Exclusive Nightclubs and Lonely Hearts Columns: Non-monotone Participation in Optional Intermediation

In many decentralised markets, the traders who benefit most from an exchange do not employ intermediaries even though they can easily afford them. For other traders, those who benefit little from trade, intermediaries are too expensive. Together, these observations lead to empirically observed participation choices which are non-monotone in “type”. This paper provides a theoretical foundation for this hitherto unexplained phenomenon. We build a dynamic model, where the equilibrium bargaining share of a trader is a convex increasing function of her type. This characteristic ensures the existence of equilibria where only traders of middle type employ the intermediary, while the rest, the high and the low types, prefer to search for a trading partner directly.Keywords: Decentralised markets, Price formation, Walrasian equilibrium