Generating functional analysis of batch minority games with arbitrary strategy numbers
arXiv:cond-mat/0606448 · doi:10.1088/0305-4470/39/45/005
Abstract
Both the phenomenology and the theory of minority games (MG) with more than two strategies per agent are different from those of the conventional and extensively studied case S=2. MGs with exhibit nontrivial statistics of the frequencies with which the agents select from their available decision making strategies, with far-reaching implications. In the few theoretical MG studies with published so far, these statistics could not be calculated analytically. This prevented solution even in ergodic stationary states; equations for order parameters could only be closed approximately, using simulation data. Here we carry out a generating functional analysis of fake history batch MGs with arbitary values of , and give an analytical solution of the strategy frequency problem. This leads to closed equations for order parameters in the ergodic regime, exact expressions for strategy selection statistics, and phase diagrams. Our results find perfect confirmation in numerical simulations.
16 pages LaTex, 17 eps figures (reduced in size; for high resolution versions please see http://www.mth.kcl.ac.uk/~nima/MG_MixS)
References in corpus (9)
- Emergence of Cooperation and Organization in an Evolutionary Game
- Irrelevance of memory in the minority game
- Modeling Market Mechanism with Minority Game
- Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact
- 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
- Generating functional analysis of Minority Games with real market histories