On Stackelberg Equilibria with Differentiated Products: The Critical Role of the Strategy Space

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Comparing the Nash and Stackelberg equilibria in a differentiated products model under price and for quantity strategy spaces, it is shown that, whatever the role (leader, follower, Nash competitor), it is always more profitable to be a quantity (price) setter if the goods are substitutes (complements). However for the consumers price competition is always the best. Concerning total surpluses the ranking is first the Bertrand equilibrium, then the price Stackelberg, followed by the mixed Nash, the quantity Stackelberg and the Cournot equilibria for both the complement and substitute cases.