Approximating the Core via Iterative Coalition Sampling

The core is a central solution concept in cooperative game theory, defined as the set of feasible allocations or payments such that no subset of agents has incentive to break away and form their own subgroup or coalition. However, it has long been known that the core (and approximations, such as the least-core) are hard to compute. This limits our ability to analyze cooperative games in general, and to fully embrace cooperative game theory contributions in domains such as explainable AI (XAI), where the core can complement the Shapley values to identify influential features or instances supporting predictions by black-box models. We propose novel iterative algorithms for computing variants of the core, which avoid the computational bottleneck of many other approaches; namely solving large linear programs. As such, they scale better to very large problems as we demonstrate across different classes of cooperative games, including weighted voting games, induced subgraph games, and marginal contribution networks. We also explore our algorithms in the context of XAI, providing further evidence of the power of the core for such applications. This work is licensed under a Creative Commons Attribution International 4. 0 License. Proc. of the 23rd International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2024), N. Alechina, V. Dignum, M. Dastani, J. S. Sichman (eds.), May 6 – 10, 2024, Auckland, New Zealand. © 2024 International Foundation for Autonomous Agents and Multiagent Systems (www. ifaamas. org).

Authors

• Ian Gemp Google DeepMind
• Marc Lanctot Google DeepMind
• Luke Marris Google DeepMind
• Yiran Mao
• Edgar Duéñez-Guzmán Google DeepMind
• Sarah Perrin
• Andras Gyorgy
• Romuald Elie
• Georgios Piliouras
• Michael Kaisers Google DeepMind
• Daniel Hennes Google DeepMind
• Kalesha Bullard Google DeepMind
• Kate Larson University of Waterloo
• Yoram Bachrach Meta FAIR

Keywords

• Cooperative Game Theory
• Core
• Explainable AI