A kinetic model for an agent based market simulation

Abstract

A kinetic model for a specific agent based simulation to generate the sales curves of successive generations of high-end computer chips is developed. The resulting continuum market model consists of transport equations in two variables, representing the availability of money and the desire to buy a new chip. In lieu of typical collision terms in the kinetic equations that discontinuously change the attributes of an agent, discontinuous changes are initiated via boundary conditions between sets of partial differential equations. A scaling analysis of the transport equations determines the different time scales that constitute the market forces, characterizing different sales scenarios. It is argued that the resulting model can be adjusted to generic markets of multi-generational technology products where the innovation time scale is an important driver of the market.

Modeling human behavior in economics and social science

“…Methods drawn from the kinetic theory have been applied in several fields of social sciences. Opinion formation is an example where these methodologies are adopted (among others, see [12,48,52,54,78,89,113,133], together with questions raised when modeling behavior of financial markets is of interest [17,67,68]. Kinetic equations with game theory type interactions was first introduced in [16], and then in [43], that extended the analysis to modeling social systems with discrete microscopic states.…”

Elastic and inelastic collisions of swarms

“…Since we are interested in the interplay between swarms and walls, we fix all the parameters in the system with the exception of λ. Specifically, we choose l = 3 4 and C = 10 9 , placing us into the parameter region labelled catastrophic in the analysis presented in [14]. For this case, the pairwise interaction potential has a well defined minimum (see Figure 1a).…”

“…The collective behavior of many self-propelled particles has been the focus of research: applications range from fish, bird, and locust swarms [1,9,11,19] to computer bots [23], pedestrian and crowd behavior [18], markets [3], and opinion dynamics [17].…”