Phase coexistence in a forecasting game

Individual choices are either based on personal experience or on information provided by peers. The latter case, causes individuals to conform to the majority in their neighborhood. Such herding behavior may be very efficient in aggregating disperse private information, thereby revealing the optimal choice. However if the majority relies on herding, this mechanism may dramatically fail to aggregate correctly the information, causing the majority adopting the wrong choice. We address these issues in a simple model of interacting agents who aim at giving a correct forecast of a public variable, either seeking private information or resorting to herding. As the fraction of herders increases, the model features a phase transition beyond which a state where most agents make the correct forecast coexists with one where most of them are wrong. Simple strategic considerations suggest that indeed such a system of agents self-organizes deep in the coexistence region. There, agents tend to agree much more among themselves than with what they aim at forecasting, as found in recent empirical studies.

[1]  Matteo Marsili,et al.  Minority games with finite score memory , 2004 .

[2]  S. Bikhchandani,et al.  You have printed the following article : A Theory of Fads , Fashion , Custom , and Cultural Change as Informational Cascades , 2007 .

[3]  Steven Huddart.  Employee Stock Options , 1994 .

[4]  Mark P. Taylor,et al.  The Role of Asymmetries and Regime Shifts in the Term Structure of Interest Rates , 2005 .

[5]  Guillaume Deffuant,et al.  Meet, discuss, and segregate! , 2002, Complex..

[6]  Alessio Sancetta,et al.  Copula Based Monte Carlo Integration in Financial Problems , 2004 .

[7]  Paolo Zaffaroni,et al.  Gaussian inference on certain long-range dependent volatility models , 2003 .

[8]  Walter Distaso,et al.  Testing and Modelling Market Microstructure Effects with an Application to the Dow Jones Industrial Average , 2004 .

[9]  Alessio Sancetta,et al.  Decoupling and Convergence to Independence with Applications to Functional Limit Theorems , 2004 .

[10]  Norman R. Swanson,et al.  Predictive Density Accuracy Tests , 2004 .

[11]  Roel C. A. Oomen,et al.  Properties of realized variance for a pure jump process: calendar time sampling versus business time sampling , 2004 .

[12]  Andrew J. Patton,et al.  Properties of Optimal Forecasts under Asymmetric Loss and Nonlinearity , 2007 .

[13]  V. Corradi,et al.  Testing for One Factor Models versus Stochastic Volatility Models, in the Presence of Jumps. ∗ , 2004 .

[14]  Tilman Börgers,et al.  Learning Through Reinforcement and Replicator Dynamics , 1997 .

[15]  Walter Distaso,et al.  Estimating and Testing Sochastic Volatility Models using Realized Measures , 2004 .

[16]  M. Salmon,et al.  Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index , 2005 .

[17]  Florian Wagener,et al.  Equivalence and Bifurcations of Finite Order Stochastic Processes , 2005 .

[18]  Dietrich Stauffer.  Percolation Models of Financial Market Dynamics , 2001, Adv. Complex Syst..

[19]  D. Thornton,et al.  The Empirical Failure of the Expectations Hypothesis of the Term Structure of Bond Yields , 2005, Journal of Financial and Quantitative Analysis.

[20]  Wim Schoutens,et al.  A multivariate jump-driven financial asset model , 2005 .

[21]  Soosung Hwang,et al.  Smoothing, Nonsynchronous Appraisal and Cross-Sectional Aggregation in Real Estate Price Indices , 2005 .

[22]  J. Bouchaud,et al.  Of songs and men: a model for multiple choice with herding , 2006, physics/0606224.

[23]  J. Bouchaud,et al.  HERD BEHAVIOR AND AGGREGATE FLUCTUATIONS IN FINANCIAL MARKETS , 1997, Macroeconomic Dynamics.

[24]  V. Eguíluz,et al.  Transmission of information and herd Behavior: an application to financial markets. , 1999, Physical review letters.

[25]  R. Oomen.  Properties of Bias-Corrected Realized Variance Under Alternative Sampling Schemes , 2005 .

[26]  M. Bacharach.  Economics and the Theory of Games , 2019 .

[27]  Ginestra Bianconi,et al.  Emergence of large cliques in random scale-free networks , 2006 .