In Boolean games, each agent controls a set of Boolean variables and has a goal represented by a propositional formula. We initiate a study of inference in Boolean games assuming the presence of a Principal who has the ability to control the agents and impose taxation schemes. Previous work used taxation schemes to guide a game towards certain equilibria. We show how taxation schemes can also be used to infer agents' goals. In our formulation, agents' goals are assumed to be unknown and the objective of the Principal is to infer the goals of all the agents using appropriate taxation queries. Using an undirected graph (called the goal overlap graph) associated with a Boolean game, we establish necessary and sufficient conditions for the existence of a Nash equilibrium for any taxation query. Using these conditions, we develop an algorithm that uses taxation queries to learn agents' goals. Using a valid node coloring of the goal overlap graph, we show that goals of many agents can be inferred simultaneously. We also present more efficient (in terms of number of queries) goal inference algorithms for two special classes of Boolean functions, namely threshold and symmetric functions.
|Title of host publication||Proceedings of the 19th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2020|
|Editors||Bo An, Amal El Fallah Seghrouchni, Gita Sukthankar|
|Publisher||International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)|
|Number of pages||3|
|State||Published - 2020|
|Event||19th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2020 - Virtual, Auckland, New Zealand|
Duration: 19 May 2020 → …
|Name||Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS|
|Conference||19th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2020|
|Period||19/05/20 → …|
Bibliographical noteFunding Information:
We presented upper bounds on the number of taxation queries used for inference. It is of interest to develop appropriate lower bounds. Our work uses representation-dependent learning; in that setting, if a goal function is from a class C, then the inference algorithm must produce the correct function from that class. It is of interest to extend the results to the representation-independent setting where the learner may produce an equivalent function from another class. Finally, one can also study inference problems for other components of the Boolean game (e.g., control variables). Acknowledgments. We thank the AAMAS 2020 reviewers for their comments. This work was partially supported by NSF Grants ACI-1443054 (DIBBS), IIS-1633028 (BIG DATA), CMMI-1745207 (EAGER), IIS-1908530 and by the Ministry of Science & Technology, Israel and the Ministry of Education, Science, Research and Sport of the Slovak Republic.
© 2020 International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS). All rights reserved.
- Boolean games
- Goal inference
- Node coloring
- Taxation scheme