Combining the endogenous choice of price/quantity and timing

This paper builds a theory of endogenous role distribution (leader, follower, and Nash player) and of endogenous choice for the type of competition strategy (price and quantity) in a product differentiated duopoly model. We examine an extended game by adding a pre-play stage in which duopoly firms simultaneously decide whether to select a price contract or a quantity contract and also whether to move in the first period or in the second period before market competition. We demonstrate that the unique equilibrium outcome is simultaneous quantity competition if the goods are substitutes and simultaneous price competition if the goods are complements.