Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minority games, evolving capitals and replicator dynamics   We discuss a simple version of the Minority Game (MG) in which agents hold
only one strategy each, but in which their capitals evolve dynamically
according to their success and in which the total trading volume varies in time
accordingly. This feature is known to be crucial for MGs to reproduce stylised
facts of real market data. The stationary states and phase diagram of the model
can be computed, and we show that the ergodicity breaking phase transition
common for MGs, and marked by a divergence of the integrated response is
present also in this simplified model. An analogous majority game turns out to
be relatively void of interesting features, and the total capital is found to
diverge in time. Introducing a restraining force leads to a model akin to
replicator dynamics of evolutionary game theory, and we demonstrate that here a
different type of phase transition is observed. Finally we briefly discuss the
relation of this model with one strategy per player to more sophisticated
Minority Games with dynamical capitals and several trading strategies per
agent.

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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys