實驗經濟學一：行為賽局論 Experimental Economics I: Behavioral Game Theory 第三講：經濟學實驗設計原理 Lecture 3: Basic Principles of Experimental Design 授課教師：國立臺灣大學 經濟學系 王道一教授（Joseph Tao-yi Wang ） 本課程指定教材: Colin E. Camerer, Behavioral Game Theory: Experiments in Strategic Interaction. New York: Russell Sage Foundation; New Jersey: Princeton UP, 2003. 【本著作除另有註明外，採取創用CC「姓名標示－非商業性－相同方式分享」臺灣3.0版授權釋出】

Define Economic Experiment 定義經濟學實驗 An Economic Experiment Constructs a controlled environment to observe how people make economic decisions under real incentives, to answer questions raised by the researcher, testing a hypothesis or which theory matches reality better 建構一個控制的環境，在有真實誘因的情況下，觀察人們如何做決定（經濟決策），為要回答研究者所提出的問題，檢驗哪個假說或理論比較符合現實。 Experimental Design

Define Economic Experiment 定義經濟學實驗 4 Components of a Controlled Environment Real Incentives: Choices have real consequences (真實後果或誘因) A Good Control Group (對照組的設計) Random Assignment (隨機分組) No deception (完全不欺騙受試者) Experimental Design

Principles of Experimental Design 實驗設計原理 Control, Measure, or Assume (控制,測量或假設) Instructions (實驗說明) Anonymity (匿名性) Matching Protocols & Reputation Building (配對方式與受試者信譽) Incentives (金錢誘因) Order Effects (不同實驗的先後次序) Controlling Risk Tastes (控制風險偏好) Within-Subject and Between-Subject Design (同一 vs. 不同受試者) Experimetrics (實驗計量) No Deception (不欺騙受試者) Experimental Design

Control, Measure or Assume 控制/測量/假設 Taking an action to affect a variable’s value (主動賦予該變因的參數值) “Induced” value theory (賦予參數理論) Measurement (測量) Measure the value of a variable (測量該變因的參數值) Via various methods (see below) (用下頁所列不同方法) Assumption (假設) Pseudo-control (直接假設該變因的參數值) Accept a maintain hypothesis about the value of a variable Experimental Design

Control, Measure or Assume 控制/測量/假設 Methods of Measurement (測量方法): Psychometric measures (surveys) (心理測驗/問卷) Risk-aversion measures (certainty equiv)(風險偏好) Probability judgments (scoring rules) (主觀機率判斷) Information acquisition (mouse/eye-tracking) 資訊取得：滑鼠追蹤或眼球追蹤 Psychophsiological measures (測量心理生理學上的反應) fMRI (功能性磁振造影), GSR (皮膚電阻反應), PDR (瞳孔放大反應), EEG (頭皮腦電波), etc. Experimental Design

Tell subjects what they need to know (目的：告知所需資訊) Instructions 實驗說明 Tell subjects what they need to know (目的：告知所需資訊) Public Knowledge (公共知識): Established by reading instructions out loud (來自公開朗讀說明) How much to reveal? (要告訴受試者多少？) Entire payoff structure (default) (原則上要完整告知報酬如何決定) Since we’re not sure what subjects would think about what they are not told (如果不揭露所有資訊，我們不知道他們會怎麼想) Withhold some information: Study how people/markets learn under limited information (不告知某些資訊：用以研究人們或市場如何在有限資訊下學習探索) Experimental Design

Use the anonymity case as a benchmark Who’s Who? Subject behavior can change knowing opponent’s identity due to 見面三分情？受試者的行為會因為知道對方是誰而改變，因為 Appearance, gender, (長相外貌、性別) Fear of retaliation, etc. (害怕被報復等等) Use the anonymity case as a benchmark (因此，我們通常用匿名實驗來當作基準實驗) Measure opponent characteristics (appearance) and compare to benchmark 要研究這些變因時，可以測量對方特質(例如長相多好看)，同時把它們顯示給受試者看，然後把實驗結果和基準實驗作比較 Experimental Design

