Equilibrium bidding protocols for price stabilization 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 can show the prices will reach an equilibrium by iterating buy and sell operations. First, we present a framework of protocols 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). In this situation, the number of bidding agents is uncertain if several selling agents exist in the neighborhood. Just like a usual auction, each agent has a value of goods and decides a bidding price from it. We apply equilibrium bidding strategies for the first-price auction and the second-price auction to our framework. called a first-price protocol and a second-price protocol, respectively. Though the best bidding strategies are derived from Bayesian-Nash equilibrium, which assumes the certain number of bidding agents in contrast to our model. So we consider an expected number of bidding agents by assuming their values are uniformly distributed over (0,1). Next, we examine whether or not the prices reach an equilibrium for the protocols. Finally, we show the second-price protocol outperforms the first-price protocol from a fund-spreading point of view. Our results have an application to a monetary policy and a management using agent information.