Narrow Results

We developed a mean-field approach to the Minority Game, that allows us to reproduce the behavior of the model in the phase in which a so-called "dynamics of period two" is present. This dynamics describes the situation where the model is controlled by the presence of crowds of agents participating in the game. Our approach is based on the hypothesis that we can introduce states representative of the system, in such a form that averages over time can be replaced by averages over those states. The main idea is to work with virtual agents, rather than working with the actual set of agents of a particular game. Virtual agents are built from all the possible pairs of the strategies available in the model (the Full Strategy Space FSS). Moreover, we define an ensemble of microstates and, thereafter, states compatible with the specifications of the game. In this work we explain in detail how to introduce these elements, and how to actually calculate the ensemble of states and microstates. We have developed one generalization of the Minority Game as an attempt to make the model more realistic, by introducing interactions among the agents. We also discuss and explain the adequate ensemble of states and microstates for that generalization.

We develop an asset pricing model based on the interaction of heterogeneous trading groups. In addition to the two main trader groups, fundamentalists and trend-chasing chartists, we include a third significant group known as contrarian chartists. We model the case of opportunistic contrarian behavior, where the contrarian group disagrees with the trend-chasing chartists only when the return differential is high. We also consider absolute contrarian behavior, in which the contrarians consistently disagree with trend-chasers. The models are nonlinear planar maps, exhibiting period doubling, Neimark–Sacker and global bifurcations leading to local chaotic behavior. Absolute contrarian behavior is found to have a moderating effect on price change, while opportunistic contrarian behavior is found to further complicate the price cycles present in other models.

New continuous and stochastic extensions of the Minority Game, devised as a fundamental model for a market of competitive agents, are introduced and studied in the context of statistical physics. The new formulation reproduces the key features of the original model, without the need for some of its special assumptions and, most importantly, it demonstrates the crucial role of stochastic decision-making. Furthermore, this formulation provides the exact but novel nonlinear equations for the dynamics of the system.

The finding of clustered volatility and ARCH effects is ubiquitous in financial data. This paper presents a possible explanation for this phenomenon within a multi-agent framework of speculative activity. In the model, both chartist and fundamentalist strategies are considered with agents switching between both behavioural variants according to observed differences in pay-offs. Price changes are brought about by a market maker reacting to imbalances between demand and supply. Most of the time, a stable and efficient market results. However, its usual tranquil performance is interspersed by sudden transient phases of destabilisation. An outbreak of volatility occurs if the fraction of agents using chartist techniques surpasses a certain threshold value, but such phases are quickly brought to an end by stabilising tendencies. Formally, this pattern can be understood as an example of a new type of dynamic behaviour known as "on-off intermittency" in physics literature. Statistical analysis of simulated time series shows that the main stylised facts (unit roots in levels together with heteroscedasticity and leptokurtosis of returns) can be found in this "artificial" market.

We consider a generalization of replicator dynamics as a non-cooperative evolutionary game-theoretic model of a community of N agents. All agents update their individual mixed strategy profiles to increase their total payoff from the rest of the community. The properties of attractors in this dynamics are studied. Evidence is presented that under certain conditions the typical attractors of the system are corners of state space where each agent has specialized to a pure strategy, and/or the community exhibits diversity, i.e., all strategies are represented in the final states. The model suggests that new pure strategies whose payoff matrix elements satisfy suitable inequalities with respect to the existing ones can destabilize existing attractors if N is sufficiently large, and be regarded as innovations that enhance the diversity of the community.