Coalitional Approaches to Collusive Agreements in Oligopoly Games

Abstract

In this paper we review a number of coalitional solution concepts for the analysis of cartel and merger stability in oligopoly. We show that, although so far the industrial organization and the cooperative game theoretic literature have proceeded somehow independently on this topic, the two approaches are highly inter‐connected. We show that different assumptions on the behaviour and on the timing of the coalitions of firms yield very different results on the associations of firms which are stable. We conclude by reviewing some recent extensions of the coalitional analysis to oligopolistic markets with heterogeneous firms and incomplete information.

Core existence in vertically differentiated markets

“…In a di §erentiated quantity oligopoly with three (or four Örms) Watanabe and Matsubayashi (2013) show that for any degree of product di §erentiation the "#core is nonempty while the #-core only exists in presence of high product di §erentiation. For a more detailed account of the works dealing with coalitional agreements in oligopoly games, see Marini 2009 andCurrarini andMarini 2015. 2 This means that every Örm is advantaged when rivals merge in coalitions.…”

“…In such cases, core allocations may fail to exist even in convex games, for instance when players in the complementary coalition are expected to remain together, as in the delta core (Hart and Kurz 1983), also denoted projection core in the recent axiomatization by Bloch and van den Nouweland 2014. Moreover, since in the case of vertically di §erentiated markets the coalitional worth possesses positive coalition externalities, 2 the delta or projection-core is the smallest core and, therefore, its existence implies the existence of all other possible versions of core in games with simultaneous moves. In this paper, we use this notion of core to provide the strongest existence result for the class of games considered here.…”

Collusive Agreements in Vertically Differentiated Markets

“…In a di¤erentiated quantity oligopoly with three (or four …rms) Watanabe and Matsubayashi (2013) show that for any degree of product di¤erentiation the core is nonempty while the -core only exists in presence of high product di¤erentiation. For a more detailed account of the works dealing with coalitional agreements in oligopoly games, see Marini (2009) and Currarini and Marini (2015). Then we have the following result:…”

Jeux de coalitions et oligopoles

“…. Currarini et Marini (2015) montrent que la capacité de chaque coalition devient alors trop élevée et ne permet plus de garantir la non-vacuité du coeur.…”

“…Proposition 3.25 (Currarini et Marini 2015). Sous les Hypothèses 3.3, 3.6 et 3.7 où z −→ +∞, pour chaque jeu…”