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Learning Dynamics for Mechanism Design An Experimental Comparison of Public Goods Mechanisms

P.J. Healy pj@hss.caltech.edu California Institute of Technology. Learning Dynamics for Mechanism Design An Experimental Comparison of Public Goods Mechanisms. The Repeated Public Goods Implementation Problem. Example: Condo Association “special assessment”

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Learning Dynamics for Mechanism Design An Experimental Comparison of Public Goods Mechanisms

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  1. P.J. Healy pj@hss.caltech.edu CaliforniaInstituteofTechnology Learning Dynamics for Mechanism DesignAn Experimental Comparison of Public Goods Mechanisms

  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 => 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? • k=5 is the most accurate

  11. Experimental Results: 5-B.R. vs. Equilibrium • Null Hypothesis: • Non-stationarity => period-by-period tests • Non-normality of errors => 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.

  12. Simulated Test Power

  13. 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

  14. Interesting properties of the2-parameter cVCG mechanism • Best response line in 2-dimensional strategy space

  15. Best Response in the cVCG mechanism • Convert data to polar coordinates • Dom. Strat. = origin, B.R. line = 0-degree line

  16. Experimental Results III: Efficiency • Outcomes are closest to Pareto optimal in cVCG • cVCG > GL ≥ PT > VC > 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

  17. 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

  18. Voluntary Contribution Mechanism Results

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