Generating functional analysis of Minority Games with real market histories

Abstract

It is shown how the generating functional method of De Dominicis can be used to solve the dynamics of the original version of the minority game (MG), in which agents observe real as opposed to fake market histories. Here one again finds exact closed equations for correlation and response functions, but now these are defined in terms of two connected effective non-Markovian stochastic processes: a single effective agent equation similar to that of the `fake' history models, and a second effective equation for the overall market bid itself (the latter is absent in `fake' history models). The result is an exact theory, from which one can calculate from first principles both the persistent observables in the MG and the distribution of history frequencies.

39 pages, 5 postscript figures, iop style

References in corpus (6)

• Generating Functional Analysis of the Dynamics of the Batch Minority Game with Random External Information
• Continuum time limit and stationary states of the Minority Game
• Dynamics of the Batch Minority Game with Inhomogeneous Decision Noise
• Dynamical Solution of the On-Line Minority Game
• Dynamics of a spherical minority game
• Learning to coordinate in a complex and non-stationary world

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• Generating functional analysis of minority games with inner product strategy definitions
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• Theory of agent-based market models with controlled levels of greed and anxiety
• Phenomenology of minority games in efficient regime
• Multiplpe Choice Minority Game With Different Publicly Known Histories
• Structure-preserving desynchronization of minority games
• Market response to external events and interventions in spherical minority games
• From Minority Game to Black & Scholes pricing
• Diffusion and localization of relative strategy scores in the Minority Game