Multi-Stage Intermediation in Display Advertising

We consider a setting where an advertiser seeks to acquire an impression from an advertising exchange through a chain of intermediaries, and provide a game theoretic model to study the mechanisms offered by strategic intermediaries when the advertiser’s value is private. We characterize the subgame perfect equilibrium of the game among intermediaries within a practically relevant class of mechanisms, and show that economic incentives are not necessarily aligned along the chain, i.e., profit-maximizing intermediaries have incentives to shade bids and not to allocate impressions, even when profitable for their customers. We also provide the equilibrium mechanisms and profits in closed-form for cases where the advertiser has (i) exponential, (ii) Pareto, (iii) uniform value distribution. Our results indicate that when the advertiser has exponential value distribution, the expected profits of all intermediaries are identical. On the other hand, for Pareto and uniform distributions, downstream and upstream intermediaries have higher profits, respectively. This result indicates that the position in the intermediation process has a significant impact on the profits of the intermediaries, and the most profitable position depends on the underlying value distribution. Moreover, we extend our characterization to tree networks and analyze the impact of different network structures on the profits of intermediaries and the seller’s revenue.