1,125 research outputs found
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
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
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
Theory of Self-organized Criticality for Problems with Extremal Dynamics
We introduce a general theoretical scheme for a class of phenomena
characterized by an extremal dynamics and quenched disorder. The approach is
based on a transformation of the quenched dynamics into a stochastic one with
cognitive memory and on other concepts which permit a mathematical
characterization of the self-organized nature of the avalanche type dynamics.
In addition it is possible to compute the relevant critical exponents directly
from the microscopic model. A specific application to Invasion Percolation is
presented but the approach can be easily extended to various other problems.Comment: 11 pages Latex (revtex), 3 postscript figures included. Submitted to
Europhys. Let
On the High-dimensional Bak-Sneppen model
We report on extensive numerical simulations on the Bak-Sneppen model in high
dimensions. We uncover a very rich behavior as a function of dimensionality.
For d>2 the avalanche cluster becomes fractal and for d \ge 4 the process
becomes transient. Finally the exponents reach their mean field values for
d=d_c=8, which is then the upper critical dimension of the Bak Sneppen model.Comment: 4 pages, 3 eps figure
From Minority Games to real markets
We address the question of market efficiency using the Minority Game (MG)
model. First we show that removing unrealistic features of the MG leads to
models which reproduce a scaling behavior close to what is observed in real
markets. In particular we find that i) fat tails and clustered volatility arise
at the phase transition point and that ii) the crossover to random walk
behavior of prices is a finite size effect. This, on one hand, suggests that
markets operate close to criticality, where the market is marginally efficient.
On the other it allows one to measure the distance from criticality of real
market, using cross-over times. The artificial market described by the MG is
then studied as an ecosystem with different_species_ of traders. This clarifies
the nature of the interaction and the particular role played by the various
populations.Comment: 9 pages, 7 figures, to appear in Quantitative Financ
Topology-Induced Inverse Phase Transitions
Inverse phase transitions are striking phenomena in which an apparently more
ordered state disorders under cooling. This behavior can naturally emerge in
tricritical systems on heterogeneous networks and it is strongly enhanced by
the presence of disassortative degree correlations. We show it both
analytically and numerically, providing also a microscopic interpretation of
inverse transitions in terms of freezing of sparse subgraphs and coupling
renormalization.Comment: 4 pages, 4 figure
Strategy correlations and timing of adaptation in Minority Games
We study the role of strategy correlations and timing of adaptation for the
dynamics of Minority Games, both simulationally and analytically. Using the
exact generating functional approach a la De Dominicis we compute the phase
diagram and the behaviour of batch and on-line games with correlated
strategies, complementing exisiting replica studies of their statics. It is
shown that the timing of adaptation can be relevant; while conventional games
with uncorrelated strategies are nearly insensitive to the choice of on-line
versus batch learning, we find qualitative differences when anti-correlations
are present in the strategy assignments. The available standard approximations
for the volatility in terms of persistent order parameters in the stationary
ergodic states become unreliable in batch games under such circumstances. We
then comment on the role of oscillations and the relation to the breakdown of
ergodicity. Finally, it is discussed how the generating functional formalism
can be used to study mixed populations of so-called `producers' and
`speculators' in the context of the batch minority games.Comment: 15 pages, 13 figures, EPJ styl
Emergence of Cooperation and Organization in an Evolutionary Game
A binary game is introduced and analysed. N players have to choose one of the
two sides independently and those on the minority side win. Players uses a
finite set of ad hoc strategies to make their decision, based on the past
record. The analysing power is limited and can adapt when necessary.
Interesting cooperation and competition pattern of the society seem to arise
and to be responsive to the payoff function.Comment: 8 pages, 13 figure
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
- …