A Geometric Proof of Calibration
We provide yet another proof of the existence of calibrated forecasters; it has two merits. First, it is valid for an arbitrary finite number of outcomes. Second, it is short and simple and it follows from a direct application of Blackwell's approachability theorem to carefully chosen vector-valued payoff function and convex target set. Our proof captures the essence of existing proofs based on approachability (e.g., the proof by Foster, 1999 in case of binary outcomes) and highlights the intrinsic connection between approachability and calibration.
|Date of creation:||17 Dec 2009|
|Date of revision:|
|Note:||View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00442042/en/|
|Contact details of provider:|| Web page: http://hal.archives-ouvertes.fr/|
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.:
- S. Hart & A. Mas-Collel, 2010.
"A Simple Adaptive Procedure Leading to Correlated Equilibrium,"
Levine's Working Paper Archive
572, David K. Levine.
- Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
- Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
- Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997.
- Chen, Xiaohong & White, Halbert, 1996. "Laws of Large Numbers for Hilbert Space-Valued Mixingales with Applications," Econometric Theory, Cambridge University Press, vol. 12(02), pages 284-304, June.
- Dean P Foster, 1997.
"A proof of Calibration via Blackwell's Approachability Theorem,"
Levine's Working Paper Archive
591, David K. Levine.
- Foster, Dean P., 1999. "A Proof of Calibration via Blackwell's Approachability Theorem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 73-78, October.
- Dean P. Foster, 1997. "A Proof of Calibration Via Blackwell's Approachability Theorem," Discussion Papers 1182, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Fudenberg, Drew & Levine, David K., 1999.
"An Easier Way to Calibrate,"
Games and Economic Behavior,
Elsevier, vol. 29(1-2), pages 131-137, October.
- Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.
When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00442042. 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: (CCSD)
If references are entirely missing, you can add them using this form.