Purification and Independence
We show that concepts introduced by Aumann more than thirty years ago throw a new light on purification in games with extremely dispersed private information. We show that one can embed payoff-irrelevant randomization devices in the private information of players and use these randomization devices to implement mixed strategies as deterministic functions of the private information. This approach gives rise to very short, elementary, and intuitive proofs for a number of purification results that previously required sophisticated methods from functional analysis or nonstandard analysis. We use our methods to prove a general purification theorem for games with private information in which a player's payoffs can depend in arbitrary ways on events in the private information of other players and in which we allow for shared information in a general way.
|Date of creation:||Jul 2013|
|Date of revision:|
|Contact details of provider:|| Postal: Universitätsstraße 15, A - 6020 Innsbruck|
Web page: http://www.uibk.ac.at/fakultaeten/volkswirtschaft_und_statistik/index.html.en
More information through EDIRC
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.:
- Wang, Jianwei & Zhang, Yongchao, 2010.
"Purification, Saturation and the Exact Law of Large Numbers,"
22119, University Library of Munich, Germany.
- Jianwei Wang & Yongchao Zhang, 2012. "Purification, saturation and the exact law of large numbers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 527-545, August.
- Carmona, Guilherme & Podczeck, Konrad, 2013.
"Existence of Nash Equilibrium in games with a measure space of players and discontinuous payoff functions,"
44263, University Library of Munich, Germany.
- Carmona, Guilherme & Podczeck, Konrad, 2014. "Existence of Nash equilibrium in games with a measure space of players and discontinuous payoff functions," Journal of Economic Theory, Elsevier, vol. 152(C), pages 130-178.
- Khan, M. Ali & Rath, Kali P., 2009. "On games with incomplete information and the Dvoretsky-Wald-Wolfowitz theorem with countable partitions," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 830-837, December.
- Rustichini, Aldo, 1993. "Mixing on Function Spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 183-91, January.
- M. Khan & Kali Rath & Yeneng Sun, 2006. "The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 91-104, April.
- Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 1-22, October.
When requesting a correction, please mention this item's handle: RePEc:inn:wpaper:2013-18. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Janette Walde)
If references are entirely missing, you can add them using this form.