Transcript Lecture 10: Test of Iterative Dominance Principle II

Outline
In-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-threshold
Allow 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
• David D. Ho
• Donald L. Bren
• Gordon E. Moore
Chairman of the Board
The Irvine Company
• Eli Broad
Chairman
SunAmerica Inc.
• Lounette M. Dyer
Chairman
Silk Route Technology
Director
The Aaron Diamond AIDS Research Center
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 Trustees
ALL
CEOs only
Mean
Target
Standard Deviation
Sample Size
42.6
29.8
23.4
70
37.8
26.5
18.9
20
Results from Two Other Smart
Subject Pools
Mean
Target
Standard Deviation
Sample Size
Portfolio
Managers
Economics
PhDs
24.3
17.0
16.2
26
27.4
19.2
18.7
16
Results from College Students
Mean
Target
Standard Deviation
Sample Size
Caltech
UCLA
Wharton
Germany
Singapore
21.9
42.3
37.9
15.3
29.6
26.5
10.4
18.0
18.8
27
28
35
36.7
25.7
20.2
67
46.1
32.2
28.0
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 (7person) 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
Bin 1
Bin 0
x
p(n  1) 2
p(n  1)
100
[
] 100
n p
n p
1
B( x)   wLb  BL ( x)  w01  B0 ( x)  w11  B1 ( x)
0
100
Infinite-Threshold pBC
Maximum Likelihood Estimates
Further Analysis on Iterated BestResponse
Special Cases
 Cournot Best Response (R=1, b1 = 1.0)
 Fictitious Play (bs= 1/R)
 Weighted Fictitious Play (bs=bs)
Maximum Likelihood Estimates