Matching Protocol/Reputation 配對方式/信譽 Random matching (random switch) Empirically kills repeated game effects 隨機配對：每回合重新洗牌，實證上可除去重複賽局效果 Mean-matching (play with everyone) 與所有人配對：每個決定都跟其他每個人各配對一次 Other more strict matching protocols:(更嚴格配對方式) Non-repeat matching (meet only once) 不重複配對：整個實驗中只跟每個對手配對一次，所需實驗參與者人數的魔術數字是2的n次方，因為能做2n-1回合不重複配對 Non-contagion matching (no chain-of-influence) 不污染配對：整場沒有「我跟你配、你再跟他配，最後我遇到他」的情形 Experimental Design

Incentives 真實誘因 Hypothetical vs. Real Money Decisions This distinguishes economic and psychological experiments 假設性問題 vs.「玩真的」：經濟學實驗和心理學實驗一大分野 Assumption behind money payments: “Everybody likes having more money and nobody gets tired of having more of it.” 使用金錢報酬只需要一個行為假設：「每個人都喜歡獲得更多金錢，而且多多益善(沒有人會覺得拿太多了)」 Cost of deviation without real money is 0 只是假設性問題的話，亂講亂選沒有成本 Paying money reduces variation & outliers 故金錢報酬會降低亂選的噪音，減少極端的特例 Experimental Design

Pay Less vs. Pay More (付得少/多是否影響結果？) Incentives 真實誘因 Pay Less vs. Pay More (付得少/多是否影響結果？) Comparison studies not done often enough Expensive to double/triple the payments 目前有一些做這種比較的實驗，但還不夠多 因為要把報酬乘上兩倍、三倍很貴 Some experiments done in poor countries (不過仍有些實驗會特別到貧窮的國家去做) Vietnam (越南：試字率高、人民卻很窮、鮮少遷徙) Few results that disconfirm theory have been overturned by paying more money 這些少數重複實驗結果顯示：如果原本的實驗結果不支持理論預測，多付錢也大概不會讓實驗結果變得合乎理論的預測 Experimental Design

Flat Maximum Critique (「作什麼都沒差」) Incentives 真實誘因 Flat Maximum Critique (「作什麼都沒差」) Is it worthwhile (high stakes) to think hard? 想得深入一點到底值不值得？ (重賞之下必有勇夫？沒有勇夫表示賞金不夠？) EX: Costless to deviate from (1/3, 1/3, 1/3) in rock-paper-scissors (例如：「剪刀石頭布」不按照均衡策略(1/3, 1/3, 1/3)來做沒有損失，因為不管出什麼報酬都相同) No ideal solution yet… (尚未有很好的解決辦法，不過…) Design steep marginal incentives 可以設計得讓「邊際誘因」很高 Modest effect on high stakes anyway 高獎金對結果的影響雖不是0，但也沒那麼大 Experimental Design

Order Effects 不同實驗的先後次序 AB: A came first; B came second Is this why we see different behavior? AB即「先做實驗A，再做實驗B」 行為的改變是否只是因為先後次序不同？ Try BA and include order dummies in analysis 必須也做BA(次序反過來)，然後在資料分析的時候加上次序的虛擬變數(dummies)來檢驗是否有影響 What if ABC? ACB/BAC/BCA/CBA/CAB or simplify design 有ABC怎麼辦？ 做ACB/BAC/BCA/CBA/CAB或簡化實驗設計 Experimental Design

Control Risk Preferences 控制風險偏好 Binary Lottery Procedure: (發樂透彩券當報酬) Widely used to control risk preferences, but not much evidence that it works (控制風險偏好的常用辦法，但沒有太多證據顯示有效，且需假設人們能把複合樂透簡化為簡單樂透) Alternatives: (其他辦法) Assume risk neutrality (假設受試者是風險中立) Measure risk preferences (測量風險偏好) Holt and Laury (2002) or Tanaka et al. (2010) Choi, Fisman, Gale and Kariv (2007) Andreoni and Sprenger (2012a, b) Experimental Design

