Price vs quantity in a duopoly supergame with Nash punishments

Abstract

We examine the endogenous choice between price and quantity behaviour in a duopoly supergame with product differentiation. We find that (i) if cartel profits are evenly split between firms, then only symmetric equilibria obtains; (i) if instead the additional profits available through collusion are split according to the Nash bargaining solution, there are parameter regions where all subgame perfect equilibria are asymmetric, with firms colluding in price-quantity supergames.JEL Classification: C72, D43, L13

Price and quantity competition in an asymmetric duopoly with licensing

“…One focus of the subsequent literature is to find under what conditions heterogeneous competition strategies-the conditions under which one firm chooses a quantity strategy and the other a price strategy-will appear in equilibrium. 3 To establish a heterogeneous-strategy equilibrium, the original model setting in Singh and Vives (1984) is modified in several ways, such as allowing collusion in the final product market (Albk & Lambertini, 2004;Baldelli & Lambertini, 2006;Lambertini, 1997;Rothschild, 1995), allowing the manager, rather than the owner of a firm, to choose a competition strategy (Dasgupta & Shin, 2004;Lambertini, 2000;Miller & Pazgal, 2001), introducing uncertainty about market demand (Klemperer & Meyer, 1986;Reisinger & Ressner, 2009), considering a mixed duopoly in which a profit-maximizing private firm competes against a welfare-maximizing public firm (Choi, 2012;Ghosh & Mitra, 2010;Matsumura & Ogawa, 2012), and making the marginal production cost endogenous by adding a vertical structure (union or input supplier) to the duopoly model (Correa-López, 2007).…”