Generating functional analysis of batch minority games with arbitrary strategy numbers
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Publication:3419345
DOI10.1088/0305-4470/39/45/005zbMATH Open1148.91315arXivcond-mat/0606448OpenAlexW3104473354MaRDI QIDQ3419345
Publication date: 6 February 2007
Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/cond-mat/0606448
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