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 pice, and then compete in selling horizontally differentiated products. Here product substitutability is endogenized by allowing firms to undertake R&D investments to increase differentitation. 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 chossing the strategic competition as unique outcome. For higher market size, the firms face A Prisoner's Dilemma where Bertrand competion would be Pareto optimal, but Cournot competition is the non-cooperative Nash Equilibrium. As market size further increases, the game of ch\ooing market variables becomes a Hawk-Dove game where, in pure strategy equilibrium, one firm sets quanitity and the other sets price. When makret size increase 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 sufficiently high makret size all equilibria corresponding to differentiated duopoly abruptly disappear and market separates into two monopolies.