6 research outputs found
On the transition to efficiency in Minority Games
The existence of a phase transition with diverging susceptibility in batch
Minority Games (MGs) is the mark of informationally efficient regimes and is
linked to the specifics of the agents' learning rules. Here we study how the
standard scenario is affected in a mixed population game in which agents with
the `optimal' learning rule (i.e. the one leading to efficiency) coexist with
ones whose adaptive dynamics is sub-optimal. Our generic finding is that any
non-vanishing intensive fraction of optimal agents guarantees the existence of
an efficient phase. Specifically, we calculate the dependence of the critical
point on the fraction of `optimal' agents focusing our analysis on three
cases: MGs with market impact correction, grand-canonical MGs and MGs with
heterogeneous comfort levels.Comment: 12 pages, 3 figures; contribution to the special issue "Viewing the
World through Spin Glasses" in honour of David Sherrington on the occasion of
his 65th birthda
Minority games, evolving capitals and replicator dynamics
We discuss a simple version of the Minority Game (MG) in which agents hold
only one strategy each, but in which their capitals evolve dynamically
according to their success and in which the total trading volume varies in time
accordingly. This feature is known to be crucial for MGs to reproduce stylised
facts of real market data. The stationary states and phase diagram of the model
can be computed, and we show that the ergodicity breaking phase transition
common for MGs, and marked by a divergence of the integrated response is
present also in this simplified model. An analogous majority game turns out to
be relatively void of interesting features, and the total capital is found to
diverge in time. Introducing a restraining force leads to a model akin to
replicator dynamics of evolutionary game theory, and we demonstrate that here a
different type of phase transition is observed. Finally we briefly discuss the
relation of this model with one strategy per player to more sophisticated
Minority Games with dynamical capitals and several trading strategies per
agent.Comment: 19 pages, 7 figure
Generating functional analysis of Minority Games with real market histories
It is shown how the generating functional method of De Dominicis can be used
to solve the dynamics of the original version of the minority game (MG), in
which agents observe real as opposed to fake market histories. Here one again
finds exact closed equations for correlation and response functions, but now
these are defined in terms of two connected effective non-Markovian stochastic
processes: a single effective agent equation similar to that of the `fake'
history models, and a second effective equation for the overall market bid
itself (the latter is absent in `fake' history models). The result is an exact
theory, from which one can calculate from first principles both the persistent
observables in the MG and the distribution of history frequencies.Comment: 39 pages, 5 postscript figures, iop styl
Statistical Mechanics of Dilute Batch Minority Games with Random External Information
We study the dynamics and statics of a dilute batch minority game with random
external information. We focus on the case in which the number of connections
per agent is infinite in the thermodynamic limit. The dynamical scenario of
ergodicity breaking in this model is different from the phase transition in the
standard minority game and is characterised by the onset of long-term memory at
finite integrated response. We demonstrate that finite memory appears at the
AT-line obtained from the corresponding replica calculation, and compare the
behaviour of the dilute model with the minority game with market impact
correction, which is known to exhibit similar features.Comment: 22 pages, 6 figures, text modified, references updated and added,
figure added, typos correcte