Bargaining and Communication in Games

Abstract: Chapter 2 investigates an infinitely repeated Bertrand duopoly where firms with different discount factors bargain over which collusive price and market share to implement. The bargaining is modelled as a strategic game and the main results of the paper is that it shows existence of a unique subgame perfect equilibrium and that the least patient firm's equilibrium market share is not monotone in its own discount factor. Moreover, the least patient firm may in some cases have the highest market share. However, the most patient firm will always earn the highest profit. In chapter 3 Bertrand supergames with non-binding communication are used to study price formation and stability of collusive agreements on experimental duopoly markets. The experimental design consists of three treatments with different costs of communication: zero-cost, low-cost and high-cost. Prices are found to be significantly higher when communication is costly. Moreover, costly communication decreases the number of messages, but more importantly, it enhances the stability of collusive agreements. McCutcheon (1997) presents an interesting application to antitrust policy by letting the cost of communication symbolize the presence of an antitrust law that prohibits firms from discussing prices. Although the experimental results do not support the mechanism of McCutcheon's (1997) argument, the findings point in the direction of her prediction that antitrust laws might work in the interest of firms. Chapter 4 starts out by noting that Farrell and Maskin's (1989) notion of Weak Renegotiation-Proofness (WRP) singles out marginal cost pricing in every period as a unique pure strategy equilibrium of the infinitely repeated Bertrand duopoly. This stands in stark contrast to the result of the folk theorem. Chapter 4 shows that the uniqueness result crucially depends on the approximation of the best response function. As soon as we move to a discrete strategy space, the uniqueness result breaks down and WRP does not eliminate any relevant subgame perfect equilibrium outcome. Chapter 5 experimentally investigates cooperation and non-binding communication in a two-stage game. The game has a subgame perfect equilibrium where subjects can sustain cooperation in the first stage by threatening to punish deviant behavior in the second stage. In contrast, renegotiation-proofness rules out cooperation in the first stage when intra-play communication is possible. The results provide some support for this argument. Less cooperation is observed in the first stage when intra-play communication is possible. Moreover, pre-play communication only has a significant impact on actions when intra-play communication is not allowed. The experimental design also enables us to perform an in-depth analysis of communication. Chapter 6 explores the effects of communication in market entry games experimentally. It is shown that communication increases coordination success substantially and generate inferior outcomes for consumers when market entry costs are symmetric. Such effects are not observed when costs are asymmetric, since asymmetries provide a tacit coordination cue used by experienced players (as a substitute to communication). It is also shown that although communication is used both to achieve market domination equilibria and cooperative market separating equilibria, the latter type of communication is much more common and successful.

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