Market participation in delegated and intrinsic common-agency games.

We study how competition in nonlinear pricing between two principals (sellers) affects' market participation by a privately informed agent (consumer). When participation is restricted to all or nothing ("intrinsic" agency), the agent must choose between both principals' contracts and selecting her outside option. When the agent is afforded the additional possibilities of choosing only one contract ("delegated" agency), competition is' more intense. The two games have distinct predictions for participation. Intrinsic agency always induces more distortion in participation relative to the monopoly outcome, and equilibrium allocations are discontinuous for the marginal consumer. Under delegated agency, relative to monopoly, market participation increases (respectively, decreases) when contracting variables are substitutes (respectively, complements) on the intensive margin. Equilibrium allocations are continuous for the marginal consumer and the range of product offerings is identical to both the first-best and the monopoly outcome.

1. Introduction

* This article studies common-agency games between competing principals using screening contracts targeted at a distribution of privately informed agents. Many interesting economic applications fit into such a setting. For example, when two noncooperating regulatory bodies regulate the same privately informed firm but on different dimensions (e.g., output and pollution), the outcome can be modelled as an equilibrium to a common-agency game. As a second example, when two firms sell non-homogeneous goods to the same consumer using nonlinear pricing as a price discrimination strategy, the price schedules which arise can also be modelled as an equilibrium to a common-agency game. There is a critical difference between these two examples, which is the subject of this article. In the first example, theregulated firm does not have a choice to be regulated by only one regulator; that is, the firm can choose to leave the industry and face no regulation, or it can choose to abide by both sets of regulations. Here, common agency and nonparticipation are the only potential outcomes, and therefore common agency is intrinsic to the game. In the second example, it is natural to allow the consumer the option of purchasing exclusively from one firm, and so common agency is no longer intrinsic to the game but a choice variable that is delegated (1) to the agent. In this article, we explore both the intrinsic and delegated variations of common-agency games. We are especially interested in how these variations impact the familiar misallocations that arise in monopoly screening settings and, in particular, the distortions on the external participation margin.

Early efforts by Martimort (1992, 1996) and Stole (1991), as well as most subsequent applications of common agency with asymmetric information to date, have been in the context of intrinsic (1) common-agency games--games in the form of our regulation example. (2) In the canonical form of this common-agency game, an agent learns some private preference parameter regarding the margins of two economic activities, say [q.sub.1] and [q.sub.2]. Both principals simultaneously and noncooperatively offer selection contracts with the restriction that principal i's contract cannot depend upon activity [q.sub.j], j [not equal to] i. Hence, the contracting variables are private rather than public. Following the offers, the agent must decide between accepting and rejecting both contracts; the agent is not allowed to accept one contract and reject the other. Activities are subsequently chosen and payoffs are awarded in accord with the activities and the contracts. Such a modelling is naturally appropriate when the agent is a regulated firm and the principals are distinct regulatory bodies, each with authority over a mutually exclusive set of activities. A firm may decide to exit the industry (i.e., "reject" the regulatory contracts), but the firm can never decide to accept one set of regulations and reject the other.

The delegated common-agency game that allows the agent the extra options of accepting a subset of the principals' contract offers has received far less attention than its intrinsic counterpart. (3) The value of exclusivity for the agent, however, depends upon the agent's private information and, as a consequence, delegated agency games require the imposition of type-dependent participation constraints. (4)

To the best of our knowledge, no one has studied the economic consequences of common agency (both intrinsic and delegated) on distortions in contractual activities and participation. In our early papers, Martimort (1992) and Stole (1991), we study the equilibrium outcomes of the intrinsic agency game under the assumption of full participation and argue that the analysis also applies to the case of delegation when contracting activities are complements. Moreover, when the activities are substitutes, the economics of the intrinsic agency distortions still provide considerable insight into the marginal distortions in delegated agency games. One has to pay closer attention to the agent's rents and participation constraints, however, when common agency is delegated. Calzolari and Scarpa (2004) explore non-intrinsic common agency and prove that the agent obtains greater rents in a non-intrinsic game but that otherwise the productive allocations are identical. This conclusion relies, however, on the assumption of full participation. When the market is not covered, as we show below, the participation distortions typically depend upon whether the common-agency game is delegated or intrinsic. The primary contribution of the present article is to provide an analysis of the two forms of distortions--intensive margins (activity levels) and extensive margins (participation)--and to relate the directions and magnitudes of these distortions to the underlying game form and the preferences of the agent.

Our article also contributes to an understanding of the interactions between competition and price discrimination. Because theoretical work in multi-principal contractgames has largely restricted attention to intrinsic settings, it has remained unclear how competition affects the character of nonlinear pricing between duopolists. (5) In addition, most competitive nonlinear pricing applications have assumed one-stop shopping or exclusive purchasing in which the consumer may buy from only one firm in equilibrium, thereby incorporating all competitive pressures in the outside option. (6) Other papers that have allowed for purchasing from multiple vendors in equilibrium have also restricted preferences such that full coverage arises in equilibrium. (7) The present article allows for multiple vendors and exclusivity. It also allows for less-than-full coverage. In this sense, our results indicate which intuitions from nonlinear pricing are robust with respect to incomplete market coverage and the possibility of purchasing from both firms as well as just one.