Collusive Agreements in Vertically Differentiated Markets

Marini, Marco A. (2016): Collusive Agreements in Vertically Differentiated Markets. Forthcoming in: Handbook in Game Theory and Industrial Organization (1 June 2017)

Abstract

This survey introduces a number of game-theoretic tools to model collusive agreements among firms in vertically differentiated markets. I firstly review some classical literature on collusion between two firms producing goods of exogenous different qualities. I then extend the analysis to a n-firm vertically differentiated market to study the incentive to form either a whole market alliance or partial alliances made of subsets of consecutive firms in order to collude in prices. Within this framework I explore the price behaviour of groups of colluding firms and their incentive to either pruning or proliferating their products. It is shown that a selective pruning within the cartel always occurs. Moreover, by associating a partition function game to the n-firm vertically differentiated market, it can be shown that a sufficient condition for the cooperative (or coalitional) stability of the whole industry cartel is is the equidistance of firms' products along the quality spectrum. Without this property, and in presence of large quality differences, collusive agreements easily loose their stability. In addition, introducing a standard infinitely repeated-game approach, I show that an increase in the number of firms in the market may have contradictory effects on the incentive of firms to collude: it can make collusion easier for bottom and intermediate firms and harder for the top quality firm. Finally, by means of a three-firm example, I consider the case in which alliances can set endogenously qualities, prices and number of variants on sale. I show that, in every formed coalition, (i) market pruning dominates product proliferation and (ii) partial cartelisation always arises in equilibrium, with the bottom quality firm always belonging to the alliance.

• Item Type: MPRA Paper
• Language: English
• Keywords: Vertically differentiated market, price collusion, product pruning, product proliferation, endogenous qualities, endogenous alliance formation, coalition structures, grand coalition, coalition stability, core, simultaneous and sequential game of coalition formation.
• Subjects: L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L12 - Monopoly ; Monopolization Strategies; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets; L - Industrial Organization > L2 - Firm Objectives, Organization, and Behavior; L - Industrial Organization > L2 - Firm Objectives, Organization, and Behavior > L22 - Firm Organization and Market Structure

References

Berry, S. and J. Waldfogel, (2001). "Do Mergers increase product varieties", Quarterly Journal of Economics, 116, 1009-1025.

Bloch, F. (1995). "Endogenous Structures of Associations in Oligopolies", Rand Journal of Economics, 26, 537-556.

Bloch, F. (1996). "Sequential Formation of Coalitions with Fixed Payoff Division", Games and Economic Behaviour, 14, 90-123.

Bloch, F, van den Nouweland, A., (2014) "Expectation Formation Rules and the Core of Partition Function Games", Games and Economic Behavior, 88, 339-353.

Bos, I., Marini, M. A. (2016), "Sustaining Price Collusion in Vertically Differentiated Oligopolies", mimeo.

Byrne, D. P., (2015),"The impact of consolidation on cable TV prices and product quality", International Economic Review, 56, 805-850.

Brekke, K. R., Siciliani, L., Straume, O. R. (2014), "Horizontal Mergers and Product Quality", NHH Discussion Paper, February 2014.

Caplow, T. (1956). "A Theory of Coalitions in the Triad", American Sociological Review, 21, 489-493.

Caplow, T. (1959). "A Theory of Coalitions in the Triad", American Journal of Sociology, 64, 488-493.

Caplow, T. (1968). Two Against One: Coalitions in Triads, Prentice-Hall, Englewood Cliff, NJ.

Cesi, B., (2010), "Mergers under Minimum Quality Standard: a Note", Economics Bulletin, 30, 4, 3260-66.

Chen Y. and M. Schwartz (2013), "Product Innovation Incentives: Monopoly vs. Competition", Journal of Economics & Management Strategy, 22, 3, 513-528.

Chu, C. S., "The Effect of Satellite Entry on Cable Television Prices and Product Quality", RAND Journal of Economics, 2010, 41, 730-764.

Crawford, G. S., Shum, M. (2006), "The Welfare Effects of Endogenous Quality Choice: the Case of Cable Television", mimeo, University of Arizona.

