Smooth calibration, leaky forecasts, finite recall, and Nash dynamics

• 成果类型: Article
• 署名作者: Foster, Dean P.; Hart, Sergiu
• 署名单位: Amazon.com; University of Pennsylvania; Hebrew University of Jerusalem; Hebrew University of Jerusalem
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2017.12.022
• 发表日期: 2018
• 页码: 271-293
• 关键词: Calibration; Nash dynamics; Fixed points; Deterministic calibration; Smooth calibration; Finite recall

摘要

We propose to smooth out the calibration score, which measures how good a forecaster is, by combining nearby forecasts. While regular calibration can be guaranteed only by randomized forecasting procedures, we show that smooth calibration can be guaranteed by deterministic procedures. As a consequence, it does not matter if the forecasts are leaked, i.e., made known in advance: smooth calibration can nevertheless be guaranteed (while regular calibration cannot). Moreover, our procedure has finite recall, is stationary, and all forecasts lie on a finite grid. To construct the procedure, we deal also with the related setups of online linear regression and weak calibration. Finally, we show that smooth calibration yields uncoupled finite-memory dynamics in n-person games-smooth calibrated learning in which the players play approximate Nash equilibria in almost all periods (by contrast, calibrated learning, which uses regular calibration, yields only that the time averages of play are approximate correlated equilibria). (C) 2018 Elsevier Inc. All rights reserved.