Competing resource allocation in two-dimension

Strategies of resource allocation for companies competing in a metropolis can be investigated in the context of statistical physics using the technique of Monte Carlo simulation. In this paper we focus on several topological arrangements for two competing companies in a hexagonal world. We have investigated six classes of patterns: random graph, random walk, clusters, straight lines, small rings, and big rings. The aim of each company is to find the best strategy of initial distribution of resource to achieve market dominance in the shortest time. Two measures of the fitness of the configuration are introduced. The first one measures the speed of one company to achieve dominance with a given percentage of market share. The second one measures the market share by the dominant company within a fixed period (in terms of Monte Carlo steps) of evolution. Numerical simulations indicate that initial patterns with certain topological properties do evolve faster to market dominance.