Stable core partitions in a cartel formation game with licensing

This study investigates how licensing opportunity for the new technology on process innovation affects firms’ collusion behavior. To this end, we consider stable coalition structures in a Cournot oligopoly market with homogeneous goods. Each firm’s payoff is affected by the coalition to which it belongs and other firms’ coalitions; therefore, we consider a coalition formation game with externalities to address this problem. For stability concepts, we consider three stylized cores of coalition structures: projective, optimistic, and pessimistic cores. As a benchmark, we first show that the pessimistic core is always non-empty, whereas the projective and optimistic cores are always empty except for a duopoly market, without licensing opportunity. However, with licensing opportunity where a fixed fraction of the total profit is paid to the patent holder, we show that the projective core and even the optimistic core are non-empty under certain conditions. Moreover, we also show that the pessimistic core can support more varieties of coalition structures, the results of which imply that the licensing opportunity may enhance collusion. We also observe that such a collusion enhancement effect is not always detrimental to the welfare; in particular, it may increase consumer welfare.