We provide an incomplete information bargaining framework that captures the effects of differential bargaining power in markets with multiple buyers and multiple suppliers. The market is modeled as a mechanism that maximizes the expected weighted welfare of the firms, subject to the constraints of incentive compatibility, individual rationality, and no deficit. We show that, in this model, there is no basis for the presumption that vertical integration increases equally weighted social surplus, while it is possible that horizontal mergers that appropriately change bargaining weights increase social surplus. Moreover, efficient bargaining implies that in equilibrium noncontractible investments are efficient.

We provide a parsimonious and unified explanation for randomized selling mechanisms widely used in practice yet commonly perceived as puzzling. Optimality of randomization in the form of conflation and rationing implies that revenue under market-clearing pricing is nonconcave. Randomization is implementable via opaque pricing and underpricing. Relative to market-clearing pricing, randomization increases the equilibrium quantity and quality of goods sold and, consequently, may increase consumer surplus. For fixed quantities, resale increases consumer surplus. However, resale can decrease the equilibrium quantity and quality of goods sold. Thus, resale prohibition, which always benefits the seller, may also increase consumer surplus.

We analyze the competitive effects of mergers in markets with buyer power. Using mechanism design arguments, we show that without cost synergies, mergers harm buyers, regardless of buyer power. However, buyer power mitigates the harm to a buyer from a merger of symmetric suppliers. With buyer power, a merger increases incentives for entry, increases investment incentives for rivals, and can increase investment incentives for merging parties. Because buyer power reduces the profitability of a merger, it increases the profitability of perfect collusion relative to a merger. Cost synergies can eliminate merger harm but also render otherwise profitable mergers unprofitable.

We discuss the economics literature relevant to the design of centralized two-sided market mechanisms for environments in which both buyers and sellers have private information. The existing literature and the history of spectrum auctions, including the incentive auction currently being designed by the FCC, can be employed to analyze such mechanisms. We compare the revenue– efficiency trade-off in an environment with private information on one side of the market versus the trade-off with private information on both sides of the market; we provide an impossibility theorem for the efficient allocation of goods using a deficit-free mechanism when there is private information on both sides of the market; we discuss practical deficit-free mechanisms for various environments with two-sided private information; and we provide a synthesis to guide market design efforts and related research going forward.

Consignment auctions are two-stage mechanisms to (re)allocate emission permits. Firms are first endowed with permits and then allowed to trade them. We determine theoretically endowments that enable efficient allocation, subject to incentive compatibility, individual rationality, and no deficit. All firms prefer efficient consignment auctions to efficient standard auctions, making them politically palatable. Firms’ investment incentives align with the first-best in efficient consignment auctions. Grandfathering based on efficient long-run allocations induces efficiency-permitting endowments. A simple calibration to data from Southern California’s RECLAIM program validates our no-deficit assumption and shows that grandfathering provides the best theoretical match for the empirically observed endowments.