多期競賽中以「高風險」戰術求勝的理論與實驗

Abstract

本文提出一個理性模型來解釋在贏者全拿的多期競賽中，人們為何會使用違 反直覺的戰術，例如在籃球中的「長射」。此模型可合理解釋為何在共同基 金市場，職業運動，和高階主管卡位等激烈競爭中，領先和落後者皆存心使 用「高風險」的戰術以贏得最後勝利。由於此結論直接來自輸贏的機率，不 受參與者的風險偏好影響，因此，一般認為是「高風險」的戰術，其實不見 得跟參與者的風險偏好有關。接著我們用經濟學實驗來驗證這種即時公佈成 績的多期競賽，發現實驗結果在下列三方面皆與理論預測相符：第一：78% 的競爭者選擇和理論預測相同的戰術。第二：迴歸分析顯示：當理論預測人 們應使用「保守」（論件計酬）的戰術時，95%的受試者選擇與理論相符。 而當理論預測人們應使用「高風險」（長射）的戰術時，71%（81%當此為 優勢策略）的受試者行為與理論相符。即使控制受試者之能力、性別及風險 偏好後，此結果仍顯著不變。第三：受試者最終相對成績的分佈亦與理論預 測相符。此外，當參與者大幅領先、使得理論預測兩種戰術一樣好的時候， 男性與比較愛好風險的參與者更傾向選擇「高風險」的戰術。

We propose a rational model to explain the use of counter-intuitive tactics in dynamic (two-person) tournaments. The model predicts when and why both leaders and trailers sometimes intentionally take “risky” tactics in order to win the final victory in high incentive tournaments in the mutual fund market, professional sports, competition for executive positions and so on. We then conduct a controlled laboratory experiment on this dynamic tournament with interim performance feedback, and find results that coincide with theoretical predictions in the following three ways: First, players follow model prediction 78% of the time. Second, regression analysis shows that 95% of players follow prediction when theory suggests the “safe” (piece-rate) tactic, while when theory suggests the “risky” (long shot) scheme, trailers follow this prediction 74% (81% when it dominant) of the time, even after controlling for players’ ability, gender and risk attitude. Also, we find that gender and risk preferences play a role in leaders’ behavior when theory predicts indifference. Finally, the experimental distribution of final performance difference is also close to what theory predicts.