Optimal Second-degree Price Discrimination and Arbitrage: On the Role of Asymmetric Information among Buyers

The traditional theory of second-degree price discrimination tackles individual self selection but does not address the possibility that buyers could form a coalition to conduct arbitrage, that is, to coordinate their purchases and to reallocate the goods. In this paper, we design the optimal sale mechanism which takes into account both individual and coalition incentive compatibility when buyers can form a coalition under asymmetric information. We show that the monopolist can achieve the same profit regardless of whether or not buyers can form a coalition. Although marginal rates of substitution are not equalized across buyers of different types in the optimal sale mechanism (hence there exists potential room for arbitrage), they fail to realize the gains from arbitrage because of the transaction costs in coalition formation generated by asymmetric information.