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題名 認知能力與認知階層 : 選美賽局的實驗分析
Cognitive Capacity and Cognitive Hierarchy: Experimental Evidence from Keynes`s Beauty Contest
作者 杜業榮
Ye-Rong Du
貢獻者 陳樹衡
Shu-Heng Chen
杜業榮
Ye-Rong Du
關鍵詞 選美賽局
智力
工作記憶
k層次思考
認知階層
強化學習
信念學習
經驗加權吸引力學習
Beauty contest experiment
Intelligence
Working memory capacity
Level-k reasoning
Cognitive hierarchies
Reinforcement learning
Belief learning
Experience-weighted attraction learning
日期 2012
上傳時間 2-Sep-2013 17:19:22 (UTC+8)
摘要 晚近行為實驗的發展, 特別是在賽局實驗的研究中, 認知所扮演的角色漸受重視。認知階層與認知能力, 是文獻上兩個相關並且廣被討論的概念。 雖然這兩者往往出現在同樣的實驗中, 但仍少有研究正式地探討兩者之間的關係。 在本研究中, 我們透過15至20人為一組的重複選美賽局觀察受試者的認知階層, 並以工作記憶測驗測量其認知能力, 試圖檢驗認知能力對於認知階層的影響。 總的來說, 我們發現認知能力對於認知階層有正向的影響, 即認知能力較高的受試者, 所觀察到的認知階層也較高。 在最初幾個回合中, 認知能力的影響顯著。 接下來的回合中雖然效果漸弱, 但並不會完全消失。 這意謂著認知能力可能進一步影響其學習行為, 因此透過認知階層的馬可夫轉移動態與經驗加權吸引力學習模型, 我們檢驗此一可能性。 證據顯示認知能力不同反映學習行為的差異, 尤其相較於強化學習, 認知能力較高的受試者可能更傾向信念學習。
Recent developments in behavioral experiments, in particular game experiments, have placed human cognition in a pivotal place. Two related ideas are proposed and are popularly used in the literature, namely, cognitive hierarchy and cognitive capacity. While these two often meet in the same set of experiments and observations, few studies have formally addressed their relationship. In this study, based on six series of 15- to 20-person beauty contest experiments and the associated working memory tests, we examine the effect of cognitive capacity on the observed cognitive hierarchy. It is found that cognitive capacity has a positive effect on the observed cognitive hierarchy. This effect is strong in the initial rounds, and may become weaker, but without disappearing, in subsequent rounds, which suggests the possibility that cognitive capacity may further impact learning. We examine this possibility using the Markov transition dynamics of cognitive hierarchy and experience-weighted attraction learning. There is evidence to show that subjects with different cognitive capacities may learn differently, which may cause strong convergence to be difficult to observe.
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描述 博士
國立政治大學
經濟學系
94258502
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0942585021
資料類型 thesis
dc.contributor.advisor 陳樹衡zh_TW
dc.contributor.advisor Shu-Heng Chenen_US
dc.contributor.author (Authors) 杜業榮zh_TW
dc.contributor.author (Authors) Ye-Rong Duen_US
dc.creator (作者) 杜業榮zh_TW
dc.creator (作者) Ye-Rong Duen_US
dc.date (日期) 2012en_US
dc.date.accessioned 2-Sep-2013 17:19:22 (UTC+8)-
dc.date.available 2-Sep-2013 17:19:22 (UTC+8)-
dc.date.issued (上傳時間) 2-Sep-2013 17:19:22 (UTC+8)-
dc.identifier (Other Identifiers) G0942585021en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/59520-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 經濟學系zh_TW
dc.description (描述) 94258502zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 晚近行為實驗的發展, 特別是在賽局實驗的研究中, 認知所扮演的角色漸受重視。認知階層與認知能力, 是文獻上兩個相關並且廣被討論的概念。 雖然這兩者往往出現在同樣的實驗中, 但仍少有研究正式地探討兩者之間的關係。 在本研究中, 我們透過15至20人為一組的重複選美賽局觀察受試者的認知階層, 並以工作記憶測驗測量其認知能力, 試圖檢驗認知能力對於認知階層的影響。 總的來說, 我們發現認知能力對於認知階層有正向的影響, 即認知能力較高的受試者, 所觀察到的認知階層也較高。 在最初幾個回合中, 認知能力的影響顯著。 接下來的回合中雖然效果漸弱, 但並不會完全消失。 這意謂著認知能力可能進一步影響其學習行為, 因此透過認知階層的馬可夫轉移動態與經驗加權吸引力學習模型, 我們檢驗此一可能性。 證據顯示認知能力不同反映學習行為的差異, 尤其相較於強化學習, 認知能力較高的受試者可能更傾向信念學習。zh_TW
