Unique Ergodicity in the Interconnections of Ensembles with Applications to Two-Sided Markets

There has been much recent interest in two-sided markets and dynamics thereof. In a rather a general discrete-time feedback model, which we show conditions that assure that for each agent, there exists the limit of a long-run average allocation of a resource to the agent, which is independent of any initial conditions. We call this property the unique ergodicity. Our model encompasses two-sided markets and more complicated interconnections of workers and customers, such as in a supply chain. It allows for non-linearity of the response functions of market participants. It allows for uncertainty in the response of market participants by considering a set of the possible responses to either price or other signals and a measure to sample from these. Finally, it allows for an arbitrary delay between the arrival of incoming data and the clearing of a market.