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On Eliciting Beliefs in Strategic Games

Palfrey, Thomas R. and Wang, Stephanie W. (2007) On Eliciting Beliefs in Strategic Games. Social Science Working Paper, 1271R. California Institute of Technology , Pasadena, CA. (Unpublished)

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Several recent studies in experimental economics have tried to measure beliefs of subjects engaged in strategic games with other subjects. Using data from one such study (Nyarko-Schotter, 2002) we conduct an experiment where our experienced subjects observe early rounds of strategy choices from that study and are given monetary incentives to report forecasts of choices in later rounds. We elicit beliefs using three different scoring rules: linear, logarithmic, and quadratic. There are differences between the elicited beliefs under quadratic and logarithmic scoring rules in spite of both being proper scoring rules. The (improper) linear scoring rule frequently elicits boundary forecasts as theory predicts, and is poorly calibrated. We compare the forecasts of our trained observers to forecasts of the actual players in the Nyarko-Schotter experiment and identify several differences. There was a significant positive correlation between observer forecasts and the choice behavior in the game under both proper scoring rules, but no significant correlation between the players’ own forecasts and the actual play. This raises doubts about whether beliefs can be reliably elicited from players who simultaneously have a stake in the target of their forecast, in this case the opponent’s choice. The distribution of player forecasts also tended to be more extreme than the observer forecasts using either of the proper scoring rules. We also find evidence of belief convergence when beliefs are elicited iteratively from a group.

Item Type:Report or Paper (Working Paper)
Palfrey, Thomas R.0000-0003-0769-8109
Additional Information:Revised. Original dated to March 2007. We gratefully acknowledge the financial support of the National Science Foundation (SES-0079301, SES-0450712, SES-0094800), The Princeton Laboratory for Experimental Social Science, and the Social Science Experimental Laboratory at Caltech. We are grateful for comments from Juan Carrillo, audience members at the 2007 meeting of the Public Choice Society in Amsterdam, and participants at the 2007 conference at the University of Exeter on Risk, Forecast, and Decision.
Group:Social Science Working Papers
Funding AgencyGrant Number
Princeton Laboratory for Experimental Social Science (PLESS)UNSPECIFIED
Caltech Social Science Experimental LaboratoryUNSPECIFIED
Subject Keywords:Scoring rules; Experiment; Game theory; Forecasting; Beliefs
Series Name:Social Science Working Paper
Issue or Number:1271R
Record Number:CaltechAUTHORS:20171129-145253122
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83572
Deposited By: Jacquelyn Bussone
Deposited On:29 Nov 2017 23:40
Last Modified:22 Nov 2019 09:58

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