Equilibrium Selling Mechanisms

Yongmin Chen

and

Ruqu Wang

We consider the equilibrium choice of selling mechanisms by competing firms. For a model where a number of sellers choose sequentially between any two selling mechanisms, there is a unique (subgame perfect) equilibrium under fairly natural assumptions about the monotonicity and differences of the two mechanisms. All sellers choose the mechanism that has the higher per-seller surplus at a critical mass number of sellers. If a mechanism is efficient or is favored by the buyer in some "strong" sense, it will be selected as the equilibrium mechanism. Otherwise, the less efficient mechanism can emerge in equilibrium, even when the number of sellers is arbitrarily large. An increase in the number of sellers need not increase the buyer's surplus, and can sometimes lead to a less efficient equilibrium mechanism. When more than two selling mechanisms are available, however, the equilibrium may no long be unique; and there are usually multiple equilibria when sellers choose selling mechanisms simultaneously.