| R. Savit, R. Manuca, and R. Riolo. Adaptive competition, market e#ciency, phase transition. Phys. Rev. Lett., 82(10):2203, 1999. |
....of attendance, the volatility, becomes smaller than in the random choice game, where each agents makes either choice with probability 1 2. Coordination is achieved for memory sizes for which the dimension of the reduced strategy space is comparable to the number of agents in the system, 2 N [7, 22]. It was later pointed out that the dynamics of the game remains mostly unchanged if one replaces the string with the actual histories with a random one [4] provided that all the agents act on the same signal. Analytical studies based on this simplification has revealed many interesting ....
R. Savit, R. Manuca, and R. Riolo. Adaptive competition, market e#ciency, phase transition. Phys. Rev. Lett., 82(10):2203, 1999.
....The strategies were quenched randomlychosen Boolean functions acting on this information, the binary output determining the buy sell decision. The strategy used by any agent at any time was the one with the currently greatest point score from those at his her disposal. Numerical simulations showed [9] that while the average in time (and over the realizations of the disorder) of the total action was just an equality of buyers and sellers, due to the symmetric nature of y A strategy is an operator which acts on a set of data, referred to as the information , to yield an outcome which is a buy ....
....and reaches a minimum at a critical value of the memory m c ; it then starts to grow monotonically with m, asymptotically approaching the random value from below. This non trivial behaviour of the fluctuations was interpreted as an indication of a cooperative phase transition in the system [9, 10] (see, e.g. 11] for a introduction to phase transitions) Simulations also showed [9] that the relevant scaling variable was the reduced dimension of the space of strategies d = 2 m =N , and that the volatility scaled with the number of agents as p N . A second interesting observation was ....
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R. Savit, R. Manuca and R. Riolo 1999 Adaptive competition, market efficiency, and phase transitions Phys. Rev. Lett. 82, 2203.
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Savit, R., R. Manuca and R. Riolo, (1998), Adaptive Competition, Market Eciency and Phase Transition, Phys. Rev. Lett., vol. 82
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