Phase transition and symmetry breaking in the minority game

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 6, 1999, Pages

  Challet, Damien ^a   Marsili, Matteo ^b  

^a UNIVERSITY OF FRIBOURG   (Switzerland)

^b INFM   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE;

EID: 0000212039     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.R6271     Document Type: Article

References (19)

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6. A strategic player has to consider, for any given strategy she can actually play, how each of her opponents would react knowing that she is playing that strategy, and how that affects her payoff. On this basis, which assumes that also her opponents behave the same, she has to find out what the best strategy is.
7. See, e.g., D. Fudenberg and J. Tirole, Game Theory (MIT Press, Cambridge, MA, 1991).
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14. An example of labeling is binary coding. (Formula presented) is then given by: (Formula presented)
15. M. Mezard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
16. A. Cavagna, Phys. Rev. E 59, R3787 (1999) has shown that replacing the dynamics of (Formula presented) by random sampling does not change, to a very good approximation, the behavior of the model. The assumption that each history (Formula presented) is sampled with the same frequency is strictly true only in the symmetric phase (Formula presented) but it holds qualitatively also for (Formula presented)
17. This approximation is justified by the fact that the “linear” minority model obtained replacing Eq. (4) by (Formula presented) gives results very similar to those presented here. An analytic derivation is also possible from the identity (Formula presented) 14.
18. D. Challet, M. Marsili, and R. Zecchina (unpublished).
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