On the study of commodity trading of agents with power utility preferences in a closed market

The commodity trading of agents is considered in a closed market. Suppose that agents are divided into groups A and B, who possess different trading strategies and commodity preference, which is characterized by power utility function on the basis of price theory. Assume that the agents in group A do not take any measures in the transaction, but allow the agents in group B to take appropriate actions on the percentage of traded goods to obtain the maximum utility from the transaction. We discuss the effects of agents’ transaction policies on price of goods. A nonlinear Boltzmann type system for the distribution of commodity is used to discuss the pricing problem of commodity exchange. We obtain a steady state solution of the Fokker–Planck equation under a special case. Through numerical experiments, the effects of wealth involving different parameters on price evolution are analyzed. It is illustrated how the agent’s strategy in group B changes commodity prices when the agents in group B take appropriate actions on the percentage of traded goods.