In this thesis, we study an agent-based trading model based on statistical mechanics. Agents with different resource capacities set the selling prices of their resources in order to compete in the market to satisfy their demands and reduce their cost functions. The price of each agent is updated by discrete gradient descent. We also consider the effects on the market due to the inventory level, which is the level of excess resource kept by the agents to buffer fluctuations in the market. When the model parameters (such as the inventory level, average capacity and learning rate) change, phase transitions of the stable solution to unstable ones arise....[ Read more ]

In this thesis, we study an agent-based trading model based on statistical mechanics. Agents with different resource capacities set the selling prices of their resources in order to compete in the market to satisfy their demands and reduce their cost functions. The price of each agent is updated by discrete gradient descent. We also consider the effects on the market due to the inventory level, which is the level of excess resource kept by the agents to buffer fluctuations in the market. When the model parameters (such as the inventory level, average capacity and learning rate) change, phase transitions of the stable solution to unstable ones arise.

Particularly, we focus on the fluctuation of prices, demands and cost of the agents in a network in the high connectivity limit. We study how the model parameters affect the dynamical behavior of the agents by simulation. In the mean field approximation, we derive the analytical stability condition of the system. We also suggest a simplified quantitative iterative model to predict the price dynamics. The validity of the iterative model is confirmed by comparison with the simulation results.

The iterative model demonstrates various interesting chaotic behaviors in systems with different model parameters. These are discussed under the framework of nonlinear dynamics. Nonlinear dynamics analyses are useful to explain the chaos in simulation results. These findings may give us insights to understand the chaos in real markets.