Decompositions and potentials for normal form games
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Sandholm, William H., 2009. "Large population potential games," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1710-1725, July.
- Slade, Margaret E, 1994.
"What Does an Oligopoly Maximize?,"
Journal of Industrial Economics,
Wiley Blackwell, vol. 42(1), pages 45-61, March.
- Slade, M.E., 1989. "What Does An Oligopoly Maximize?," G.R.E.Q.A.M. 89a14, Universite Aix-Marseille III.
- Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
- Sandholm, William H., 2007. "Pigouvian pricing and stochastic evolutionary implementation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 367-382, January.
- Ui, Takashi, 2000. "A Shapley Value Representation of Potential Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 121-135, April.
- Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
- William H. Sandholm, 2005. "Negative Externalities and Evolutionary Implementation," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 885-915.
- William H. Sandholm, 2002. "Evolutionary Implementation and Congestion Pricing," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 667-689.
- Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May. Full references (including those not matched with items on IDEAS)