Optimal Contracts for Intermediaries in Online Advertising

In online advertising, the prevalent method advertisers employ to acquire impressions is to contract with an intermediary. These contracts involve upfront payments made by the advertisers to the intermediary, in exchange for running campaigns on their behalf. This paper studies the optimal contract offered by the intermediary in a setting where advertisers' budgets and targeting criteria are private. This problem can naturally be formulated as a multidimensional mechanism design problem, which in general is hard to solve. We tackle this problem by combining a performance space characterization technique, which relies on delineating the expected cost and value achievable by any feasible (dynamic) bidding policy, and a duality-based approach, which reduces the optimal contract design problem to a tractable convex optimization problem. This approach yields a crisp characterization of the intermediary's optimal bidding policy: the policy is stationary and bids a weighted average of the values associated with different types (to guarantee that the advertiser reports her type truthfully) that is appropriately shaded (to account for budget constraints). Additionally, when advertisers have identical value distributions, our formulation yields a closed-formcharacterization of the optimal contract. Our results indicate that an intermediary can profitably provide bidding service to a budget-constrained advertiser and at the same time increase the overall market efficiency.