Double auction mechanisms on Markovian networks

•A double auction mechanism has been studied for a class of exchange economies.•Buyers and sellers each form a time non-homogeneous Markovian chain.•Convergence results with and without noises are established.•A numerical example is given to demonstrate the formation of bubbles and crashes.

This paper studies the double auction (DA) mechanism in Ma and Li (2011) for a class of exchange economies. We extend their results to more general cases where sellers and buyers each form a complex time non-homogeneous Markovian chain, as specified in Ram et al. (2009), in the communication of their private information. A numerical example is also provided. Both bubbles and crashes are observed in the example, consistent with results of our theorems. Our example and theoretical results provide new evidence that a DA mechanism, widely utilized in real exchange markets, may contribute to the excess volatility identified in Shiller (1981) and LeRoy and Porter (1981).