dc.description.abstract (摘要) Recent developments in behavioral experiments, in particular game experiments, have placed human cognition in a pivotal place. Two related ideas are proposed and are popularly used in the literature, namely, cognitive hierarchy and cognitive capacity. While these two often meet in the same set of experiments and observations, few studies have formally addressed their relationship. In this study, based on six series of 15- to 20-person beauty contest experiments and the associated working memory tests, we examine the effect of cognitive capacity on the observed cognitive hierarchy. It is found that cognitive capacity has a positive effect on the observed cognitive hierarchy. This effect is strong in the initial rounds, and may become weaker, but without disappearing, in subsequent rounds, which suggests the possibility that cognitive capacity may further impact learning. We examine this possibility using the Markov transition dynamics of cognitive hierarchy and experience-weighted attraction learning. There is evidence to show that subjects with different cognitive capacities may learn differently, which may cause strong convergence to be difficult to observe.en_US
dc.description.tableofcontents Contents
1 Introduction 9
1.1 Background . . . . . . . . . . . . . . . . . . . . 9
1.2 Overview . . . . . . . . . . . . . . . . . . . . . 12
2 Literature Review 13
2.1 BCG and Cognitive Hierarchy . . . . . . . . . . . . 13
2.2 BCG and Cognitive Capacity . . . . . . . . . . . . 14
2.3 Cognitive Capacity and Cognitive Hierarchy . . . . 17
2.4 Cognitive Capacity and Learning . . . . . . . . . . 19
2.4.1 Cognitive Capacity, Cognitive Hierarchy and
Learning . . . . . . . . . . . . . . . . . . 19
2.4.2 Cognitive Capacity and EWA Learning . . . . . 20
2.5 A Summary of Literature . . . . . . . . . . . . . . 22
3 Method 24
3.1 Beauty Contest Experiment . . . . . . . . . . . . . 24
3.2 Working Memory Task . . . . . . . . . . . . . . . . 25
3.3 Cognitive Hierarchy . . . . . . . . . . . . . . . . 26
3.4 EWA Learning Model . . . . . . . . . . . . . . . . 28
3.4.1 The Model . . . . . . . . . . . . . . . . . . 28
3.4.2 Estimation Strategy . . . . . . . . . . . . . 31
4 Results 33
4.1 WMC and Guessing Performance . . . . . . . . . . . 33
4.2 WMC and Cognitive Hierarchy . . . . . . . . . . . . 37
4.2.1 Static Analysis: Conditional Distribution and
Regression . . . . . . . . . . . . . . . . . 38
4.2.2 Dynamic Analysis: Evolution of Distributions 43
4.2.3 Dynamic Analysis: Markov Transition Matrix . 46
4.3 Guessing Performances and Cognitive Hierarchy . . . 51
4.4 WMC and EWA Learning . . . . . . . . . . . . . . . 53
4.4.1 Camerer`s EWA Learning . . . . . . . . . . . 53
4.4.2 EWA Rule Learning . . . . . . . . . . . . . . 57
5 Discussion and Conclusions 64

A Instructions of BCG 74
B Instructions of WMC Task 76
C Level-k Distribution Conditional on WMC Percentiles: Pe-
riod 3 to 10 82

List of Figures
1.1 An Overview of the Research Backgrounds . . . . . . . 11
3.1 Level classification procedure for guesses in period
1 . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Reinforcement and the corresponding interval for winner
and loser in beauty contest experiments . . . . . . . 30
4.1 Guessing Errors between the High WMC groups and the Low
WMC roups . . . . . . . . . . . . . . . . . . . . . . 36
4.2 Level-k distribution conditional on WMC percentiles . 39
4.3 Level-k distribution conditional on WMC percentiles in
period 1 . . . . . . . . . . . . . . . . . . . . . . 44
4.4 Level-k distribution conditional on WMC percentiles in
period 2 . . . . . . . . . . . . . . . . . . . . . . 45
4.5 Markov Transition Matrix of the State Space of Reasoning
Levels, Estimated Using the Pool of 10 Periods . . . .47
4.6 Markov Transition Matrix of the State Space of Reasoning
Levels, Estimated Using the Pool of the Initial 5
Periods . . . . . . . . . . . . . . . . . . . . . . . 48
4.7 Markov Transition Matrix of the State Space of Reasoning
Levels, Estimated Using the Pool of the Last 5 Periods49
4.8 Guess distribution and predicted guess distribution . 56
4.9 Level distribution and predicted level distribution . 60

B.1 Instruction for backward digit span task(Dspan) . . . 77
B.2 Instruction for spatial short-term memory test(SSTM) 78
B.3 Instruction for memory updating task(MU) . . . . . . 79
