The shapley value in knapsack budgeted games

Smriti Bhagat, Udi Weinsberg, Anthony Kim, Shanmugavelayutham Muthukrishnan

    Research output: Contribution to journalArticle

    Abstract

     We propose the study of computing the Shapley value for a new class of cooperative games that we call budgeted games, and investigate in particular knapsack budgeted games, a version modeled after the classical knapsack problem. In these games, the “value” of a set S of agents is determined only by a critical subset T ⊆ S of the agents and not the entirety of S due to a budget constraint that limits how large T can be. We show that the Shapley value can be computed in time faster than by the naィıve exponential time algorithm when there are sufficiently many agents, and also provide an algorithm that approximates the Shapley value within an additive error. For a related budgeted game associated with a greedy heuristic, we show that the Shapley value can be computed in pseudo-polynomial time. Furthermore, we generalize our proof techniques and propose what we term algorithmic representation framework that captures a broad class of cooperative games with the property of efficient computation of the Shapley value. The main idea is that the problem of determining the efficient computation can be reduced to that of finding an alternative representation of the games and an associated algorithm for computing the underlying value function with small time and space complexities in the representation size.

    Original languageEnglish (US)
    Pages (from-to)106-119
    Number of pages14
    JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume8877
    StatePublished - Jan 1 2014

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    Shapley Value
    Knapsack
    Game
    Cooperative Game
    Greedy Heuristics
    Budget Constraint
    Polynomials
    Approximate Algorithm
    Computing
    Space Complexity
    Exponential time
    Knapsack Problem
    Value Function
    Time Complexity
    Polynomial time
    Generalise
    Subset
    Alternatives
    Term

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    The shapley value in knapsack budgeted games. / Bhagat, Smriti; Weinsberg, Udi; Kim, Anthony; Muthukrishnan, Shanmugavelayutham.

    In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 8877, 01.01.2014, p. 106-119.

    Research output: Contribution to journalArticle

    Bhagat, Smriti ; Weinsberg, Udi ; Kim, Anthony ; Muthukrishnan, Shanmugavelayutham. / The shapley value in knapsack budgeted games. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 2014 ; Vol. 8877. pp. 106-119.
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