Currarini, S., M. A., Marini, (2015) "Coalitional Approaches to Collusive Agreements in Oligopoly Games", The Manchester School, 83, 3, 253-287.

Demange, G. (1994), "Intermediate preferences and stable coalition structures", Journal of Mathematical Economics, 23, 45-58.

Deneckere, R. and Davidson, C., (1985), "Incentive to form coalitions with Bertrand competition", Rand Journal of Economics, 16 , pp.473-486.

Draganska, M., Mazzeo, M., Seim, K., (2009) "Beyond Plain Vanilla: Modeling Joint Product Assortment and Pricing Decisions", Quantitative Marketing and Economics, 7, 105-146.

Ecchia, G. and L. Lambertini (1997), "Minimum Quality Standards and Collusion," Journal of Industrial Economics, 45, 1, 101-13.

Einav, L. (2010) "Not all Rivals Look Alike: Estimating an equilibrium Model of the Release Date Timing Game", Economic Inquiry, 48, 2, 369--390.

Fan, Y. (2013), "Ownership consolidation and product characteristics: A study of the U.S. daily newspaper market", American Economic Review, 103, 1598--1628.

Friedman, J.W. (1989), Game Theory with Applications to Economics. Oxford, Oxford University Press.

Gabszewicz, J. J., J-F. Thisse. (1979) Price Competition, Quality and Income Disparities. Journal of Economic Theory, 20, 340-359.

Gabszewicz, J. J., J-F. Thisse. (1980) Entry (and Exit) in a Differentiated Industry. Journal of Economic Theory, 22, 327-338. Gabszewicz, J. J., A. Shaked, J. Sutton, J-F. Thisse, (1986). "Segmenting the Market: the Monopolist's Optimal Product Mix" Journal of Economic Theory, 39, 2, 273-289.

Gabszewicz, J. J., X. Y.,Wauthy (2002). "Quality Underprovision by a Monopolist when Quality is not Costly" Economics Letters, 77, 1, 65-72.

Gabszewicz J.J., Marini, M. A. and Tarola, O. (2015), "Alliance Formation in Vertically Differentiated Markets", CORE Discussion Papers, 30/2015, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.

Gabszewicz J.J., Marini, M. A. and Tarola, O. (2016a), "Vertical Differentiation and Collusion: Proliferation or Cannibalization?", Research in Economics, forthcoming.

Gabszewicz J.J., Marini, M. A. and Tarola, O. (2016b), "Core Existence in Vertically Differentiated Markets", Economics Letters, 149, 28-32.

Gamson, W. A. (1961). "A Theory of Coalitions in the Triad", American Sociological Review, 21, 489-493.

Gandhi, A., Froeb, L., Tschanz, S., & Werden, G. (2008) "Post-merger product repositioning", Journal of Industrial Economics, 56, 49--67.

George, L. (2007). "What's fit to print: the effect of ownership concentration on product variety in daily newspapers markets", Information Economics and Policy, 19, 285-303.

Giraud-Heraud, E., H. Hammoudi, M. Mokrane, (2003), "Multiproduct Firm Behaviour in a Differentiated Market", Canadian Journal of Economics, 36, 1, 41-61.

Hackner, J. (1994). "Collusive pricing in markets for vertically differentiated products", International Journal of Industrial Organization, 12, 2, 155-177.

Hart S, M. Kurz (1983), "Endogenous Formation of Coalitions", Econometrica, 52, 1047-1064.

Johnson J. P, Myatt, D. (2003), "Multiproduct Quality Competition: Fighting Brands and Product Line Pruning," American Economic Review, 93, 748-774.

Lambertini, L. (2000) "Technology and Cartel Stability under Vertical Differentiation", German Economic Review, 1, 4, 421-444.

Lambertini, L., S. Poddar and D. Sasakic (2002). "Research joint ventures, product differentiation, and price collusion", International Journal of Industrial Organization 20, 829--854.

