Minority games with score-dependent and agent-dependent payoffs.

Score-dependent and agent-dependent payoffs of the strategies are introduced into the standard minority game. The intrinsic periodicity is consequently removed, and the stylized facts arise, such as long-range volatility correlations and "fat tails" in the distribution of the returns. The agent dependence of the payoffs is essential in producing the long-range volatility correlations. The new payoffs lead to a better performance in the dynamic behavior nonlocal in time, and can coexist with the inactive strategy. We also observe that the standard deviation sigma2/N is significantly reduced, thus the efficiency of the system is distinctly improved. Based on this observation, we give a qualitative explanation for the long-range volatility correlations.

[1]  M. Marsili,et al.  From Minority Games to real markets , 2000, cond-mat/0011042.

[2]  J. Bouchaud,et al.  Theory Of Financial Risk And Derivative Pricing , 2000 .

[3]  Rama Cont,et al.  A Langevin approach to stock market fluctuations and crashes , 1998 .

[4]  M. Marchesi,et al.  Scaling and criticality in a stochastic multi-agent model of a financial market , 1999, Nature.

[5]  Thomas Lux,et al.  The stable Paretian hypothesis and the frequency of large returns: an examination of major German stocks , 1996 .

[6]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[7]  M. Marsili,et al.  A Prototype Model of Stock Exchange , 1997, cond-mat/9709118.

[8]  Matteo Marsili,et al.  Stylized Facts of Financial Markets and Market Crashes in Minority Games , 2001, cond-mat/0101326.

[9]  Dietrich Stauffer,et al.  Sharp peaks in the percolation model for stock markets , 2000 .

[10]  Paulsamy Muruganandam,et al.  Time series analysis for minority game simulations of financial markets , 2003 .

[11]  P. Cizeau,et al.  Statistical properties of the volatility of price fluctuations. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  D. Helbing,et al.  Volatility clustering and scaling for financial time series due to attractor bubbling. , 2002, Physical review letters.

[13]  Bing-Hong Wang,et al.  Statistical properties of the attendance time series in the minority game , 2001 .

[14]  Li-Xin Zhong,et al.  Effects of contrarians in the minority game. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Marcia M. A. Schafgans,et al.  The tail index of exchange rate returns , 1990 .

[16]  Stylized facts in minority games with memory: a new challenge , 2004, cond-mat/0401628.

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

[18]  Rick L. Riolo,et al.  Adaptive Competition, Market Efficiency, and Phase Transitions , 1999 .

[19]  PERSISTENCE PROBABILITY IN FINANCIAL DYNAMICS , 2002 .

[20]  Jean-Philippe Bouchaud,et al.  Bubbles, crashes and intermittency in agent based market models , 2002 .

[21]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[22]  V. Plerou,et al.  Scaling of the distribution of price fluctuations of individual companies. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Yi-Cheng Zhang,et al.  Emergence of cooperation and organization in an evolutionary game , 1997 .

[24]  C Y Lee.  Is memory in the minority game irrelevant? , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  A. Cavagna.  Irrelevance of memory in the minority game , 1998, cond-mat/9812215.

[26]  Yi Li,et al.  The minority game with variable payoffs , 2000, nlin/0002004.

[27]  E. Bacry,et al.  Modelling fluctuations of financial time series: from cascade process to stochastic volatility model , 2000, cond-mat/0005400.

[28]  Generalized persistence probability in a dynamic economic index , 2003 .

[29]  Bo Zheng,et al.  Monte Carlo simulations of short-time critical dynamics , 1999 .

[30]  Matteo Marsili,et al.  Minority Games and stylized facts , 2001 .

[31]  P. Hui,et al.  The minority game with different payoff functions: crowd–anticrowd theory , 2003 .

[32]  W. Arthur.  Inductive Reasoning and Bounded Rationality , 1994 .

[33]  Bingyong Tang,et al.  Minority game and anomalies in financial markets , 2004 .

[34]  Bo Zheng,et al.  A generalized dynamic herding model with feed-back interactions , 2004 .

[35]  Persistence probabilities of the German DAX and Shanghai Index , 2005, nlin/0511048.

[36]  Ingve Simonsen,et al.  Optimal investment horizons , 2002 .

[37]  R. Mantegna,et al.  Scaling behaviour in the dynamics of an economic index , 1995, Nature.

[38]  M. Mézard,et al.  Microscopic models for long ranged volatility correlations , 2001, cond-mat/0105076.

[39]  B. Zheng,et al.  Two-phase phenomena, minority games, and herding models. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  V. Plerou,et al.  Scaling of the distribution of fluctuations of financial market indices. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[41]  B. Zheng,et al.  On return-volatility correlation in financial dynamics , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  H. Eugene Stanley,et al.  Econophysics: Two-phase behaviour of financial markets , 2003, Nature.

[43]  Ingve Simonsen,et al.  Inverse statistics in economics: the gain–loss asymmetry , 2002 .

[44]  Gopikrishnan,et al.  Economic fluctuations and anomalous diffusion , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[45]  P. M. Hui,et al.  From market games to real-world markets , 2001 .

[46]  R. Mantegna,et al.  An Introduction to Econophysics: Contents , 1999 .

[47]  Dietrich Stauffer,et al.  MONTE CARLO SIMULATION OF VOLATILITY CLUSTERING IN MARKET MODEL WITH HERDING , 1999 .