We present a new model of dynamic Bertrand competition, where a quota is treated as an intertemporal constraint rather than as a capacity constraint as is common in the literature. The firm under a quota then can still vary the rates of exports over time provided that its total sales within the period do not exceed the quota. We show that a quota results in higher prices than a tariff of equal imports. We also show that firms never play mixed strategies, which contrasts from the result from a one-shot game, in which the only equilibrium under a quota is in mixed strategies.
dynamic Bertrand competition quotas tariffs differential game