On the equivalence of large individualized and distributionalized games
2017; Econometric Society; Volume: 12; Issue: 2 Linguagem: Inglês
10.3982/te1806
ISSN1933-6837
AutoresM. Ali Khan, Kali P. Rath, Haomiao Yu, Yongchao Zhang,
Tópico(s)Evolutionary Game Theory and Cooperation
ResumoTheoretical EconomicsVolume 12, Issue 2 p. 533-554 Original ArticlesOpen Access On the equivalence of large individualized and distributionalized games Mohammed Ali Khan, Mohammed Ali Khan akhan@jhu.edu Department of Economics, Johns Hopkins UniversitySearch for more papers by this authorKali P. Rath, Kali P. Rath rath.1@nd.edu Department of Economics, University of Notre DameSearch for more papers by this authorHaomiao Yu, Haomiao Yu haomiao@ryerson.ca Department of Economics, Ryerson UniversitySearch for more papers by this authorYongchao Zhang, Yongchao Zhang zyongao@gmail.com School of Economics, Shanghai University of Finance and Economics Some of the results reported here were presented at the IMS Workshop on Probabilistic Impulse in Modern Economic Theory at the National University of Singapore, January 11–18, 2011, at the 13th Conference of the Society for the Advancement of Economic Theory at MINES Paris Tech, July 22–26, 2013, and at the AMES, Singapore, August 2–4, 2013. The authors thank Hülya Eraslan, Kevin Reffet, Larry Samuelson, Xiang Sun, Yeneng Sun, Metin Uyanik, and Rajiv Vohra for stimulating conversation and/or correspondence. They are also indebted to the co-editor and an anonymous referee for their comments that led to this extensively revised version of the original submission. An earlier version was completed when Khan was a Visiting Research Fellow at the Australian National University, February 15–April 15, 2016. Yu's research is supported by SHHRC IDG (430-2014-00007); Zhang's research is supported by NSFC (11201283). Search for more papers by this author Mohammed Ali Khan, Mohammed Ali Khan akhan@jhu.edu Department of Economics, Johns Hopkins UniversitySearch for more papers by this authorKali P. Rath, Kali P. Rath rath.1@nd.edu Department of Economics, University of Notre DameSearch for more papers by this authorHaomiao Yu, Haomiao Yu haomiao@ryerson.ca Department of Economics, Ryerson UniversitySearch for more papers by this authorYongchao Zhang, Yongchao Zhang zyongao@gmail.com School of Economics, Shanghai University of Finance and Economics Some of the results reported here were presented at the IMS Workshop on Probabilistic Impulse in Modern Economic Theory at the National University of Singapore, January 11–18, 2011, at the 13th Conference of the Society for the Advancement of Economic Theory at MINES Paris Tech, July 22–26, 2013, and at the AMES, Singapore, August 2–4, 2013. The authors thank Hülya Eraslan, Kevin Reffet, Larry Samuelson, Xiang Sun, Yeneng Sun, Metin Uyanik, and Rajiv Vohra for stimulating conversation and/or correspondence. They are also indebted to the co-editor and an anonymous referee for their comments that led to this extensively revised version of the original submission. An earlier version was completed when Khan was a Visiting Research Fellow at the Australian National University, February 15–April 15, 2016. Yu's research is supported by SHHRC IDG (430-2014-00007); Zhang's research is supported by NSFC (11201283). Search for more papers by this author First published: 26 May 2017 https://doi.org/10.3982/TE1806Citations: 3 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The theory of large one-shot simultaneous-play games with a biosocial typology has been presented in both the individualized and distributionalized forms—large individualized games (LIG) and large distributionalized games (LDG), respectively. Using an example of an LDG with two actions and a single trait in which some Nash equilibrium distributions cannot be induced by the Nash equilibria of the representing LIG, this paper offers three equivalence results that delineate a relationship between the two game forms. Our analysis also reveals the different roles that the Lebesgue unit interval and a saturated space play in the theory. References 1 Aliprantis, Charalambos D. and Kim C. Border (2006), Infinite Dimensional Analysis: A Hitchhiker's Guide, thirdedition. Springer, Berlin. 10.1007/978-3-662-03961-8 1 Balbus, Lukasz, Pawel Dziewulski, Kevin Reffett, and Lukasz Woźny (2015), “Differential information in large games with strategic complementarities.” Economic Theory, 59, 201– 243. 10.1007/s00199-014-0827-x 1 Bergemann, Dirk and Stephen Morris (2013), “Robust predictions in games with incomplete information.” Econometrica, 81, 1251– 1308. 10.3982/ECTA11105 1 Bergin, James (1992), “Player type distributions as state variables and information revelation in zero sum repeated games with discounting.” Mathematics of Operations Research, 17, 640– 656. 1 Bergin, James and Dan Bernhardt (1992), “Anonymous sequential games with aggregate uncertainty.” Journal of Mathematical Economics, 21, 543– 562. 