Essays on Negotiation and Renegotiation in Bertrand Games

Abstract: This licentiate thesis consists of three separate papers that investigate the effects of negotiation and renegotiation in Bertrand games. The first paper investigates collusion in an infinitely repeated Bertrand duopoly where firms have different discount factors. In order to study how a collusive agreement is reached we model the equilibrium selection as an alternating-offer bargaining game. The main contribution of the paper is that it derives a unique subgame perfect equilibrium. Moreover, the selected equilibrium has several appealing features: First, it is efficient in the sense that it entails immediate agreement on the monopoly price. Second, the equilibrium shows how discount factors affect equilibrium market shares. A comparative statics analysis on equilibrium market shares reveals that changes in discount factors may have ambiguous effects. The second paper investigates the n-firm Bertrand game with convex costs. Dastidar (1995) has previously shown that, when firms are identical, this game has a continuum of symmetric pure-strategy Nash equilibria. This paper determines the entire set of pure-strategy Nash equilibria. However, the main contributions of this paper is that it shows existence and, under a weak auxiliary assumption, uniqueness of a Coalition-Proof Nash Equilibrium. Weak Renegotiation-Proofness singles out marginal cost pricing as the unique pure-strategy equilibrium of the infinitely repeated Bertrand duopoly. The third paper (coauthored with Erik Wengström) shows that, with a discrete strategy space, Weak Renegotiation-Proofness does, however, not eliminate any relevant subgame perfect equilibrium outcome.