P.J. Healy

1
Learning Dynamics for Mechanism DesignAn
Experimental Comparison of Public Goods Mechanisms

• P.J. Healy
• pj_at_hss.caltech.edu
• California Institute of Technology

2
The Repeated Public Goods Implementation Problem

• Example Condo Association special assessment
• Fixed set of agents regularly choosing public
  good levels.
• Goal is to maximize efficiency across all periods
• What mechanism should be used?
• Questions
• Are the one-shot mechanisms the best solution
  to the repeated problem?
• Can one simple learning model approximate
  behavior in a variety of games with different
  equilibrium properties?
• Which existing mechanisms are most efficient in
  the dynamic setting?

3
Previous Experiments on Public Goods Mechanisms I

• Dominant Strategy (VCG) mechanism experiments
• Attiyeh, Franciosi and Isaac 00
• Kawagoe and Mori 01 99 pilot
• Cason, Saijo, Sjostrom, Yamato 03
• Convergence to strict dominant strategies
• Weakly dominated strategies are observed

4
Previous Experiments onPublic Goods Mechanisms II

• Nash Equilibrium mechanisms
• Voluntary Contribution experiments
• Chen Plott 96
• Chen Tang 98
• Convergence iff supermodularity (stable equil.)
• Results consistent with best response behavior

5
A Simple Learning Model

• k-period Best Response model
• Agents best respond to pure strat. beliefs
• Belief unweighted average of the others
  strategies in the previous k periods
• Needs convex strategy space
• Rational behavior, inconsistent beliefs
• Pure strategies only

6
A Simple Learning Model Predictions

• Strictly dominated strategies never played
• Weakly dominated strategies possible
• Always converges in supermodular games
• Stable/convergence gt Nash equilibrium
• Can be very unstable (cycles w/ equilibrium)

7
A New Set of Experiments

• New experiments over 5 public goods mechanisms
• Voluntary Contribution
• Proportional Tax
• Groves-Ledyard
• Walker
• Continuous VCG (cVCG) with 2 parameters
• Identical environment (endow., prefs., tech.)
• 4 sessions each with 5 players for 50 periods
• Computer Interface
• History window What-If Scenario Analyzer

8
The Environment

• Agents
• Private Good Public Good
  Endowments
• Preferences
• Technology
• Mechanisms

9
The Mechanisms

• Voluntary Contribution
• Proportional Tax
• Groves-Ledyard
• Walker
• VCG

10
Experimental Results I Choosing k

• Which value of k minimizes the M.A.D. across all
  mechanisms, sessions, players and periods?
• k5 is the most accurate

11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
Experimental Results 5-B.R. vs. Equilibrium

• Null Hypothesis
• Non-stationarity gt period-by-period tests
• Non-normality of errors gt non-parametric tests
• Permutation test with 2,000 sample permutations
• Problem If then the test
  has little power
• Solution
• Estimate test power as a function of
• Perform the test on the data only where power is
  sufficiently large.

15
Simulated Test Power
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
5-period B.R. vs. Equilibrium

• Voluntary Contribution (strict dom. strats)
• Groves-Ledyard (stable Nash equil)
• Walker (unstable Nash equil) 73/81 tests reject
  H0
• No apparent pattern of results across time
• Proportional Tax 16/19 tests reject H0

21
Interesting properties of the2-parameter cVCG
mechanism

• Best response line in 2-dimensional strategy space

22
Best Response in the cVCG mechanism

• Convert data to polar coordinates
• Dom. Strat. origin, B.R. line 0-degree line

23
(No Transcript)
24
Experimental Results III Efficiency

• Outcomes are closest to Pareto optimal in cVCG
• cVCG gt GL PT gt VC gt WK (same for efficiency)
• Sensitivity to parameter selection
• Variance of outcomes
• cVCG is lowest, followed by Groves-Ledyard
• Walker has highest
• Walker mechanism performs very poorly
• Efficiency below the endowment
• Individual rationality violated 42 of last 10
  periods

25
Discussion Conclusions

• Data are consistent with the learning model.
• Repercussions for theoretical research
• Should worry about dynamics
• k-period best response studied here, but other
  learning models may apply
• Example Instability of the Walker mechanism
• cVCG mechanism can perform efficiently
• Open questions
• cVCG behavior with stronger conflict between
  incentives and efficiency
• Sensitivity of results to parameter changes
• Effect of What-If Scenario Analyzer tool

26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29

• Voluntary Contribution Mechanism
• Results