Mixed population Minority Game with generalized strategies

We present a quantitative theory, based on crowd effects, for the market volatility in a Minority Game played by a mixed population. Below a critical concentration of generalized strategy players, we find that the volatility in the crowded regime remains above the random coin-toss value regardless of the "temperature" controlling strategy use. Our theory yields good agreement with numerical simulations.Comment: Revtex file + 3 figure

Deterministic Dynamics in the Minority Game

The Minority Game (MG) behaves as a stochastically perturbed deterministic system due to the coin-toss invoked to resolve tied strategies. Averaging over this stochasticity yields a description of the MG's deterministic dynamics via mapping equations for the strategy score and global information. The strategy-score map contains both restoring-force and bias terms, whose magnitudes depend on the game's quenched disorder. Approximate analytical expressions are obtained and the effect of `market impact' discussed. The global-information map represents a trajectory on a De Bruijn graph. For small quenched disorder, an Eulerian trail represents a stable attractor. It is shown analytically how anti-persistence arises. The response to perturbations and different initial conditions are also discussed.Comment: 16 pages, 5 figure

From market games to real-world markets

This paper uses the development of multi-agent market models to present a unified approach to the joint questions of how financial market movements may be simulated, predicted, and hedged against. We examine the effect of different market clearing mechanisms and show that an out-of-equilibrium clearing process leads to dynamics that closely resemble real financial movements. We then show that replacing the `synthetic' price history used by these simulations with data taken from real financial time-series leads to the remarkable result that the agents can collectively learn to identify moments in the market where profit is attainable. We then employ the formalism of Bouchaud and Sornette in conjunction with agent based models to show that in general risk cannot be eliminated from trading with these models. We also show that, in the presence of transaction costs, the risk of option writing is greatly increased. This risk, and the costs, can however be reduced through the use of a delta-hedging strategy with modified, time-dependent volatility structure.Comment: Presented at APFA2 (Liege) July 2000. Proceedings: Eur. Phys. J. B Latex file + 10 .ps figs. [email protected]

The effect of short ray trajectories on the scattering statistics of wave chaotic systems

In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system specific information into the statistical model, such as the introduction of the average scattering matrix in the Poisson kernel. Here it is shown that the average impedance matrix, which also characterizes the system-specific properties, can be expressed in terms of classical trajectories that travel between ports and thus can be calculated semiclassically. Theoretical results are compared with numerical solutions for a model wave-chaotic system

Crowd-Anticrowd Theory of Multi-Agent Market Games

We present a dynamical theory of a multi-agent market game, the so-called Minority Game (MG), based on crowds and anticrowds. The time-averaged version of the dynamical equations provides a quantitatively accurate, yet intuitively simple, explanation for the variation of the standard deviation (`volatility') in MG-like games. We demonstrate this for the basic MG, and the MG with stochastic strategies. The time-dependent equations themselves reproduce the essential dynamics of the MG.Comment: Presented at APFA2 (Liege) July 2000. Proceedings: Eur.Phys.J. B [email protected]

Scattering a pulse from a chaotic cavity: Transitioning from algebraic to exponential decay

The ensemble averaged power scattered in and out of lossless chaotic cavities decays as a power law in time for large times. In the case of a pulse with a finite duration, the power scattered from a single realization of a cavity closely tracks the power law ensemble decay initially, but eventually transitions to an exponential decay. In this paper, we explore the nature of this transition in the case of coupling to a single port. We find that for a given pulse shape, the properties of the transition are universal if time is properly normalized. We define the crossover time to be the time at which the deviations from the mean of the reflected power in individual realizations become comparable to the mean reflected power. We demonstrate numerically that, for randomly chosen cavity realizations and given pulse shapes, the probability distribution function of reflected power depends only on time, normalized to this crossover time.Comment: 23 pages, 5 figure

Enhanced winnings in a mixed-ability population playing a minority game

We study a mixed population of adaptive agents with small and large memories, competing in a minority game. If the agents are sufficiently adaptive, we find that the average winnings per agent can exceed that obtainable in the corresponding pure populations. In contrast to the pure population, the average success rate of the large-memory agents can be greater than 50 percent. The present results are not reproduced if the agents are fed a random history, thereby demonstrating the importance of memory in this system.Comment: 9 pages Latex + 2 figure