Bargaining over Collusion Profits under Cost Asymmetry and Demand Uncertainty

In this paper we borrow from Ciarreta and Gutierrez-Hita (2012) a duopolistic industry structure with cost asymmetry and demand uncertainty, and using this structure we build a bargaining model to study the division of collusion profits -obtained from the joint selection of supply functions- under the possibility of side payments. In our model, we consider potential disagreement points obtained from the non-cooperative equilibrium of either the quantity competition or the supply function competition, and potential bargaining solutions splitting the gains from agreement either equally or proportionally according to the relative disagreement payoffs of the duopolists. Given any of these disagreement points and any of these bargaining solutions, we find that each duopolist has always incentive to join a collusive agreement. On the other hand, irrespective of whether the bargaining solution splits the gains from agreement equally or proportionally respecting the relative disagreement payoffs, the more efficient firm (the less efficient firm) in the cartel always obtains a higher agreement payoff when the disagreement point is obtained from the equilibrium of supply function competition (quantity competition). Given the studied disagreement points and bargaining solutions, we also find that bargaining over collusion profits always makes the more efficient firm worse off and the less efficient firm better off in comparison to a collusive agreement equalizing the marginal costs of these two firms.