Mean Field Equilibria of Pricing Games in Internet Marketplaces

We model an Internet marketplace using a set of servers that choose prices for performing jobs. Each server has a queue of unfinished jobs, and is penalized for delay by the market maker via a holding cost. A server completes jobs with a low or high "quality", and jobs truthfully report the quality with which they were completed. The best estimate of quality based on these reports is the "reputation" of the server. A server bases its pricing decision on the distribution of its competitors offered prices and reputations. An entering job is given a random sample of servers, and chooses the best one based on a linear combination of price and reputation. We seek to understand how prices would be determined in such a marketplace using the theory of Mean Field Games. We show the existence of a Mean Field Equilibrium and show how reputation plays a role in allowing servers to declare larger prices than their competitors. We illustrate our results by a numerical study of the system via simulation with parameters chosen from data gathered from existing Internet marketplaces.