Lee, J. (2013) "Endogenous Product Characteristics in Merger Simulation: A Study of the U.S. Airline Industry", mimeo.

Lommerud, K. and Sorgard, L. (1997), "Merger and Product Range Rivalry,", International Journal of Industrial Organization, 16, 1, 21-42.

Marini, M. A. (2009) "Games of Coalition & Network Formation: a Survey", in Naizmada A.K. et al. (eds.). Networks, Topology and Dynamics. Lectures Notes in Economics & Mathematical Systems, 613, 67-93, Berlin Heidelberg, Springer-Verlag.

Marini, M. A., Petit M. L., Sestini R. (2014), "Strategic Timing in R&D Agreements", Economics of Innovation and New Technology, 23, 3, 274-303.

Martin, S., (1995). "R&D Joint ventures and tacit product market collusion", European Journal of Political Economy, 11, 733--741.

Mesterton-Gibbons, M., , S. Gavriletz, G. Janko, E. Akcay, (2011), "Models of Coalition or Alliance Formation", Journal of Theretical Biology, 274, 187-204.

Mazzeo, M., (2002), "Product Choice and Oligopoly Market Structure," Rand Journal of Economics, 33, 221-242.

Mazzeo, M., (2003), "Competition and service quality in the U.S. airline industry", Review of Industrial Organization, 22, 275--296.

Mc Millan, M., (2012). "Quality collusion: news, if it ain't broke, why fix it?", Fordham Urban Law Journal, 39, 5, 1895-1942.

Moldovanu, B. (1992). "Coalition-Proof Nash Equilibrium and the Core in Three-Player Games", Games and Economic Behavior, 9, 21-34.

Motta, M., (1992). "Cooperative R&D and vertical product differentiation", International Journal of Industrial Organization 10, 643--661.

Mussa, M. and S. Rosen (1978). "Monopoly and product quality", Journal of Economic Theory, 18, 301--317.

Pezzino, M. (2010). "Minimum Quality Standards with More Than Two Firms Under Cournot Competition.", The IUP Journal of Managerial Economics, 8, 3, 26-45.

Peters, C. (2006) "Evaluating the performance of merger simulation: evidence from the U.S. airline industry", Journal of Law and Economics, 2006, 49 (2), 627--649.

Ray, D. and R. Vohra (1999). "A Theory of Endogenous Coalition Structures", Games and Economic Behavior, 26, 2, 286-336.

Salant, S.W., Switzer, S..and Reynolds,-R.,J. (1983), "Losses from Horizontal Merger: the Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium", Quarterly Journal of Economics; 98, 2, 185-99.

Scarpa, C. (1998). "Minimum quality standards with more than two firms", International Journal of Industrial Organization, 16, 5, 665-676.

Seim, K. (2006), "An empirical model of firm entry with endogenous product-type choices", Rand Journal of Economics, 37, 619-640.

Steven T. B., J.Waldfogel, (2001). "Do Mergers Increase Product Variety? Evidence from Radio Broadcasting", Quarterly Journal of Economics, 116, 3, 1009-1025.

Sweeting, A. (2010). "The Effects of Mergers on Product Positioning: Evidence from the Music Radio Industry", Rand Journal of Economics, 41, 372-397.

Vinacke, V. E. and A. Arkoff (1957). "An Experimental Study of Coalitions in the Triad", American Sociological Review, 22, 406-414.

Vives, X. (2000), Oligopoly Pricing. Old Ideas and New Tools. MIT Press, Cambridge, Mass.

Wauthy, X. (1996). "Quality Choice in Models of Vertical Differentiation", Journal of Industrial Economics, 44, 3, 345-53.

Watanabe, T. and N. Matsubayashi, (2013), "Note on Stable Mergers in Markets with Asymmetric Substitutability", Economics Bulletin, 33, 2024-2033.

Wieczner, J. (2015) "The real reasons for the pharma merger boom", Fortune, July 28, 2015.

Zhao J (2013) "The Most Reasonable Solution for an Asymmetric Three-firm Oligopoly", mimeo, Saskatchewan, Canada, March 2013.