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Non-Atomic Games on Loeb Spaces

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  • M Ali Khan
  • Yeneng Sun

Abstract

In the setting of non-cooperative game theory strategic negligibility of individual agents or diffuseness of information has been modelled as a non-atomic measure space typically the unit interval endowed with Lebesgue measure However recent work has shown that with uncountable action sets as for example the unit interval there do not exist pure-strategy Nash equilibria in such non-atomic games In this brief announcement we show that there is a perfectly satisfactory existence theory for non-atomic games provided this non-atomicity is formulated on the basis of a particular class of measure spaces hyperfinite Loeb spaces We also emphasize other desirable properties of games on hyperfinite Loeb spaces and present a synthetic treatment embracing both large games as well as those with incomplete information

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Bibliographic Info

Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 374.

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Date of creation: Apr 1996
Date of revision: Aug 1996
Handle: RePEc:jhu:papers:374

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Cited by:
  1. Van Zandt, Timothy & Vives, Xavier, 2003. "Monotone Equilibria in Bayesian Games of Strategic Complementarities," CEPR Discussion Papers 4103, C.E.P.R. Discussion Papers.
  2. Fu, Haifeng & Xu, Ying & Zhang, Luyi, 2007. "Characterizing Pure-strategy Equilibria in Large Games," MPRA Paper 7514, University Library of Munich, Germany.
  3. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.
  4. Khan, M. Ali Khan, 2007. "Perfect Competition," MPRA Paper 2202, University Library of Munich, Germany.
  5. Khan, M. Ali & Zhang, Yongchao, 2014. "On the existence of pure-strategy equilibria in games with private information: A complete characterization," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 197-202.

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