B.4 Instruction for sentence-span task(SentSpan) . . . . 80
B.5 Instruction for operation-span task(OpsSpan) . . . . 81
C.1 Level-k distribution conditional on WMC percentiles in
period 3 . . . . . . . . . . . . . . . . . . . . . . 82
C.2 Level-k distribution conditional on WMC percentiles in
period 4 . . . . . . . . . . . . . . . . . . . . . . .83
C.3 Level-k distribution conditional on WMC percentiles in
period 5 . . . . . . . . . . . . . . . . . . . . . . 83
C.4 Level-k distribution conditional on WMC percentiles in
period 6 . . . . . . . . . . . . . . . . . . . . . . 84
C.5 Level-k distribution conditional on WMC percentiles in
period 7 . . . . . . . . . . . . . . . . . . . . . . 84
C.6 Level-k distribution conditional on WMC percentiles in
period 8 . . . . . . . . . . . . . . . . . . . . . . .85
C.7 Level-k distribution conditional on WMC percentiles in
period 9 . . . . . . . . . . . . . . . . . . . . . . 85
C.8 Level-k distribution conditional on WMC percentiles in
period 10 . . . . . . . . . . . . . . . . . . . . . . 86

List of Tables
2.1 Literature on the Effect of Cognitive Capacity on
Strategic Thinking . . . . . . . . . . . . . . . . . 15
3.1 Summary of Estimated Learning Models . . . . . . . . 31
4.1 Correlation coefficients between WMC scores and
guessing differences in the beauty contest experiment34
4.2 Level-k thinking and working memory capacity . . . . 41
4.3 Do High and Low WMC subjects exhibit similar level/guess
distributions? . . . . . . . . . . . . . . . . . . . 43
4.4 Target-d istribution . . . . . . . . . . . . . . . . 52
4.5 Model Parameter Estimates of EWA Following Camerer and
Ho (1999) . . . . . . . . . . . . . . . . . . . . . . 54
4.6 Model Parameter Estimates of EWA Following Camerer, Ho
and Chong (2002) . . . . . . . . . . . . . . . . . . 55
4.7 Model Parameter Estimates of EWA Rule Learning: Model
IV . . . . . . . . . . . . . . . . . . . . . . . . . .58
4.8 Model Parameter Estimates of EWA Rule Learning: Model V
. . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.9 LR Test for the Significance of Difference in Parameter
Estimates: Model V . . . . . . . . . . . . . . . . . 62		zh_TW
dc.format.extent 5946654 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0942585021en_US
dc.subject (關鍵詞) 選美賽局zh_TW
dc.subject (關鍵詞) 智力zh_TW
dc.subject (關鍵詞) 工作記憶zh_TW
dc.subject (關鍵詞) k層次思考zh_TW
dc.subject (關鍵詞) 認知階層zh_TW
dc.subject (關鍵詞) 強化學習zh_TW
dc.subject (關鍵詞) 信念學習zh_TW
dc.subject (關鍵詞) 經驗加權吸引力學習zh_TW
dc.subject (關鍵詞) Beauty contest experimenten_US
dc.subject (關鍵詞) Intelligenceen_US
dc.subject (關鍵詞) Working memory capacityen_US
dc.subject (關鍵詞) Level-k reasoningen_US
dc.subject (關鍵詞) Cognitive hierarchiesen_US
dc.subject (關鍵詞) Reinforcement learningen_US
dc.subject (關鍵詞) Belief learningen_US
dc.subject (關鍵詞) Experience-weighted attraction learningen_US
dc.title (題名) 認知能力與認知階層 : 選美賽局的實驗分析zh_TW
dc.title (題名) Cognitive Capacity and Cognitive Hierarchy: Experimental Evidence from Keynes`s Beauty Contesten_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Agranovy M, Caplin A, Tergiman C (2011) The process of
choice in guessing games. Mimeo. Caltech.
Arad A, Rubinstein A (2010) Colonel Blotto’s top secret
files: Multi-dimensional iterative reasoning in action.
Working paper.
Branas-Garza P, Garcia-Munoz T, Hernan-Gonzalez R (2012)
Cognitive effort in the beauty contest game. Journal of
Economic Behavior and Organization 83(2): 254-260.
Branas-Garza P, Meloso D, Miller L (2012) Interactive and
moral reasoning: A comparative study of response times.
IGIER, Universita Bocconi, Working Paper Series No. 440.
Brock W, Hommes C (1998) Heterogeneous beliefs and routes
to chaos in a simple asset pricing model. Journal of
Economic Dynamics and Control 22:1235-1274.
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