Within-subject vs. Between-subject 同一|不同 Within-subject Design (「比較同一受試者」的設計) Same subject observed in various treatments Pro: More statistically powerful Con: Possible demand effect 觀察同一受試者在不同實驗環境中的反應。優點：統計上解釋力強(可做paired t-test)；缺點：可能有「要求效果」 Between-subject Design (「比較不同受試者」的設計) Different subjects observed in each treatment Norm in experimental economics Con: “Impossible” for fMRI or eyetracking 觀察不同受試者在各自的實驗環境中的反應。實驗經濟學界一般的「標準做法」；缺點：幾乎不能做fMRI或眼球追蹤的實驗

Experimetrics 實驗計量 Econometrics customized for experiments Just like Econometrics is Statistics customized for economics 特別為實驗經濟學開發的計量方法，正如計量經濟學是特別為經濟學開發的統計方法 Bottom line: Use all econometrics feasible to get the most out of your (experimental) data (良心建議：請充分利用所有可能的計量工具來分析實驗資料) Experimental Design and Experimetrics are sometimes substitutes But complement each other in a good paper! 實驗設計和實驗計量有時可以互相替代，因為有好的設計，簡單的敘述統計可能就夠了。但兩者相輔相成能產生最好的論文 Experimental Design

List of Experimetrics 實驗計量方法列表 Mann-Whitney-Wilcoxon Test(s) vs. T-test Non-parametric test similar to (un-)paired t-test Regression (with random effects) Maximum Likelihood Estimations (最大概似估計) Level-k, Cognitive Hierarchy models Learning (學習理論): EWA, Reinforcement Quantal Response Equilibrium (手滑反應均衡) Simulate (模擬) and Estimate (估計) Out-of-sample Predictions (預測新的資料) Markov-switching (Eyetracking), SPM (fMRI) Experimetrics Signed Rank-sum test (non-parametric t-test) Regressions (with random effects) Maximum Likelihood Estimations Initial Responses: Level-k, Cognitive Hierarchy Learning: EWA, Reinforcement Quantal Response Equilibrium Simulate and Estimate Out-of-sample Predictions Markov Switching (Eyetracking) and SPM2 (fMRI) Experimental Design

No Deception 不欺騙受試者 Experimental Economists do not deceive their subjects (實驗經濟學家從不欺騙他們的受試者) This creates credibility (「徙木立信」) Makes monetary payments “real” (因而相信真的有金錢報酬) And avoids anticipation/strategic responses Differs from psychologists 避免預期會被騙時的鬥智反應 這和心理學家不同(他們只要事後有說明即可) Can achieve most goals with better design (except) How can we study the effect of deception? 所謂「需要欺騙的實驗」大部分都能設計另一個「不需欺騙的實驗」來達到同樣目的 (除了研究人們被實驗者欺騙時的反應)

Conclusion: The Gold Standards 設計十誡 Control, Measure, or Assume (控制,測量或假設) Instructions (實驗說明) Anonymity (匿名性) Matching Protocols & Reputation Building (配對方式與受試者信譽) Incentives (金錢誘因) Order Effects (不同實驗的先後次序) Controlling Risk Tastes (控制風險偏好) Within-Subject and Between-Subject Design (同一 vs. 不同受試者) Experimetrics (實驗計量) No Deception (不欺騙受試者) Experimental Design

版權聲明版權聲明 頁碼 作品 版權標示 來源/作者 1-19 4、19 5 12 國立臺灣大學 經濟學系 王道一 教授 1.Conctrol…10. No Deception Colin E. Camerer, Behavioral Game Theory: Experiments in Strategic Interaction. New York: Russell Sage Foundation; New Jersey: Princeton UP, 2003. pp.34-42. 依據著作權法第46、52、65條合理使用 5 Induced Value Theory Vernon. L. Smith, “Experimental Economics: Induced Value Theory,” The American Economic Review, vol.66, No. 2 (May., 1976),pp. 275. 12 Flat Maximum Critique….modest effect on high stakes any way Colin E. Camerer, Behavioral Game Theory: Experiments in Strategic Interaction. New York: Russell Sage Foundation; New Jersey: Princeton UP, 2003 pp.39.