Large games and the law of large numbers
AbstractThis paper introduces discrete large games where the set of players is a countable dense 'grid' with a finitely additive distribution. In these games any function from player names to mixed actions is a legitimate strategy profile. No extraneous continuity or measurability conditions are assumed. Randomness can be modeled explicitly and an exact law of large numbers holds. Equilibria enjoy a strong purification property: every realization of every mixed strategy equilibrium is a pure strategy equilibrium almost surely. Every continuum-player game has a discrete large game representation that preserves the original payoffs, strategy profiles and equilibria. It is argued that strategy profiles in continuum-player games have an ambiguous meaning because measurability requirements force the smoothing out of individual variations. These variations have clear strategic meaning in finite-player games and can be expressed in discrete large games, but not when the set of players is the continuum.
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Bibliographic InfoArticle provided by Elsevier in its journal Games and Economic Behavior.
Volume (Year): 64 (2008)
Issue (Month): 1 (September)
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Web page: http://www.elsevier.com/locate/inca/622836
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- Ehud Kalai, 2004.
"Large Robust Games,"
Econometric Society, vol. 72(6), pages 1631-1665, November.
- Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
- Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
- Nabil I. Al-Najjar & Luca Anderlini & Leonardo Felli, 2003.
CESifo Working Paper Series
1092, CESifo Group Munich.
- Harald Uhlig, 2010.
"A Law of Large Numbers for Large Economies,"
Levine's Working Paper Archive
2070, David K. Levine.
- Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
- Al-Najjar, Nabil Ibraheem, 1995. "Decomposition and Characterization of Risk with a Continuum of Random Variables," Econometrica, Econometric Society, vol. 63(5), pages 1195-1224, September.
- Dubey, Pradeep & Shapley, Lloyd S., 1994. "Noncooperative general exchange with a continuum of traders: Two models," Journal of Mathematical Economics, Elsevier, vol. 23(3), pages 253-293, May.
- Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
- Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
- Al-Najjar, Nabil I., 2004. "Aggregation and the law of large numbers in large economies," Games and Economic Behavior, Elsevier, vol. 47(1), pages 1-35, April.
- Patrizia Berti & Michele Gori & Pietro Rigo, 2010.
"A note on the law of large numbers in economics,"
Quaderni di Dipartimento
131, University of Pavia, Department of Economics and Quantitative Methods.
- Rubinchik, Anna & Samaniego, Roberto M., .
"Demand For Contract Enforcement in A Barter Environment,"
WP2011/15, University of Haifa, Department of Economics, revised 06 Dec 2011.
- Anna Rubinchik & Roberto Samaniego, 2013. "Demand for contract enforcement in a barter environment," Social Choice and Welfare, Springer, vol. 41(1), pages 73-97, June.
- Carmona, Guilherme & Podczeckz, Konrad, 2008.
"On the Existence of Pure-Strategy Equilibria in Large Games,"
FEUNL Working Paper Series
wp531, Universidade Nova de Lisboa, Faculdade de Economia.
- Carmona, Guilherme & Podczeck, Konrad, 2009. "On the existence of pure-strategy equilibria in large games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1300-1319, May.
- Tolvanen, Juha & Soultanis, Elefterios, 2012. "A correction to “Large games and the law of large numbers” [Games Econom. Behav. 64 (2008) 1–34]," Games and Economic Behavior, Elsevier, vol. 76(1), pages 340-343.
- Hannu Salonen, 2010. "On the existence of Nash equilibria in large games," International Journal of Game Theory, Springer, vol. 39(3), pages 351-357, July.
- Yang, Jian, 2011. "Asymptotic interpretations for equilibria of nonatomic games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 491-499.
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