338 research outputs found
The Local Minority Game
Ecologists and economists try to explain collective behavior in terms of
competitive systems of selfish individuals with the ability to learn from the
past. Statistical physicists have been investigating models which might
contribute to the understanding of the underlying mechanisms of these systems.
During the last three years one intuitive model, commonly referred to as the
Minority Game, has attracted broad attention. Powerful yet simple, the minority
game has produced encouraging results which can explain the temporal behaviour
of competitive systems. Here we switch the interest to phenomena due to a
distribution of the individuals in space. For analyzing these effects we modify
the Minority Game and the Local Minority Game is introduced. We study the
system both numerically and analytically, using the customary techniques
already developped for the ordinary Minority Game
How does informational heterogeneity affect the quality of forecasts?
We investigate a toy model of inductive interacting agents aiming to forecast
a continuous, exogenous random variable E. Private information on E is spread
heterogeneously across agents. Herding turns out to be the preferred
forecasting mechanism when heterogeneity is maximal. However in such conditions
aggregating information efficiently is hard even in the presence of learning,
as the herding ratio rises significantly above the efficient-market expectation
of 1 and remarkably close to the empirically observed values. We also study how
different parameters (interaction range, learning rate, cost of information and
score memory) may affect this scenario and improve efficiency in the hard
phase.Comment: 11 pages, 5 figures, updated version (to appear in Physica A
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
Theory of the Three-Group Evolutionary Minority Game
Based on the adiabatic theory for the evolutionary minority game (EMG) that
we proposed earlier[1], we perform a detail analysis of the EMG limited to
three groups of agents. We derive a formula for the critical point of the
transition from segregation (into opposing groups) to clustering (towards
cautious behaviors). Particular to the three-group EMG, the strategy switching
in the "extreme" group does not occur at every losing step and is strongly
intermittent. This leads to an correction to the critical value of the number
of agents at the transition, . Our expression for is in agreement
with the results obtained from our numerical simulations.Comment: 4 pages and 2 figure
News and price returns from threshold behaviour and vice-versa: exact solution of a simple agent-based market model
Starting from an exact relationship between news, threshold and price return
distributions in the stationary state, I discuss the ability of the
Ghoulmie-Cont-Nadal model of traders to produce fat-tailed price returns. Under
normal conditions, this model is not able to transform Gaussian news into
fat-tailed price returns. When the variance of the news so small that only the
players with zero threshold can possibly react to news, this model produces
Levy-distributed price returns with a -1 exponent. In the special case of
super-linear price impact functions, fat-tailed returns are obtained from
well-behaved news.Comment: 4 pages, 3 figures. This is quite possibly the final version. To
appear in J. Phys
Self-Segregation vs. Clustering in the Evolutionary Minority Game
Complex adaptive systems have been the subject of much recent attention. It
is by now well-established that members (`agents') tend to self-segregate into
opposing groups characterized by extreme behavior. However, while different
social and biological systems manifest different payoffs, the study of such
adaptive systems has mostly been restricted to simple situations in which the
prize-to-fine ratio, , equals unity. In this Letter we explore the dynamics
of evolving populations with various different values of the ratio , and
demonstrate that extreme behavior is in fact {\it not} a generic feature of
adaptive systems. In particular, we show that ``confusion'' and
``indecisiveness'' take over in times of depression, in which case cautious
agents perform better than extreme ones.Comment: 4 pages, 4 figure
Temporal oscillations and phase transitions in the evolutionary minority game
The study of societies of adaptive agents seeking minority status is an
active area of research. Recently, it has been demonstrated that such systems
display an intriguing phase-transition: agents tend to {\it self-segregate} or
to {\it cluster} according to the value of the prize-to-fine ratio, . We
show that such systems do {\it not} establish a true stationary distribution.
The winning-probabilities of the agents display temporal oscillations. The
amplitude and frequency of the oscillations depend on the value of . The
temporal oscillations which characterize the system explain the transition in
the global behavior from self-segregation to clustering in the case.Comment: 5 pages, 5 figure
Theory of Phase Transition in the Evolutionary Minority Game
We discover the mechanism for the transition from self-segregation (into
opposing groups) to clustering (towards cautious behaviors) in the evolutionary
minority game (EMG). The mechanism is illustrated with a statistical mechanics
analysis of a simplified EMG involving three groups of agents: two groups of
opposing agents and one group of cautious agents. Two key factors affect the
population distribution of the agents. One is the market impact (the
self-interaction), which has been identified previously. The other is the
market inefficiency due to the short-time imbalance in the number of agents
using opposite strategies. Large market impact favors "extreme" players who
choose fixed strategies, while large market inefficiency favors cautious
players. The phase transition depends on the number of agents (), the
reward-to-fine ratio (), as well as the wealth reduction threshold () for
switching strategy. When the rate for switching strategy is large, there is
strong clustering of cautious agents. On the other hand, when is small, the
market impact becomes large, and the extreme behavior is favored.Comment: 5 pages and 3 figure
Structure-preserving desynchronization of minority games
Perfect synchronicity in -player games is a useful theoretical dream, but
communication delays are inevitable and may result in asynchronous
interactions. Some systems such as financial markets are asynchronous by
design, and yet most theoretical models assume perfectly synchronized actions.
We propose a general method to transform standard models of adaptive agents
into asynchronous systems while preserving their global structure under some
conditions. Using the Minority Game as an example, we find that the phase and
fluctuations structure of the standard game subsists even in maximally
asynchronous deterministic case, but that it disappears if too much
stochasticity is added to the temporal structure of interaction. Allowing for
heterogeneous communication speeds and activity patterns gives rise to a new
information ecology that we study in details.Comment: 6 pages, 7 figures. New version removed a section and found a new
phase transitio
Kolkata Restaurant Problem as a generalised El Farol Bar Problem
Generalisation of the El Farol bar problem to that of many bars here leads to
the Kolkata restaurant problem, where the decision to go to any restaurant or
not is much simpler (depending on the previous experience of course, as in the
El Farol bar problem). This generalised problem can be exactly analysed in some
limiting cases discussed here. The fluctuation in the restaurant service can be
shown to have precisely an inverse cubic behavior, as widely seen in the stock
market fluctuations.Comment: 2 column RevTeX4, 4 pages, 3 eps figs; to be published in
'Econophysics of Markets and Business Networks', [Proc. Econophys-Kolkata
III], Eds. A. Chatterjee, B. K. Chakrabarti, New Economic Windows Series,
Springer, Milan, 2007, pp. 220-22
- …