Topology for dominance for network of multi-agent system

The resource allocation problem in evolving two-dimensional point patterns is investigated for the existence of good strategies for the construction of initial configuration that leads to fast dominance of the pattern by one single species, which can be interpreted as market dominance by a company in the context of multi-agent systems in econophysics. For hexagonal lattice, certain special topological arrangements of the resource in two-dimensions, such as rings, lines and clusters have higher probability of dominance, compared to random pattern. For more complex networks, a systematic way to search for a stable and dominant strategy of resource allocation in the changing environment is found by means of genetic algorithm. Five typical features can be summarized by means of the distribution function for the local neighborhood of friends and enemies as well as the local clustering coefficients: (1)The winner has more triangles than the loser has. (2) The winner likes to form clusters as the winner tends to connect with other winner rather than with losers; while the loser tends to connect with winners rather than losers. (3) The distribution function of friends as well as enemies for the winner is broader than the corresponding distribution function for the loser. (4) The connectivity at which the peak of the distribution of friends for the winner occurs is larger than that of the loser; while the peak values for friends for winners is lower. (5) The connectivity at which the peak of the distribution of enemies for the winner occurs is smaller than that of the loser; while the peak values for enemies for winners is lower. These five features appear to be general, at least in the context of two-dimensional hexagonal lattices of various sizes, hierarchical lattice, Voronoi diagrams, as well as high-dimensional random networks. These general local topological properties of networks are relevant to strategists aiming at dominance in evolving patterns when the interaction between the agents is local.