Probability Elicitation, Scoring Rules, and Competition Among Forecasters
研究预测者在评分规则下不仅关心得分，还关心相对表现时的行为，发现竞争性预测者会报告更极端的概率，并探讨了决策者如何修正这些偏差以及如何通过联合评分规则促进合作。
Probability forecasters who are rewarded via a proper scoring rule may care not only about the score, but also about their performance relative to other forecasters. We model this type of preference and show that a competitive forecaster who wants to do better than another forecaster typically should report more extreme probabilities, exaggerating toward zero or one. We consider a competitive forecaster's best response to truthful reporting and also investigate equilibrium reporting functions in the case where another forecaster also cares about relative performance. We show how a decision maker can revise probabilities of an event after receiving reported probabilities from competitive forecasters and note that the strategy of exaggerating probabilities can make well-calibrated forecasters (and a decision maker who takes their reported probabilities at face value) appear to be overconfident. However, a decision maker who adjusts appropriately for the misrepresentation of probabilities by one or more forecasters can still be well calibrated. Finally, to try to overcome the forecasters' competitive instincts and induce cooperative behavior, we develop the notion of joint scoring rules based on business sharing and show that these scoring rules are strictly proper.