Boolean Games: Inferring Agents' Goals Using Taxation Queries

IJCAI 2020, pp. 1585-1591, 2020.

Cited by: 0|Bibtex|Views40|DOI:https://doi.org/10.24963/ijcai.2020/220
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When there is an Nash Equilibrium for a {0,1}-taxation query, we show that the value of the goals of selected agents for the zero cost assignment can be determined regardless of which Nash Equilibrium is reached by the agents

Abstract:

In Boolean games, each agent controls a set of Boolean variables and has a goal represented by a propositional formula. We study inference problems 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...More

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Introduction
Highlights
  • Boolean games [Harrenstein et al, 2001] are a class of games where agents’ goals are represented by a propositional logic formula
  • When there is an Nash Equilibrium for a {0,1}-taxation query, we show that the value of the goals of selected agents for the zero cost assignment can be determined regardless of which Nash Equilibrium is reached by the agents (Section 3)
  • We show experimentally that our coloring-based inference algorithm uses significantly fewer queries compared to inferring goals one at a time
  • We show that goal inference is possible in a context where the response to a query only provides the values assigned to the variables and not whether agents achieved their goals
  • Our algorithms reduce the number of taxation queries by querying many agents simultaneously
  • We ran an extensive set of experiments creating a large number of networks and agents’ goals by varying the number of nodes, the minimum degree, the number of variables in an agent’s goal controlled by the agent and by others and the threshold
Results
  • The authors show experimentally that the coloring-based inference algorithm uses significantly fewer queries compared to inferring goals one at a time.
  • The coloring-based approach uses significantly less time even for games with 36,000 agents (Section 5).
  • The authors use SEQ to denote the querying algorithm that infers goals one node at a time and CBQ to denote the coloring-based querying algorithm.
  • Nodes represent agents and the network itself represents the goal overlap graph
  • The authors ensured this by creating for each edge {u, v}, a variable xu,v that appears only in the goals of u and v.
  • The authors generated a random threshold value in the range [1 .. |Γi|]
Conclusion
  • Necessary and sufficient conditions for the existence of an NE for a taxation query.
  • Using an undirected graph that captures the overlaps between the sets of variables used in agents’ goals, the authors establish necessary and sufficient conditions for the existence of an NE for a Boolean game and any {0,1}-taxation query, i.e., a query with only 0 and 1 costs (Section 3).
Summary
  • Introduction:

    Boolean games [Harrenstein et al, 2001] are a class of games where agents’ goals are represented by a propositional logic formula.
  • Each agent i controls a distinct set of Boolean variables Φi, and there is a cost associated with each assignment.
  • Much of the work on Boolean games is of theoretical nature [Harrenstein et al, 2001; Sauro and Villata, 2013; Wooldridge et al, 2013; Grant et al, 2014; Agotnes et al, 2013; Bonzon et al, 2007; Levit et al, 2013b].
  • Boolean games have been used to model some real-world problems such as charging electric vehicles and traffic signalling [Levit et al, 2013b]
  • Results:

    The authors show experimentally that the coloring-based inference algorithm uses significantly fewer queries compared to inferring goals one at a time.
  • The coloring-based approach uses significantly less time even for games with 36,000 agents (Section 5).
  • The authors use SEQ to denote the querying algorithm that infers goals one node at a time and CBQ to denote the coloring-based querying algorithm.
  • Nodes represent agents and the network itself represents the goal overlap graph
  • The authors ensured this by creating for each edge {u, v}, a variable xu,v that appears only in the goals of u and v.
  • The authors generated a random threshold value in the range [1 .. |Γi|]
  • Conclusion:

