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.
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- Drew Fudenberg & David K. Levine, 1996.
"An Easier Way to Calibrate,"
Levine's Working Paper Archive
2059, David K. Levine.
- 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, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
- Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997.
- S. Hart & A. Mas-Collel, 2010. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Levine's Working Paper Archive 572, David K. Levine.
- 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.
- 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.
- 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.
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