本文透過「優勢策略可解賽局」、「同時選擇」與「先後選擇」的「空間版選美結果預測賽局」來探索人們的策略性思考能力。利用主成分分析法，我們從實驗資料中歸納出五個策略性思考能力，用以解釋人們在這些賽局中對戰所有人之期望報酬 56% 的變異: (一)、人們的逆推思考能力 (最能解釋人們在這些賽局中表現的主成分); (二)、人們的在高維空間下的逆推思考能力; (三)、人們的風險偏好; (四)、人們對於他人社會偏好的認知信念; (五)、人們對於他人認知雙方行為的高層次信念。

We employ principal component analysis to identify components of subject''s strategic IQ in the following three classes of games: The two-stage dominance-solvable game, Chen, Huang and Wang (2013)''s simultaneous spatial beauty contest game, and the first-mover spatial beauty contest game. Parallel analysis retains the first five principal components (PCs), which account for 56% of the total variance of subject''s normalized expected payoffs for each of the 33 games. We interpret these PCs as five strategic IQs: The first SIQ indicates subjects'' abilities to perform backward induction and it is also the common g-factor that can predict subjects'' performances in most games. The second SIQ could be interpreted as subjects'' abilities to perform high dimensional backward induction. The third SIQ controls for subjects'' attitudes toward risk. The fourth SIQ reflects subjects'' beliefs about social preferences. The fifth SIQ measures subjects'' accuracy of higher order beliefs about others.

Contents
1 Introduction 1
2 Game Structure and Theoretical Predictions 3
2.1 Two-Stage Dominance-Solvable Games . . . . . . . . . . . . . . . . 3
2.2 Simultaneous Spatial Beauty Contest Games . . . . . . . . . . . . . 8
2.3 First-Mover Spatial Beauty Contest Games . . . . . . . . . . . . . . 10
3 Experimental Design 13
4 Basic Results 14
4.1 Results of Dominance-Solvable Games . . . . . . . . . . . . . . . . 14
4.2 Results of Simultaneous/1st-Mover Spatial Beauty Contest Games . 17
5 Subjects’ Strategic IQ 20
5.1 Subject Performance Indicators . . . . . . . . . . . . . . . . . . . . 20
5.2 Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . 27
6 Conclusion 33
Appendix 36
A Procedure for Principal Component Analysis 36
B Additional Figures 38
B.1 Data from Practice 2nd-Mover SBC Games . . . . . . . . . . . . . . 38
B.2 Data from Simultaneously SBC Games . . . . . . . . . . . . . . . . 43
B.3 Data from 1st-Mover SBC Games . . . . . . . . . . . . . . . . . . . 49
B.4 Parallel Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
C Instructions (Slides Used in the Experiment) 56

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