Strictly Proper Mechanisms with Cooperating Players
Author: Sang In Chun
Publisher: Stanford University
Published: 2011
Total Pages: 94
ISBN-13:
DOWNLOAD EBOOKIn order to obtain accurate information about the uncertainty in a decision situation, a decision maker may rely on the judgment of experts to obtain useful probabilistic forecasts. Strictly proper scoring rules have been shown to incentivize forecasters to provide truthful probabilistic forecasts and can be interpreted as a contract between a decision maker and a risk neutral forecaster rewarding greater expertise as well as truthful revelation. In recent years, prediction markets have been created to provide an efficient means to assess uncertain quantities from forecasters, and strictly proper scoring rules have been proposed for prediction markets, where the payment depends on the forecaster's score relative to others. However, we show that when those players can cooperate, these mechanisms can instead discourage them from reporting what they really believe. When players with different beliefs are able to cooperate and form a coalition, these mechanisms admit arbitrage and there is a report that will always pay coalition members more than their truthful forecasts. If the coalition were created by an intermediary, such as a web portal, the intermediary would be guaranteed a profit from this risk free surplus. Specifically, for the three most commonly used strictly proper scoring rules, we provide a cooperative report for coalition members and show the magnitude of the surplus from cooperation with numerical examples. We analyze the optimal behavior of coalition members within a coalition. Given a choice whether to participate in any coalition, players should participate. We show conditions under which coalition members should invite new members. We evaluate the optimal strategy of each coalition member under a set of simple assumptions including a quadratic scoring rule, and show that honest revelation within the coalition is a Bayesian Nash equilibrium. We show the consequence of players' cooperation to the decision maker receiving aggregated probabilities, and conclude with open challenges in the design and understanding of strictly proper mechanisms.
