On the impact of cross-ownership in a common property renewable resource oligopoly

This paper examines a dynamic game of exploitation of a productive asset by agents who subsequently sell the outcomes of their endeavours in an oligopolistic market where a subset of the oligopolists owns a share in each other’s profits. A Markov Perfect Nash Equilibrium of the game is constructed and used to analyze the impact of cross-ownership on the equilibrium production strategies, the steady state resource stocks, the profitability of cross-ownership, and social welfare. We show that there exists an interval of resource stocks for which a symmetric cross-ownership can be profitable, even though such rival cross-shareholdings are unprofitable in the corresponding static equilibrium framework. Moreover, we demonstrate that cross-ownership may not only lead to a higher market output and social welfare in the short run, but also a higher steady-state stock, industry production, and social welfare in the long run. Thus, antitrust authorities should be cautious in ruling in the renewable resource industries.