10.1016/0304-4068(92)90026-4 1 Bergin, James and Dan Bernhardt (1995), “Anonymous sequential games: Existence and characterization of equilibria.” Economic Theory, 5, 461– 489. 10.1007/BF01212329 1 Bogachev, Vladimir I. (2007), Measure Theory, Vol. II. Springer-Verlag, Berlin. 10.1007/978-3-540-34514-5 1 Carmona, Guilherme (2008), “Large games with countable characteristics.” Journal of Mathematical Economics, 44, 344– 347. 1 Carmona, Guilherme and Konrad Podczeck (2009), “On the existence of pure-strategy equilibria in large games.” Journal of Economic Theory, 144, 1300– 1319. 10.1016/j.jet.2008.11.009 1 Fu, Haifeng and Haomiao Yu (2015), “Pareto-undominated and socially-maximal equilibria in non-atomic games.” Journal of Mathematical Economics, 58, 7– 15. 10.1016/j.jmateco.2015.02.001 1 Guesnerie, Roger and Pedro Jara-Moroni (2011), “Expectational coordination in simple economic contexts.” Economic Theory, 47, 205– 246. 10.1007/s00199-010-0556-8 1 Hildenbrand, Werner (1974), Core and Equilibria of a Large Economy, volume 5 of Princeton Studies in Mathematical Economics. Princeton University Press, Princeton, New Jersey. 1 Jara-Moroni, Pedro (2012), “Rationalizability in games with a continuum of players.” Games and Economic Behavior, 75, 668– 684. 10.1016/j.geb.2012.03.004 1 Jovanovic, Boyan and Robert W. Rosenthal (1988), “Anonymous sequential games.” Journal of Mathematical Economics, 17, 77– 88. 10.1016/0304-4068(88)90029-8 1 Kalai, Ehud (2004), “Large robust games.” Econometrica, 72, 1631– 1665. 10.1111/j.1468-0262.2004.00549.x 1 Kalai, Ehud and Eran Shmaya (2013), “Compressed equilibrium in large repeated games of incomplete information.” Discussion Paper, Center for Mathematical Studies in Economics and Management Science 1562, Northwestern University. 1 Keisler, H. Jerome and Yeneng Sun (2009), “Why saturated probability spaces are necessary.” Advances in Mathematics, 221, 1584– 1607. 1 Khan, M. Ali, Kali P. Rath, and Yeneng Sun (1997), “On the existence of pure strategy equilibria in games with a continuum of players.” Journal of Economic Theory, 76, 13– 46. 1 Khan, M. Ali, Kali P. Rath, Yeneng Sun, and Haomiao Yu (2013a), “Large games with a bio-social typology.” Journal of Economic Theory, 148, 1122– 1149. 1 Khan, M. Ali, Kali P. Rath, Yeneng Sun, and Haomiao Yu (2015), “Strategic uncertainty and the ex-post Nash property in large games.” Theoretical Economics, 10, 103– 129. 1 Khan, M. Ali, Kali P. Rath, Haomiao Yu, and Yongchao Zhang (2013b), “Large distributional games with traits.” Economics Letters, 118, 502– 505. 10.1016/j.econlet.2012.12.029 1 Khan, M. Ali and Yeneng Sun (1995), “Extremal structures and symmetric equilibria with countable actions.” Journal of Mathematical Economics, 24, 239– 248. 1 Khan, M. Ali and Yeneng Sun (2002), “ Non-cooperative games with many players.” In Handbook of Game Theory With Economic Applications, Vol. 3 ( Robert J. Aumann and Sergiu Hart, eds.), 1761– 1808, Elsevier Science, Amsterdam. 1 Khan, M. Ali and Yongchao Zhang (2012), “Set-valued functions, Lebesgue extensions and saturated probability spaces.” Advances in Mathematics, 229, 1080– 1103. 1 Mas-Colell, Andreu (1984), “On a theorem of Schmeidler.” Journal of Mathematical Economics, 13, 201– 206. 10.1016/0304-4068(84)90029-6 1 Milgrom, Paul R. and Robert J. Weber (1985), “Distributional strategies for games with incomplete information.” Mathematics of Operations Research, 10, 619– 632. 1 Morris, Stephen and Hyun Song Shin (2003), “ Global games: Theory and applications.” In Advances in Economics and Econometrics Theory and Applications, Eighth World Congress ( Mathias Dewatripont, Lars Peter Hansen, and Stephen J. Turnovsky, eds.), 56– 114, Cambridge University Press, Cambridge. 1 Noguchi, Mitsunori (2009), “Existence of Nash equilibria in large games.” Journal of Mathematical Economics, 45, 168– 184. 1 Nogushi, Mitsunori and William R. Zame (2006), “Competitive markets with externalities.” Theoretical Economics, 1, 143– 166. 1 Parthasarathy, Kalyanapuram R. (1967), Probability Measures on Metric Spaces. Academic Press, New York. 1 Qiao, Lei and Haomiao Yu (2014), “On the space of players in idealized limit games.” Journal of Economic Theory, 153, 177– 190. 1 Qiao, Lei, Haomiao Yu, and Zhixiang Zhang (2016), “On the Nash equilibrium correspondence of a large game with traits: A complete characterization.” Games and Economic Behavior, 99, 89– 98. 1 Rath, Kali P. (1995), “Representation of finite action large games.” International Journal of Game Theory, 24, 23– 35. 1 Schmeidler, David (1973), “Equilibrium points of nonatomic games.” Journal of Statistical Physics, 7, 295– 300. 1 Sun, Yeneng (2006), “The exact law of large numbers via Fubini extension and characterization of insurable risks.” Journal of Economic Theory, 126, 31– 69. Citing Literature Volume12, Issue2May 2017Pages 533-554 ReferencesRelatedInformation
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