Structure-preserving desynchronization of minority games

Perfect synchronicity in N-player games is a useful theoretical dream, but communication delays are inevitable and may result in asynchronous interactions. Some systems such as financial markets are asynchronous by design, and yet most theoretical models assume perfectly synchronized actions. We propose a general method to transform standard models of adaptive agents into asynchronous systems while preserving their global structure under some conditions. Using the minority game as an example, we find that the phase and fluctuations structure of the standard game subsists even in maximally asynchronous deterministic case, but that it disappears if too much stochasticity is added to the temporal structure of interaction. Allowing for heterogeneous communication speeds and activity patterns gives rise to a new information ecology that we study in details.

[1]  Matteo Marsili,et al.  Trading Behavior and excess volatility in Toy Markets , 2001, Adv. Complex Syst..

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

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

[4]  Paolo De Los Rios,et al.  The local minority game , 2002 .

[5]  Ton Coolen,et al.  The mathematical theory of minority games , 2005 .

[6]  Zecchina,et al.  Statistical mechanics of systems with heterogeneous agents: minority games , 1999, Physical review letters.

[7]  B. M. Fulk.  MATH , 1992 .

[8]  Anthony C. C. Coolen.  Generating functional analysis of minority games with real market histories , 2004 .

[9]  Hans-Jörg Schulz,et al.  Cooperation in the Minority Game with local information , 2000 .

[10]  B A Huberman,et al.  Evolutionary games and computer simulations. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Matteo Marsili,et al.  Modeling market mechanism with minority game , 1999, cond-mat/9909265.

[12]  Yi-Cheng Zhang,et al.  Minority Games , 2008, Encyclopedia of Complexity and Systems Science.

[13]  Damien Challet,et al.  Minority games with heterogeneous timescales , 2006 .

[14]  Tobias Galla,et al.  The transition to efficiency in minority games , 2008 .

[15]  Roger Lagunoff,et al.  Asynchronous Choice in Repeated Coordination Games , 1997 .

[16]  G. Zumbach,et al.  Market heterogeneities and the causal structure of volatility , 2003 .

[17]  F. Lillo.  Limit order placement as an utility maximization problem and the origin of power law distribution of limit order prices , 2006, physics/0612016.

[18]  M Marsili,et al.  Phase transition and symmetry breaking in the minority game. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Fernando Vega-Redondo,et al.  Asynchronous Choice and Markov Equilibria , 2002, J. Econ. Theory.

[20]  Matteo Marsili,et al.  Dynamical instabilities in a simple minority game with discounting , 2008 .

[21]  M Ali Saif,et al.  The prisoner’s dilemma with semi-synchronous updates: evidence for a first-order phase transition , 2009, 0910.0961.

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

[23]  Challet,et al.  Relevance of memory in minority games , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.