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|
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- 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.
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- Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997.
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