440 research outputs found
Continuum time limit and stationary states of the Minority Game
We discuss in detail the derivation of stochastic differential equations for
the continuum time limit of the Minority Game. We show that all properties of
the Minority Game can be understood by a careful theoretical analysis of such
equations. In particular, i) we confirm that the stationary state properties
are given by the ground state configurations of a disordered (soft) spin
system; ii) we derive the full stationary state distribution; iii) we
characterize the dependence on initial conditions in the symmetric phase and
iv) we clarify the behavior of the system as a function of the learning rate.
This leaves us with a complete and coherent picture of the collective behavior
of the Minority Game. Strikingly we find that the temperature like parameter
which is introduced in the choice behavior of individual agents turns out to
play the role, at the collective level, of the inverse of a thermodynamic
temperature.Comment: Revised version (several new results added). 12 pages, 5 figure
Reply to Comment on ``Thermal Model for Adaptive Competition in a Market''
We reply to the Comment of Challet et al. [cond-mat/0004308] on our paper
[Phys. Rev. Lett. 83, 4429 (1999)]. We show that the claim of the Comment that
the effects of the temperature in the Thermal Minority Game ``can be eliminated
by time rescaling'' and consequently the behaviour is ``independent of T'' has
no general validity.Comment: 1 page, 1 figur
Generalized strategies in the Minority Game
We show analytically how the fluctuations (i.e. standard deviation) in the
Minority Game (MG) can be made to decrease below the random coin-toss limit if
the agents use more general behavioral strategies. This suppression of the
standard deviation results from a cancellation between the actions of a crowd,
in which agents act collectively and make the same decision, and an anticrowd
in which agents act collectively by making the opposite decision to the crowd.Comment: Revised manuscript: a few minor typos corrected. Results unaffecte
Criticality and finite size effects in a simple realistic model of stock market
We discuss a simple model based on the Minority Game which reproduces the
main stylized facts of anomalous fluctuations in finance. We present the
analytic solution of the model in the thermodynamic limit and show that
stylized facts arise only close to a line of critical points with non-trivial
properties. By a simple argument, we show that, in Minority Games, the
emergence of critical fluctuations close to the phase transition is governed by
the interplay between the signal to noise ratio and the system size. These
results provide a clear and consistent picture of financial markets as critical
systems.Comment: 4 pages, 4 figure
Trading behavior and excess volatility in toy markets
We study the relation between the trading behavior of agents and volatility
in toy markets of adaptive inductively rational agents. We show that excess
volatility, in such simplified markets, arises as a consequence of {\em i)} the
neglect of market impact implicit in price taking behavior and of {\em ii)}
excessive reactivity of agents. These issues are dealt with in detail in the
simple case without public information. We also derive, for the general case,
the critical learning rate above which trading behavior leads to turbulent
dynamics of the market.Comment: 14 pages, 4 figures, minor change
Minority Game of price promotions in fast moving consumer goods markets
A variation of the Minority Game has been applied to study the timing of
promotional actions at retailers in the fast moving consumer goods market. The
underlying hypotheses for this work are that price promotions are more
effective when fewer than average competitors do a promotion, and that a
promotion strategy can be based on past sales data. The first assumption has
been checked by analysing 1467 promotional actions for three products on the
Dutch market (ketchup, mayonnaise and curry sauce) over a 120-week period, both
on an aggregated level and on retailer chain level.
The second assumption was tested by analysing past sales data with the
Minority Game. This revealed that high or low competitor promotional pressure
for actual ketchup, mayonnaise, curry sauce and barbecue sauce markets is to
some extent predictable up to a forecast of some 10 weeks. Whereas a random
guess would be right 50% of the time, a single-agent game can predict the
market with a success rate of 56% for a 6 to 9 week forecast. This number is
the same for all four mentioned fast moving consumer markets. For a multi-agent
game a larger variability in the success rate is obtained, but predictability
can be as high as 65%.
Contrary to expectation, the actual market does the opposite of what game
theory would predict. This points at a systematic oscillation in the market.
Even though this result is not fully understood, merely observing that this
trend is present in the data could lead to exploitable trading benefits. As a
check, random history strings were generated from which the statistical
variation in the game prediction was studied. This shows that the odds are
1:1,000,000 that the observed pattern in the market is based on coincidence.Comment: 19 pages, 10 figures, accepted for publication in Physica
Irrelevance of memory in the minority game
By means of extensive numerical simulations we show that all the distinctive
features of the minority game introduced by Challet and Zhang (1997), are
completely independent from the memory of the agents. The only crucial
requirement is that all the individuals must posses the same information,
irrespective of the fact that this information is true or false.Comment: 4 RevTeX pages, 4 figure
Thermal treatment of the minority game
We study a cost function for the aggregate behavior of all the agents
involved in the Minority Game (MG) or the Bar Attendance Model (BAM). The cost
function allows to define a deterministic, synchronous dynamics that yields
results that have the main relevant features than those of the probabilistic,
sequential dynamics used for the MG or the BAM. We define a temperature through
a Langevin approach in terms of the fluctuations of the average attendance. We
prove that the cost function is an extensive quantity that can play the role of
an internal energy of the many agent system while the temperature so defined is
an intensive parameter. We compare the results of the thermal perturbation to
the deterministic dynamics and prove that they agree with those obtained with
the MG or BAM in the limit of very low temperature.Comment: 9 pages in PRE format, 6 figure
Multi-market minority game: breaking the symmetry of choice
Generalization of the minority game to more than one market is considered. At
each time step every agent chooses one of its strategies and acts on the market
related to this strategy. If the payoff function allows for strong fluctuation
of utility then market occupancies become inhomogeneous with preference given
to this market where the fluctuation occured first. There exists a critical
size of agent population above which agents on bigger market behave
collectively. In this regime there always exists a history of decisions for
which all agents on a bigger market react identically.Comment: 15 pages, 12 figures, Accepted to 'Advances in Complex Systems
Generating Functional Analysis of the Dynamics of the Batch Minority Game with Random External Information
We study the dynamics of the batch minority game, with random external
information, using generating functional techniques a la De Dominicis. The
relevant control parameter in this model is the ratio of the
number of possible values for the external information over the number
of trading agents. In the limit we calculate the location
of the phase transition (signaling the onset of anomalous response),
and solve the statics for exactly. The temporal correlations
in global market fluctuations turn out not to decay to zero for infinitely
widely separated times. For the stationary state is shown to
be non-unique. For we analyse our equations in leading order in
, and find asymptotic solutions with diverging volatility
\sigma=\order(\alpha^{-{1/2}}) (as regularly observed in simulations), but
also asymptotic solutions with vanishing volatility
\sigma=\order(\alpha^{{1/2}}). The former, however, are shown to emerge only
if the agents' initial strategy valuations are below a specific critical value.Comment: 15 pages, 6 figures, uses Revtex. Replaced an old version of
volatility graph that. Rephrased and updated some reference
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