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Algorithms for the shapley and myerson values in graph-restricted games

Published: 05 May 2014 Publication History

Abstract

Graph-restricted games, first introduced by Myerson[20], model naturally-occurring scenarios where coordination between any two agents within a coalition is only possible if there is a communication channel(a path) between them. Two fundamental solution concepts that were proposed for such a game are the Shapley value and the Myerson value. While an algorithm has been proposed to compute the Shapley value in arbitrary graph-restricted games, no such general-purpose algorithm has yet been developed for the Myerson value.
Our aim in this paper is to develop a more efficient algorithm for computing the Shapley value, and to develop a general-purpose algorithm for computing the Myerson value, in graph-restricted games. Since the computation of either value involves visiting all connected induced subgraphs of the graph underlying the game, we start by developing an algorithm dedicated for this purpose, and show that it is faster that the fastest available one in the literature. This algorithm is then used as the cornerstone upon which we build two algorithms. The first is designed to compute the Shapley value, and is shown to be more efficient than the state of the art. The second is the first dedicated algorithm to compute the Myerson value in arbitrary graphs.

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  • (2019)Enumerating Connected Subgraphs and Computing the Myerson and Shapley Values in Graph-Restricted GamesACM Transactions on Intelligent Systems and Technology10.1145/323502610:2(1-25)Online publication date: 12-Jan-2019
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  1. Algorithms for the shapley and myerson values in graph-restricted games

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    Published In

    cover image ACM Other conferences
    AAMAS '14: Proceedings of the 2014 international conference on Autonomous agents and multi-agent systems
    May 2014
    1774 pages
    ISBN:9781450327381

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    • IFAAMAS

    In-Cooperation

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    International Foundation for Autonomous Agents and Multiagent Systems

    Richland, SC

    Publication History

    Published: 05 May 2014

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    Author Tags

    1. enumerating induced connected subgraphs
    2. myerson value
    3. shapley value
    4. terrorist networks

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    AAMAS '14 Paper Acceptance Rate 169 of 709 submissions, 24%;
    Overall Acceptance Rate 1,155 of 5,036 submissions, 23%

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    • (2024)Value is in the Eye of the Beholder: A Framework for an Equitable Graph Data EvaluationProceedings of the 2024 ACM Conference on Fairness, Accountability, and Transparency10.1145/3630106.3658919(467-479)Online publication date: 3-Jun-2024
    • (2019)Enumerating Connected Subgraphs and Computing the Myerson and Shapley Values in Graph-Restricted GamesACM Transactions on Intelligent Systems and Technology10.1145/323502610:2(1-25)Online publication date: 12-Jan-2019
    • (2018)Efficient computation of semivalues for game-theoretic network centralityJournal of Artificial Intelligence Research10.1613/jair.1.1123963:1(145-189)Online publication date: 1-Sep-2018
    • (2018)Axiomatic characterization of game-theoretic centralityJournal of Artificial Intelligence Research10.1613/jair.1.1120262:1(33-68)Online publication date: 1-May-2018
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    • (2017)Supermodular Games on Social NetworksProceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems10.5555/3091125.3091173(299-307)Online publication date: 8-May-2017
    • (2017)Algorithms for Graph-Constrained Coalition Formation in the Real WorldACM Transactions on Intelligent Systems and Technology10.1145/30409678:4(1-24)Online publication date: 24-Feb-2017
    • (2016)k-Coalitional Cooperative GamesProceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems10.5555/2936924.2936953(177-185)Online publication date: 9-May-2016
    • (2016)Attachment CentralityProceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems10.5555/2936924.2936952(168-176)Online publication date: 9-May-2016
    • (2015)A pseudo-polynomial algorithm for computing power indices in graph-restricted weighted voting gamesProceedings of the 24th International Conference on Artificial Intelligence10.5555/2832249.2832337(631-637)Online publication date: 25-Jul-2015
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