FEEM working papers "Note di lavoro" series
2017.029

Collusive Agreements in Vertically Differentiated Markets


Authors: Marco A. Marini
Series: Economic Theory
Editor: Carlo Carraro
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
JEL n.: D42, D43, L1, L12, L13, L41

Abstract

This paper 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  the equidistance of firms’ products along the quality spectrum. Without this property, and in presence of large quality differences, collusive agreements easily lose 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.

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Suggested citation:  Marini, M. A., (2017), 'Collusive Agreements in Vertically Differentiated Markets', Nota di Lavoro 29.2017, Milan, Italy: Fondazione Eni Enrico Mattei

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