Equilibrium Type of Competition with Horizontal Product Innovation

Singh and Vives (1984) consider a game where duopolists first commit to a strategic variable, quantity or price, and then compete in selling horizontally differentiated products. Here product substitutability is endogenized by allowing firms to undertake R&D investments to increase differentiation. This has important consequences for the determination of the equilibrium type of competition. Whereas in the original model Cournot competition always ensued in equilibrium, horizontal product innovation allows all types of market competition to be an equilibrium, depending on model parameters. As market size increases, the game of choosing the strategic variable changes structure. For small market size it is a dominance solvable game with Cournot competition as unique outcome. For higher market size, the firms face a Prisoner's Dilemma where Bertrand competition would be Pareto optimal, but Cournot competition is the non-cooperative Nash Equilibrium. As market size further increases, the game of choosing market variables becomes a Hawk-Dove game where, in pure strategy equilibrium, one firm sets quantity and the other sets price. When market size increases even further, setting prices will be the strictly dominant strategy and Bertrand competition is the unique equilibrium outcome for a relatively small parameter-range. Finally, for suffciently high market size all equilibria corresponding to differentiated duopoly abruptly dissappear and the market separates into two monopolies.