In many decentralised markets, the traders who benefit most from an exchange
do not employ intermediaries even though they could easily afford them.
At the same time, employing intermediaries is not worthwhile for traders who
benefit little from trade. Together, these decisions amount to non-monotone
participation choices in intermediation: only traders of middle “type” employ
intermediaries, while the rest, the high and the low types, prefer to search for
a trading partner directly. We provide a theoretical foundation for this, hitherto
unexplained, phenomenon. We build a dynamic matching model, where
a trader’s equilibrium bargaining share is a convex increasing function of her
type. We also show that this is indeed a necessary condition for the existence
of non-monotone equilibria
