Non-robustness of the cash-in-advance equilibrium in the trading post model

The main justification for cash-in-advance (CIA) equilibria when there are multiple assets is a Shapley-Shubik trading-post model where the agents coordinate on a particular medium of exchange. Of course, there are other equilibria. We introduce a refinement and show that the CIA equilibrium does not satisfy our refinement while there exist equilibria that do.