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Decompositions and potentials for normal form games

  • Sandholm, William H.
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    We introduce a method of decomposing a -player normal form game into simultaneously-played component games, each distinguished by the set of "active" players whose choices influence payoffs. We then prove that a normal form game is a potential game if and only if in each of the component games, all active players have identical payoff functions, and that in this case, the sum of these shared payoff functions is the original game's potential function. We conclude by discussing algorithms for deciding whether a given normal form game is a potential game.

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    File URL: http://www.sciencedirect.com/science/article/B6WFW-4Y95V37-2/2/b380b8db1c8c0f917de11ca85329c63a
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    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 70 (2010)
    Issue (Month): 2 (November)
    Pages: 446-456

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    Handle: RePEc:eee:gamebe:v:70:y:2010:i:2:p:446-456
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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    1. Sandholm, William H, 2002. "Evolutionary Implementation and Congestion Pricing," Review of Economic Studies, Wiley Blackwell, vol. 69(3), pages 667-89, July.
    2. Slade, Margaret E, 1994. "What Does an Oligopoly Maximize?," Journal of Industrial Economics, Wiley Blackwell, vol. 42(1), pages 45-61, March.
    3. Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April.
    4. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    5. Sandholm, William H., 2009. "Large population potential games," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1710-1725, July.
    6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    7. William H. Sandholm, 2005. "Negative Externalities and Evolutionary Implementation," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 885-915.
    8. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    9. Sandholm, William H., 2007. "Pigouvian pricing and stochastic evolutionary implementation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 367-382, January.
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