A Price Stabilization Model in Networks

We consider a multiagent network model consisting of nodes and edges as cities and their links to neighbors, respectively. Each network node has an agent and priced goods and the agent can buy or sell goods in the neighborhood. Though every node may not have an equal price, we show the prices will reach an equilibrium by iterating buy and sell operations. First, we present a protocol model in which each buying agent makes a bid to the lowest priced goods in the neighborhood; and each selling agent selects the highest bid, if any. Second, we derive a sufficient condition which stabilizes price in our model. We also show the equilibrium price can be derived from the total funds and the total goods for any network. This is a special case of the Fisher’s quantity equation, thus we can confirm the correctness of our model. We then examine the best bidding strategy is available to our protocol. Third, we analyze stabilization time for path and cycle networks. Finally, we perform simulation experiments for estimating the stabilization time, the number of bidders and the effects of spreading funds. Our model is suitable for investigating the effects of network topologies on price stabilization.