A Herding Model with Preferential Attachment and Fragmentation

We introduce and solve a model that mimics the herding effect in financial markets when groups of agents share information. The number of agents in the model is growing and at each time step either (i) with probability p an incoming agent joins an existing group, or (ii) with probability 1-p a group is fragmented into individual agents. The group size distribution is found to be power-law with an exponent that depends continuously on p. A number of variants of our basic model are discussed. Comparisons are made between these models and other models of herding and random growing networks

A model for the size distribution of customer groups and businesses

We present a generalization of the dynamical model of information transmission and herd behavior proposed by Eguiluz and Zimmermann. A characteristic size of group of agents s0 is introduced. The fragmentation and coagulation rates of groups of agents are assumed to depend on the size of the group. We present results of numerical simulations and mean field analysis. It is found that the size distribution of groups of agents ns exhibits two distinct scaling behavior depending on s ≤ s0 or s > s0. For s ≤ s0, ns ∼ s-(5/2 + δ), while for s > s0, ns ∼ s-(5/2 -δ), where δ is a model parameter representing the sensitivity of the fragmentation and coagulation rates to the size of the group. Our model thus gives a tunable exponent for the size distribution together with two scaling regimes separated by a characteristic size s0. Suitably interpreted, our model can be used to represent the formation of groups of customers for certain products produced by manufacturers. This, in turn, leads to a distribution in the size of businesses. The characteristic size s0, in this context, represents the size of a business for which the customer group becomes too large to be kept happy but too small for the business to become a brand name

Minority game with arbitrary cutoffs

We study a model of a competing population of N adaptive agents, with similar capabilities, repeatedly deciding whether to attend a bar with an arbitrary cutoff L. Decisions are based upon past outcomes. The agents are only told whether the actual attendance is above or below L. For L-> N/2, the game reproduces the main features of Challet and Zhang's minority game. As L is lowered, however, the mean attendances in different runs tend to divide into two groups. The corresponding standard deviations for these two groups are very different. This grouping effect results from the dynamical feedback governing the game's time-evolution, and is not reproduced if the agents are fed a random history.Comment: 4 pages (Revtex) + 6 separate pdf figure

Non-universal scaling and dynamical feedback in generalized models of financial markets

We study self-organized models for information transmission and herd behavior in financial markets. Existing models are generalized to take into account the effect of size-dependent fragmentation and coagulation probabilities of groups of agents and to include a demand process. Non-universal scaling with a tunable exponent for the group size distribution is found in the resulting system. We also show that the fragmentation and coagulation probabilities of groups of agents have a strong influence on the average investment rate of the system

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