Coordination and Learning in Dynamic Global Games: Experimental Insights

1. Coordination and Learning in Dynamic Global Games:Experimental Evidence Olga Shurchkov MIT The Economic Science Association World Meeting 2007

2. Intro: Motivation • 3 features of currency crises • Strategic complementarities (coordination games) • Heterogeneous expectations (global coordination games) • Dynamic nature (dynamic global coordination games) • Goals • Structure of equilibrium strategies • Impact of learning on dynamics of coordination • “exogenous learning” • “endogenous learning” • Multiplicity detection • Rationality assessment • Approach • First study to test the predictions of dynamic global coordination models with a laboratory experiment • Why a laboratory experiment? Coordination and Learning

3. Intro: Literature Review • Coordination models with complete information (Obstfeld, 1996) • Global coordination models with heterogeneous information (static framework) • Carlsson and van Damme, 1993 • Morris and Shin, 1998 • Global coordination models with heterogeneous information (multi-period framework) • Angeletos et al., 2006 • Experimental Evidence • Cooper, DeJong, Forsythe, and Ross, AER 1990, 1992 • Van Huyck, Battalio, and Beil, AER 1990 • Cabrales, Nagel, and Armenter, 2002 • Heinemann, Nagel, and Ockenfels, EMA 2004 • Cheung and Friedman, Working paper 2006 Coordination and Learning

4. Presentation Agenda • Introduction and Motivation • The Model Predictions • The Experiment • Data Analysis • First Period Predictions • Dynamic Predictions: Endogenous Learning • Dynamic Predictions: New Information • Rationality and Consistency • Discussion Coordination and Learning

5. Presentation Agenda • Introduction and Motivation • The Model Predictions • The Experiment • Data Analysis • First Period Predictions • Dynamic Predictions: Endogenous Learning • Dynamic Predictions: New Information • Rationality and Consistency • Discussion Coordination and Learning

6. The Model: Setup • Two-period version of Angeletos-Hellwig-Pavan (2006) • Players indexed by i take actions: A (“attack”) (ait = 1) or B (“not attack”) (ait = 0). • Status quo collapses iff the mass of agents attacking is A >q • Individual payoffs • Information structure: • is drawn from N( z,1/a ) and is not observed by the agents • z is the prior – the public signal • Additional private signal: xit = q + xitwhere Coordination and Learning

7. A Everyone 0 q* q The Model: Period 1 Predictions • Prediction 1: There exists a unique x1* such that in any equilibrium of the dynamic game, an agent chooses action A (“attack”) in the 1st period iff x1 < x1*, which implies that there exists a unique q1* such that the status quo is abandoned iff q < q1*. • Implications for experiment: • A1(q )is decreasing inq • The thresholds q1* and x1* are decreasing in the cost of attacking, c Coordination and Learning

8. The Model: Period 2 Predictions • Prediction 2: No new information not attacking is the unique equilibrium. Implication for experiment: Probability of attack should be greatly reduced in the second stage. • Prediction 3: Sufficient new information (b2 is sufficiently large) new attack becomes possible, if z is sufficiently high. Implication for experiment: Probability of attack should be higher with new information in second stage than with no new information. Notes: z is the prior (q is drawn from N( z,1/a )) b2 is the precision of private signal, x, in period 2 Coordination and Learning

9. Presentation Agenda • Introduction and Motivation • The Model Predictions • The Experiment • Data Analysis • First Period Predictions • Dynamic Predictions: Endogenous Learning • Dynamic Predictions: New Information • Rationality and Consistency • Discussion Coordination and Learning

10. The Experiment: Treatments • 6 sessions at the Institute for Empirical Research in Economics, Zurich • 30 subjects in each session • 2 groups of 15 subjects each • Different treatments for cost of attacking and information in Stage 2 • Notes: q is drawn from N( z,1/a)) • b is the precision of private signal, x • Elicitation of beliefs Table 1: Session Overview Table 2: Parameterization Coordination and Learning

11. Presentation Agenda • Introduction and Motivation • The Model Predictions • The Experiment • Data Analysis • First Period Predictions • Dynamic Predictions: Endogenous Learning • Dynamic Predictions: New Information • Rationality and Consistency • Discussion Coordination and Learning

12. Data Analysis: First Period Predictions Attack Fraction is monotonically decreasing in q Figure 1: Kernel Regression: Fraction of Agents Attacking vs. Theta (pooled data for sessions 1-4, cost 50) Coordination and Learning

13. Data Analysis: First Period Predictions Table 3: OLS Regressions of individual action on x in Stage 1, all data for sessions 1-4 Coordination and Learning

