When should a firm set its selling price to cope with gray market trade?

This study investigates the problem of timing for firms that must cope with gray market in setting its prices by applying an observable delay game. We consider a case in which a multinational firm sells a product in two countries, and a parallel importer buys the product in one country and resells it in the other country. We show that the multinational firm never sets its price at the same time when the parallel importer sets in equilibrium, and that the multinational firm's optimal timing depends on the degree of variation in consumer preferences for product quality.