    Necessary and sufficient conditions for the existence of an NE for a taxation query.
  • Using an undirected graph that captures the overlaps between the sets of variables used in agents’ goals, the authors establish necessary and sufficient conditions for the existence of an NE for a Boolean game and any {0,1}-taxation query, i.e., a query with only 0 and 1 costs (Section 3).
Tables
  • Table1: A game without a NE for some taxation schemes
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Related work
  • Harrenstein et al [2001] introduced Boolean games as a class of two-player games and Bonzon et al [2007] generalized the framework to n players. Structural and computational properties of PNE in Boolean games are well-studied. Bonzon et al [2007] define a “dependency graph” between players to characterize PNE in Boolean games, much like our goal overlap graph. Levit et al [2019; 2013b] study methods for finding a taxation scheme that incentivizes the agents to reach a stable state. Also, Levit et al [2013a] discuss an application of Boolean games to the charging of electric vehicles where some vehicles are not allowed to charge at certain time intervals to avoid overloading. This is similar to our notion of the PRINCIPAL inhibiting agents. Boolean games where players have incomplete information about each other’s goals have also been considered in the literature (e.g., [Clercq et al, 2015; Agotnes et al, 2013]).
Funding
  • This work was partially supported by NSF Grants ACI-1443054 (DIBBS), IIS-1633028 (BIG DATA), CMMI-1745207 (EAGER), OAC-1916805, IIS-1908530 and by the Ministry of Science & Technology, Israel and the Ministry of Education, Science, Research and Sport of the Slovak Republic
Reference
  • [Abasi et al., 2014] Hasan Abasi, Nader H. Bshouty, and Hanna Mazzawi. On exact learning monotone DNF from membership queries. CoRR, abs/1405.0792:1–16, 2014.
    Findings
  • [Adiga et al., 2018] Abhijin Adiga, Chris J. Kuhlman, Madhav V. Marathe, S. S. Ravi, Daniel J. Rosenkrantz, and Richard E. Stearns. Learning the behavior of a dynamical system via a “20 questions” approach. In Thirty second AAAI Conference on Artificial Intelligence, pages 4630– 4637, Palo Alto, CA, 2018. AAAI Press.
    Google ScholarLocate open access versionFindings
  • [Adiga et al., 2020] Abhijin Adiga, Sarit Kraus, Oleg Maksimov, and S. S. Ravi. Boolean Games: Inferring Agents’s Goals Using Taxation Queries. Tech Report, Biocomplexity Insitute and Initiative, University of Virginia, Charlottesville, VA, USA, 2020.
    Google ScholarFindings
  • [Agotnes et al., 2013] Thomas Agotnes, Paul Harrenstein, Wiebe Van Der Hoek, and Michael Wooldridge. Verifiable equilibria in Boolean games. In Proc. of AAAI, pages 689–695, 2013.
    Google ScholarLocate open access versionFindings
  • [Angluin and Slonim, 1994] Dana Angluin and Donna K. Slonim. Randomly fallible teachers: Learning monotone DNF with an incomplete membership oracle. Machine Learning, 14(1):7–26, 1994.
    Google ScholarLocate open access versionFindings
  • [Bonzon et al., 2007] Elise Bonzon, Marie-Christine Lagasquie-Schiex, and Jerome Lang. Dependencies between players in Boolean games. In European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, pages 743–754, Hidelberg, Germany, 2007. Springer.
    Google ScholarLocate open access versionFindings
  • [Clercq et al., 2015] Sophie De Clercq, Steven Schockaert, Ann Nowe, and Martine De Cock. Multilateral negotiation in Boolean games with incomplete information using generalized possibilistic logic. In Twenty-Fourth International Joint Conference on Artificial Intelligence, pages 2890–2896, Palo Alto, CA, 2015. AAAI Press.
    Google ScholarLocate open access versionFindings
  • [Crama and Hammer, 2011] Yves Crama and Peter L. Hammer. Boolean Functions: Theory, Algorithms, and Applications. Cambridge University Press, New York, NY, 2011.
    Google ScholarFindings
  • [Garey and Johnson, 1979] Michael R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-completeness. W. H. Freeman and Co., San Francisco, CA, 1979.
    Google ScholarFindings
  • [Grant et al., 2014] John Grant, Sarit Kraus, Michael Wooldridge, and Inon Zuckerman. Manipulating games by sharing information. Studia Logica, 102(2):267–295, 2014.
    Google ScholarLocate open access versionFindings
  • [Harrenstein et al., 2001] Paul Harrenstein, Wiebe van der Hoek, John-Jules Meyer, and Cees Witteveen. Boolean games. In Proceedings of the 8th conference on Theoretical aspects of rationality and knowledge, pages 287–298, Burlington, MA, 2001. Morgan Kaufmann Publishers Inc.
    Google ScholarLocate open access versionFindings
  • [He et al., 2016] Xinran He, Ke Xu, David Kempe, and Yan Liu. Learning influence functions from incomplete observations. In Advances in Neural Information Processing
    Google ScholarLocate open access versionFindings
  • Systems, pages 2073–2081, San Diego, CA, 2016. Neural Information Systems Processing Foundation.
    Google ScholarLocate open access versionFindings
  • [Kleinberg et al., 2017] Jon Kleinberg, Sendhil Mullainathan, and Johan Ugander. Comparison-based choices. In Proceedings of the 2017 ACM Conference on Economics and Computation, pages 127–144, New York, NY, 2017. ACM.
    Google ScholarLocate open access versionFindings
  • [Kohavi, 1970] Zvi Kohavi. Switching and Finite Automata Theory. McGraw-Hill, New York, NY, 1970.
    Google ScholarFindings
  • [Levit et al., 2013a] Vadim Levit, Tal Grinshpoun, and Amnon Meisels. Boolean games for charging electric vehicles. In Proceedings of the 2013 IEEE/WIC/ACM International Joint Conferences on Web Intelligence (WI) and Intelligent Agent Technologies (IAT)-Volume 02, pages 86–93. IEEE Computer Society, 2013.
    Google ScholarLocate open access versionFindings
  • [Levit et al., 2013b] Vadim Levit, Tal Grinshpoun, Amnon Meisels, and Ana LC Bazzan. Taxation search in Boolean games. In Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems, pages 183–190, Richland, SC, USA, 2013. International Foundation for Autonomous Agents and Multiagent Systems.
    Google ScholarLocate open access versionFindings
  • [Levit et al., 2019] Vadim Levit, Zohar Komarovsky, Tal Grinshpoun, Ana LC Bazzan, and Amnon Meisels. Incentive-based search for equilibria in Boolean games. Constraints, 24:288–319, 2019.
    Google ScholarLocate open access versionFindings
  • [Narasimhan et al., 2015] Harikrishna
    Google ScholarFindings
  • Processing Systems, pages 3186–3194, San Diego, CA, 2015. Neural Information Systems Processing Foundation.
    Google ScholarLocate open access versionFindings
  • [Sauro and Villata, 2013] Luigi Sauro and Serena Villata. Dependency in cooperative Boolean games. Journal of Logic and Computation, 23(2):425–444, 2013.
    Google ScholarLocate open access versionFindings
  • [West, 2003] Douglas West. Introduction to Graph Theory. Prentice-Hall, Inc., Englewood Cliffs, NJ, 2003.
    Google ScholarFindings
  • [Wooldridge et al., 2013] Michael Wooldridge, Ulle Endriss, Sarit Kraus, and Jerome Lang. Incentive engineering for Boolean games. Artificial Intelligence, 195:418–439, 2013.
    Google ScholarLocate open access versionFindings
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