On the Snowballing Welfare Effects of Cartels and the Allocation of Fines

We consider a homogeneous Cournot oligopoly where the inverse demand function is obtained by the utility maximization of a representative consumer, and firms may operate at different marginal costs. Assuming that some firms make a cartel while others remain independent, we introduce three new classes of TU-games, referred to as welfare TU-games, each corresponding to consumer surplus, total profit, and total welfare, respectively. Our results show that the games associated with consumer surplus and total welfare are monotonically decreasing and concave, highlighting a snowball effect of cartel formation on these two welfare measures. In contrast, the game associated with total profit is never superadditive, but it is monotonically increasing and concave when the number of firms is sufficiently small. Furthermore, we apply allocation methods, including the Shapley value and the serial method, to determine ex ante fair fines that firms must pay for participating in the cartel, allowing to differentiate fines both on the order of arrival in the cartel and on the technologies of the firms. For instance, in certain scenarios, some inefficient firms may receive lower fines for joining the cartel due to cost synergies.