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OutlineIn-Class Experiment on Centipede Game
Test of Iterative Dominance Principle I: McKelvey and Palfrey (1992)
Test of Iterative Dominance Principle II: Ho, Camerer, and Weigelt (1988)
Motivation Constant-sum games
Control for altruistic behavior
Does experience matter?
Finite-threshold versus infinite-thresholdAllow violations of higher level of iterated dominance
Group size and learning
Finite-Threshold p-BC
Infinite-Threshold pBC
Experimental Design
pBC Contest Every player simultaneously chooses a number from 0 to
100
Compute the group average
Define Target Number to be 0.7 times the group average
The winner is the player whose number is the closet to
the Target Number
The prize to the winner is US$10 + $1 x Number of
Participant
A Sample of Caltech Board of Trustees
• David Baltimore President California Institute of Technology
• Donald L. Bren
Chairman of the BoardThe Irvine Company
• Eli BroadChairmanSunAmerica Inc.
• Lounette M. Dyer Chairman Silk Route Technology
• David D. Ho Director The Aaron Diamond AIDS Research Center
• Gordon E. Moore Chairman Emeritus Intel Corporation
• Stephen A. Ross Co-Chairman, Roll and Ross Asset Mgt Corp
• Sally K. Ride President Imaginary Lines, Inc., and Hibben Professor of Physics
Results from Caltech Board of Trustees
Caltech Board of TrusteesALL CEOs only
Mean 42.6 37.8Target 29.8 26.5Standard Deviation 23.4 18.9Sample Size 70 20
Results from Two Other Smart Subject Pools
Portfolio EconomicsManagers PhDs
Mean 24.3 27.4Target 17.0 19.2Standard Deviation 16.2 18.7Sample Size 26 16
Results from College Students
Caltech UCLA Wharton Germany Singapore
Mean 21.9 42.3 37.9 36.7 46.1Target 15.3 29.6 26.5 25.7 32.2Standard Deviation 10.4 18.0 18.8 20.2 28.0Sample Size 27 28 35 67 98
Results from FT, Spektrum Readers
Basic Results
Finite-Threshold p-BC
Infinite-Threshold pBC
Infinite-Threshold Games (Inexperienced Subjects, p=0.7, n=7)
Infinite-Threshold Games, (Experienced Subjects, p=0.7, n=7)
Infinite-Threshold Games (Inexperienced Subjects, p=0.9, n=7)
Infinite-Threshold Games (Experienced Subjects, p=0.9, n=7)
Infinite-Threshold Games (Inexperienced Subjects, p=0.7, n=3)
Infinite-Threshold Games (Experienced Subjects, p=0.7, n=3)
Infinite-Threshold Games (Inexperienced Subjects, p=0.9, n=3)
Infinite-Threshold Games (Experienced Subjects, p=0.9, n=3)
Finite-Threshold Games, n=3
Finite-Threshold Games, n=7
Summary of Basic Results Result 1: First-period choices are far from equilibrium.
Choice converge towards equilibrium point over time.
Result 2: On average, choices are closer to the
equilibrium point for games with finite thresholds, and for
games with p farther from 1.
Result 3: Choices are closer to equilibrium for large (7-
person) groups than for small (3-person) groups
Result 4: Choices by experienced subjects are no
different than choices by inexperienced subjects in the
first round, but converge faster to equilibrium.
Further Analysis on Iterated Dominance
Assignment of Type in Bin b
100])1(
[ 2 pn
np100
)1(
pn
np 100
Bin 0Bin 1
)()()()( 1110
10
1
0
xBwxBwxBwxB LbL
x
Infinite-Threshold pBC
Maximum Likelihood Estimates
Further Analysis on Iterated Best-Response
Special Cases
Cournot Best Response (R=1, = 1.0)
Fictitious Play (s= 1/R)
Weighted Fictitious Play (s=s)
Maximum Likelihood Estimates