Equilibrium Distribution of Agents by Types in a Market, and Existence of Power Laws

This paper considers a market in which shares of a single asset is traded by agents with many strategies. The market behavior is examined by regarding clusters of agents with same trading rules as random combinatorial partitions of agents by types. The equilibrium distribution is shown to be the Ewens sampling formula. When agents are positively correlated, it is shown that a small number of groupings such as two types of agents dominate the markets. Distributions for large price difference or return are shown to be power-laws if a certain set of conditions is satisfied.