Michael L. Hart

Crowd effects and volatility in markets with competing agents

We present analytic and numerical results for two models, namely the minority model and the bar-attendance model, which offer simple paradigms for a competitive marketplace. Both models feature heterogeneous agents with bounded rationality who act using inductive reasoning. We find that the effects of crowding are crucial to the understanding of the macroscopic fluctuations, or ‘volatility’, in the resulting dynamics of these systems.

Application of multi-agent games to the prediction of financial time-series

We report on a technique based on multi-agent games which has potential use in the prediction of future movements of financial time series. A third-party game is trained on a black-box time series, and is then run into the future to extract next-step and multi-step predictions. In addition to the possibility of identifying profit opportunities, the technique may prove useful in the development of improved risk management strategies.

Crowd–anticrowd theory of the minority game

The Minority Game is a simple yet highly non-trivial agent-based model for a complex adaptive system. Here, we provide an explanation of the games fluctuations which is both intuitive and quantitative, and which applies over the entire parameter range of interest. The physical idea behind our theory is to describe the interplay between crowds of like-minded agents and their anticorrelated partners (anticrowds).

Activity-Dependent Exocytosis of Lysosomes Regulates the Structural Plasticity of Dendritic Spines.

Summary Lysosomes have traditionally been viewed as degradative organelles, although a growing body of evidence suggests that they can function as Ca2+ stores. Here we examined the function of these stores in hippocampal pyramidal neurons. We found that back-propagating action potentials (bpAPs) could elicit Ca2+ release from lysosomes in the dendrites. This Ca2+ release triggered the fusion of lysosomes with the plasma membrane, resulting in the release of Cathepsin B. Cathepsin B increased the activity of matrix metalloproteinase 9 (MMP-9), an enzyme involved in extracellular matrix (ECM) remodelling and synaptic plasticity. Inhibition of either lysosomal Ca2+ signaling or Cathepsin B release prevented the maintenance of dendritic spine growth induced by Hebbian activity. This impairment could be rescued by exogenous application of active MMP-9. Our findings suggest that activity-dependent exocytosis of Cathepsin B from lysosomes regulates the long-term structural plasticity of dendritic spines by triggering MMP-9 activation and ECM remodelling.

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%. The present results are not reproduced if the agents are fed a random history, thereby demonstrating the importance of memory in this system.

Generalized strategies in the minority game.

We show analytically how the fluctuations (i.e., standard deviation sigma) in the minority game can decrease below the random coin-toss limit if the agents use more general, stochastic strategies. This suppression of sigma results from a cancellation between the actions of a crowd, in which agents act collectively and make the same decision, and those of an anticrowd, in which agents act collectively by making the opposite decision to the crowd.

Dynamics of the time horizon minority game

We present numerical and analytic results for a new version of the minority game (MG) in which strategy performance is recorded over a finite time horizon. The dynamics of this time horizon minority game (THMG) exhibit many distinct features from the MG and depend strongly on whether the participants are fed real, or random, history strings. The THMG equations are equivalent to a Markov Chain, and yield exact analytic results for the volatility given a specific realization for the quenched strategy disorder.

An investigation of crash avoidance in a complex system

Complex systems can exhibit unexpected large changes, e.g. a crash in a financial market. We examine the large endogenous changes arising within a non-trivial generalization of the minority game: the grand canonical minority game. Using a Markov-Chain description, we study the many possible paths the system may take. This ‘many-worlds’ view not only allows us to predict the start and end of a crash in this system, but also to investigate how such a crash may be avoided. We find that the system can be ‘immunized’ against large changes: by inducing small changes today, much larger changes in the future can be prevented.

Managing Catastrophic Changes in a Collective

We address the important practical issue of understanding, predicting, and eventually controlling catastrophic endogenous changes in a collective. Such large internal changes arise as macroscopic manifestations of the microscopic dynamics, and their presence can be regarded as one of the defining features of an evolving complex system. We consider the specific case of a multiagent system related to the El Farol Bar model and show explicitly how the information concerning such large macroscopic changes becomes encoded in the microscopic dynamics. Our findings suggest that these large endogenous changes can be avoided either by pre-design of the collective machinery itself or in the postdesign stage via continual monitoring and occasional “vaccinations.”

Toward an Understanding of Financial Markets using Multi-agent Games

We report on our use of multi-agent games to understand financial market behavior. In addition to discussing the background to the multi-agent games themselves, we report a technique which may prove useful for forecasting future movements of financial time-series. A third-party game is trained on a black-box time-series, and is then run into the future to extract next-step and multi-step predictions. Such predictions have potential use as the basis for improved risk management and portfolio optimization strategies.