Outline In-Class Experiment on Centipede Game Test of Iterative Dominance Principle I: McKelvey...

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