14. Data Analysis: Static Predictions Table 4: Estimated Aggregate Threshold Summary • Note: • Estimated thresholds vary only slightly with cost Coordination and Learning

15. Presentation Agenda • Introduction and Motivation • The Model Predictions • The Experiment • Data Analysis • First Period Predictions • Dynamic Predictions: Endogenous Learning • Dynamic Predictions: New Information • Rationality and Consistency • Discussion Coordination and Learning

16. Data Analysis: Endogenous Learning Figure 2: Average Probability of Attack for the No-New Information Treatments Coordination and Learning

17. Data Analysis: Endogenous Learning Table 5: OLS Regressions of individual action on x, all data for sessions 1-4 Coordination and Learning

18. Presentation Agenda • Introduction and Motivation • The Model Predictions • The Experiment • Data Analysis • First Period Predictions • Dynamic Predictions: Endogenous Learning • Dynamic Predictions: New Information • Rationality and Consistency • Discussion Coordination and Learning

19. Data Analysis: New Information Stage 2 Figure 3: Average Probability of Attack for the No-New-Information (NNI) Treatments and the New-Information (NI) Treatments (only for rounds that continue into Stage 2 and for which x<100) Coordination and Learning

20. Data Analysis: New Information Table 6: Effect of the New Information Treatment on Stage 2 Actions Coordination and Learning

21. Presentation Agenda • Introduction and Motivation • The Model Predictions • The Experiment • Data Analysis • First Period Predictions • Dynamic Predictions: Endogenous Learning • Dynamic Predictions: New Information • Rationality and Consistency • Discussion Coordination and Learning

22. Data Analysis: Rationality Belief about Fraction of Agents Attacking vs. Theory Prediction Figure 4: Cost 20 Figure 5: Cost 50 Results of Rationality Test: c=20: 76.98% rational c=50: 90.79% rational c=60: 89.44% rational Figure 6: Cost 60 Coordination and Learning

23. Data Analysis: Consistency Measure of Consistency: Table 7: Test of Consistency in Stage 1 LHS: Average size of attack RHS: E[A(q )|x] is the belief of subject i E[E[A(q )|x]] is the average belief Table 8: Test of Consistency in Stage 2 Coordination and Learning

24. Presentation Agenda • Introduction and Motivation • The Model Predictions • The Experiment • Data Analysis • First Period Predictions • Dynamic Predictions: Endogenous Learning • Dynamic Predictions: New Information • Rationality and Consistency • Discussion Coordination and Learning

25. Discussion • Static Predictions • Subjects follow monotone threshold strategies • Subjects act more aggressively than the theory predicts • Dynamic Predictions • Subjects’ behavior exhibits learning • Less learning than the theory predicts (cost of attacking matters) • Rationality • Given their aggressive beliefs, agents seem to behave rationally • Actions seem to be consistent with beliefs Coordination and Learning

26. Extra Slides Coordination and Learning

27. First Period Predictions: “Mistakes” Figure A2: Proportion of “mistakes” relative to the best-response vs. rounds (Sessions 1-2) Figure A2: Proportion of “mistakes” relative to the best-response vs. rounds (Sessions 3-4) Figure A1: Estimated thresholds vs. rounds (pooled data for sessions 1-4) • Notes: • Estimated thresholds exhibit a slight upward trend • Behavior that is not consistent with best-response strategy does not decrease significantly over rounds • On average, in 91% of cases subjects followed a strategy that was a best response to the estimated threshold Coordination and Learning

28. Endogenous Learning: Strategy Space Figure A3: Probability of Attack vs. x by Stage for cost 50 treatments Figure A4: Probability of Attack vs. x by Stage for cost 20 treatments Coordination and Learning

29. New Information: Strategy Space Figure A5: Probability of Attack vs. x by Stage for the NNI and the NI Treatments Figure A5: Probability of Attack vs. x by Stage for the NNI Treatments Coordination and Learning

30. Calculation of Measure of Rationality Threshold Measure of Rationality: Expected payoff vs. Cost of attacking Results: Treatment c=20: 76.98% rational Treatment c=50: 90.79% rational Treatment c=60: 89.44% rational Figure A6: Thresholds for Different Cost Treatments Attack iff Coordination and Learning

31. Further Research: Theory • Correction for “mistakes” • Justification for excess aggressiveness  Optimism Figure A7: Modified Theoretical Beliefs for Cost-50 Treatment Coordination and Learning

32. Further Research: Experimental • Allowing for communication  “generic sunspot” • Effects of gender on coordination Coordination and Learning