning framework's generality and potential applicability to general graphical games.Comment: Journal of Machine Learning Research. (accepted, pending publication.) Last conference version: submitted March 30, 2012 to UAI 2012. First conference version: entitled, Learning Influence Games, initially submitted on June 1, 2010 to NIPS 201

An algorithm for cooperative probabilistic control design

This paper deals with the decentralized closed loop control in a pure probabilistic framework. In this framework, a system is a controlled Markov chain whose transition probabilities depend on the actions of the agents. The agents are also described in a probabilistic way. The objective is to drive the system so that the joint state and agents actions are close to a set of given target probability distributions. The Kullback-Leibler divergence is used as a performance measure. The resulting algorithm uses dynamic programming interleaved with an iterative process that computes the behavior of each agent

A Hierarchical Game-Theoretic Decision-Making for Cooperative Multi-Agent Systems Under the Presence of Adversarial Agents

Underlying relationships among Multi-Agent Systems (MAS) in hazardous scenarios can be represented as Game-theoretic models. This paper proposes a new hierarchical network-based model called Game-theoretic Utility Tree (GUT), which decomposes high-level strategies into executable low-level actions for cooperative MAS decisions. It combines with a new payoff measure based on agent needs for real-time strategy games. We present an Explore game domain, where we measure the performance of MAS achieving tasks from the perspective of balancing the success probability and system costs. We evaluate the GUT approach against state-of-the-art methods that greedily rely on rewards of the composite actions. Conclusive results on extensive numerical simulations indicate that GUT can organize more complex relationships among MAS cooperation, helping the group achieve challenging tasks with lower costs and higher winning rates. Furthermore, we demonstrated the applicability of the GUT using the simulator-hardware testbed - Robotarium. The performances verified the effectiveness of the GUT in the real robot application and validated that the GUT could effectively organize MAS cooperation strategies, helping the group with fewer advantages achieve higher performance.Comment: This paper is accepted by the ACM Symposium on Applied Computing (SAC) 2023 Technical Track on Intelligent Robotics and Multi-Agent Systems (IRMAS