An interesting problem in econophyiscs addresses the problem of resource allocation with the objective of maximizing the market share. The resource of each company is limited so that the problem of resource allocation is strategically important for the future evolution of its market share. We investigate various strategic locations of shops in shopping malls in a metropolis with the aim of finding the best strategy for final dominance of market share by a company in a competing environment. The problem is posed in the context of two competing supermarket chains in a metropolis, described in the framework of the two-dimensional Ising model. Evolutionary Algorithm is used to encode the ensemble of initial configurations and Monte Carlo method is used to evolve the pattern. Numerical simul...[ Read more ]

An interesting problem in econophyiscs addresses the problem of resource allocation with the objective of maximizing the market share. The resource of each company is limited so that the problem of resource allocation is strategically important for the future evolution of its market share. We investigate various strategic locations of shops in shopping malls in a metropolis with the aim of finding the best strategy for final dominance of market share by a company in a competing environment. The problem is posed in the context of two competing supermarket chains in a metropolis, described in the framework of the two-dimensional Ising model. Evolutionary Algorithm is used to encode the ensemble of initial configurations and Monte Carlo method is used to evolve the pattern. Numerical simulation indicates that initial patterns with certain topological properties do evolve faster to market dominance. The description of these topological properties is given and suggestions are made on the initial pattern so as to evolve faster to market dominance. We extend our investigation on the three competing companies in the context of two-dimensional three state Potts model in statistical physics. The aim of each company is to find the best strategy of initial distribution of resource to achieve market dominance in a shortest time. The fitness of the configuration is measured by the market share of a chosen company after a fixed number of Monte Carlo steps of evolution. Numerical simulation indicates that initial patterns with certain topological properties do evolve faster to market dominance. The description of these topological properties is measured by the degree distribution of each company. Insight on the initial patterns that entail fast dominance is discussed.