Multiproduct trading with a common agent under complete information: Existence and characterization of Nash equilibrium

This paper focuses on oligopolistic markets in which indivisible goods are sold by multiproduct firms to a continuum of homogeneous buyers, with measure normalized to one, who have preferences over bundles of products. Our analysis contributes to the literature on private, delegated agency games with complete information, extending the insights by Chiesa and Denicolò (2009) to multiproduct markets with indivisibilities and where the agent's preferences need not be monotone. By analyzing a kind of extended contract schedules -mixed bundling prices- that discriminate on exclusivity, the paper shows that efficient equilibria always exist in such settings. There may also exist inefficient equilibria in which the agent chooses a suboptimal bundle and no principal has a profitable deviation inducing the agent to buy the surplus-maximizing bundle because of a coordination problem among the principals. Inefficient equilibria can be ruled out by either assuming that all firms are pricing unsold bundles at the same profit margin as the bundle sold at equilibrium, or imposing the solution concept of subgame perfect strong equilibrium, which requires the absence of profitable deviations by any subset of principals and the agent. We also provide a characterization of the equilibrium strategies. More specific results about the structure of equilibrium prices and payoffs for common agency outcomes are ofered when the social surplus function is monotone and either submodular or supermodular.