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

Dean P. Foster and Sergiu Hart

Games and Economic Behavior, 2018, vol. 109, issue C, 271-293

Abstract: 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).

Keywords: Calibration; Nash dynamics; Fixed points; Deterministic calibration; Smooth calibration; Finite recall (search for similar items in EconPapers)
JEL-codes: C1 C7 D8 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Related works:
Working Paper: Smooth Calibration, Leaky Forecasts, Finite Recall, and Nash Dynamics (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:109:y:2018:i:c:p:271-293

DOI: 10.1016/j.geb.2017.12.022

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