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

June 2007 Coordination and Learning2 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?

June 2007 Coordination and Learning3 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

June 2007 Coordination and Learning4 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

June 2007 Coordination and Learning5 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

June 2007 Coordination and Learning6 The Model: Setup Two-period version of Angeletos-Hellwig-Pavan (2006) Players indexed by i take actions: A (“attack”) (a it = 1) or B (“not attack”) (a it = 0). Status quo collapses iff the mass of agents attacking is A >  Individual payoffs Information structure: is drawn from N( z,1/  ) and is not observed by the agents z is the prior – the public signal Additional private signal: x it =  +  it where

June 2007 Coordination and Learning7 Prediction 1: There exists a unique x 1 * such that in any equilibrium of the dynamic game, an agent chooses action A (“attack”) in the 1 st period iff x 1 < x 1 *, which implies that there exists a unique  1 * such that the status quo is abandoned iff  <  1 *. Implications for experiment: A 1 (  ) is decreasing in  The thresholds  1 * and x 1 * are decreasing in the cost of attacking, c The Model: Period 1 Predictions A  Everyone 0

June 2007 Coordination and Learning8 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 (  2 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 (  is drawn from N( z,1/  ))  2 is the precision of private signal, x, in period 2

June 2007 Coordination and Learning9 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

June 2007 Coordination and Learning10 The Experiment: Treatments Table 1: Session Overview Table 2: Parameterization 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:  is drawn from N( z,1/  ))  is the precision of private signal, x Elicitation of beliefs

June 2007 Coordination and Learning11 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

June 2007 Coordination and Learning12 Data Analysis: First Period Predictions Figure 1: Kernel Regression: Fraction of Agents Attacking vs. Theta (pooled data for sessions 1-4, cost 50) Attack Fraction is monotonically decreasing in 

June 2007 Coordination and Learning13 Data Analysis: First Period Predictions Table 3: OLS Regressions of individual action on x in Stage 1, all data for sessions 1-4

June 2007 Coordination and Learning14 Data Analysis: Static Predictions Table 4: Estimated Aggregate Threshold Summary Note: Estimated thresholds vary only slightly with cost

June 2007 Coordination and Learning15 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

June 2007 Coordination and Learning16 Data Analysis: Endogenous Learning Figure 2: Average Probability of Attack for the No-New Information Treatments

June 2007 Coordination and Learning17 Data Analysis: Endogenous Learning Table 5: OLS Regressions of individual action on x, all data for sessions 1-4

June 2007 Coordination and Learning18 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

June 2007 Coordination and Learning19 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) Data Analysis: New Information Stage 2

June 2007 Coordination and Learning20 Table 6: Effect of the New Information Treatment on Stage 2 Actions Data Analysis: New Information

June 2007 Coordination and Learning21 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

June 2007 Coordination and Learning22 Data Analysis: Rationality Figure 4: Cost 20 Belief about Fraction of Agents Attacking vs. Theory Prediction Figure 5: Cost 50 Figure 6: Cost 60 Results of Rationality Test: c=20:76.98% rational c=50:90.79% rational c=60:89.44% rational

June 2007 Coordination and Learning23 Data Analysis: Consistency Measure of Consistency: LHS: Average size of attack RHS: E[A(  )|x] is the belief of subject i E[E[A(  )|x]] is the average belief Table 7: Test of Consistency in Stage 1 Table 8: Test of Consistency in Stage 2

June 2007 Coordination and Learning24 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

June 2007 Coordination and Learning25 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

June 2007 Coordination and Learning26 Extra Slides

June 2007 Coordination and Learning27 First Period Predictions: “Mistakes” 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 Figure A1: Estimated thresholds vs. rounds (pooled data for sessions 1-4) 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)

June 2007 Coordination and Learning28 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

June 2007 Coordination and Learning29 New Information: Strategy Space Figure A5: Probability of Attack vs. x by Stage for the NNI Treatments Figure A5: Probability of Attack vs. x by Stage for the NNI and the NI Treatments

June 2007 Coordination and Learning30 Calculation of Measure of Rationality Figure A6: Thresholds for Different Cost Treatments Measure of Rationality: Expected payoff vs. Cost of attacking Attack iff Results: Treatment c=20: 76.98% rational Treatment c=50: 90.79% rational Treatment c=60: 89.44% rational Threshold

June 2007 Coordination and Learning31 Further Research: Theory Correction for “mistakes” Justification for excess aggressiveness  Optimism Figure A7: Modified Theoretical Beliefs for Cost-50 Treatment

June 2007 Coordination and Learning32 Further Research: Experimental Allowing for communication  “generic sunspot” Effects of gender on coordination