Economics Letters 117 (2012) 414–417 Contents lists available at SciVerse ScienceDirect Economics Letters journal homepage: www.elsevier.com/locate/ecolet Competition in non-linear pricing, market concentration and mergers ✩ Gabriella Chiesa a , Vincenzo Denicolò a,b,∗ a University of Bologna, Italy b University of Leicester, United Kingdom article info Article history: Received 11 May 2011 Received in revised form 3 May 2012 Accepted 22 May 2012 Available online 21 June 2012 JEL classification: L1 L4 Keywords: Non-linear pricing Market concentration Mergers Truthful equilibrium Pareto dominant equilibrium abstract We analyze a model of competition in non-linear pricing under complete information. Among the equilibria of the game, we focus on the truthful equilibrium and the equilibrium that is Pareto dominant for the firms. These coincide when there are only two firms, but differ with three or more firms. In truthful equilibria, more highly concentrated markets are always less competitive. In Pareto-dominant equilibria, by contrast, higher market concentration may intensify competition. As a result, buyers may benefit from a merger even in the absence of efficiency gains. © 2012 Elsevier B.V. All rights reserved. 1. Introduction We consider a simple model of competition in non-linear pric- ing under complete information, where N firms trade with a buyer. The literature has shown that under mild regularity conditions the equilibrium allocation is unique and efficient, but there are multi- ple equilibrium prices and profits. 1 Two equilibria stand out promi- nently: the truthful equilibrium, 2 and the equilibrium that is Pareto dominant for the firms. In this paper, we compare the comparative statics properties of these equilibria. We focus on the classic ques- tion of market concentration and mergers, analyzing the effects of the distribution and redistribution of productive capacity among firms. ✩ We thank, without implicating, Giacomo Calzolari, Gianni De Fraja, Colin Rowat and seminar audiences at the Midlands game theory workshop, EUI (Florence) and Copenhagen for useful comments. ∗ Correspondence to: Department of Economics, University of Bologna, Piazza Scaravilli 2, 40126 Bologna, Italy. E-mail addresses: gabriella.chiesa@unibo.it (G. Chiesa), vincenzo.denicolo@unibo.it, vd51@le.ac.uk (V. Denicolò). 1 See, among others, Bhaskar and To (2004), Chiesa and Denicolò (2009), O’Brien and Shaffer (1997), Spence (1976) and Spulber (1979). 2 In a truthful equilibrium all firms use truthful strategies. A strategy is truthful relative to a given action if it truly, and for all cases, reflects the player’s marginal preferences for another action relative to the given action (Bernheim and Whinston, 1986). Truthful equilibria are coalition proof. We find that while in the truthful equilibrium higher market concentration always raises profits and harms the buyer, in the Pareto dominant equilibrium it can benefit the buyer. The intuitive reason for this is that in the Pareto dominant equilibrium the two largest firms play a special disciplining role. That is, they constrain the profits that can be obtained by their competitors by threatening to replace them. Therefore, a market with two large firms and several smaller ones may be more competitive than one where all firms are symmetric. As a result, a merger that strengthens the second largest firm can benefit buyers even in the absence of efficiency gains. These findings can help justify why European antitrust authorities emphasize the difference between the market shares of the largest and the second-largest firm in their assessment of market dominance and mergers. 2. The model and preliminary results 3 N firms, indexed by i ∈ N ={1, 2,..., N }, sell a homogeneous product to a buyer, indexed by 0. Firms simultaneously submit price schedules, and the buyer then chooses the quantities he purchases from each firm. A price schedule is a function P i (x i ), where x i ≥ 0 is the quantity that firm i is willing to supply and 3 We refer the reader to Chiesa and Denicolò (2009) for omitted proofs and further details. 0165-1765/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2012.05.024