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That cartel formation among producers in a Cournot oligopoly may not be sustainable has been discussed seminally by Salant, Switzer and Reynolds (1983), coining the term merger paradox. Various authors have investigated how this result depends on the assumptions concerning the functional form of demand and production cost. With suffciently convex costs, for example, Perry and Porter (1985) show that the paradox disappears. Our focus here is on the stability of cartel formation in a multi-market setting. We apply convex production costs, creating both strategic substitutes and diseconomies of scope across markets—using the terminology of Bulow, Geanakoplos and Klemperer (1985). In a recent work, Bellafleme and Bloch (2008) study conditions for sustainable cooperation between two firms in a symmetric two-market setting. Our work differs from theirs in that we allow for cartel formation among three rms in asymmetric markets, i.e., the two markets may differ in size. This allows us to provide further insights on the degree of cooperation and the location of cartel based on the relative market size. We choose to employ the notion of the Core and focus on long-term stability of cooperation. We demonstrate that under certain conditions that ensure relative markets' size is similar, the unique Core element of the underlying game is one of cartel formation between the same two firms on both markets.
