Inefficient entry order in preemption games

In a preemption game, players decide when to take an irreversible action. Delaying the action exogenously increases payoffs, but there is an early mover advantage. Riordan (1992) shows that in a preemption game with two asymmetric players, players act in decreasing order of efficiency. This provides a microfoundation to the assumption that entry in a market occurs in the order of profitability, commonly used in the empirical analysis of market entry. We provide a counterexample showing that with more than two players this intuitive result can be reversed. We present a preemption game of entry into a new market. The potential entrants are three asymmetric firms: one “efficient” firm with high post-entry profits, and two “inefficient firms”. We show that the set of parameters such that the equilibrium entry order does not reflect the efficiency ranking is nonempty, and analyse which changes in post-entry profits preserve this entry order.