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The increasing competition in digital advertising induced a proliferation ofmedia agencies playing the role of intermediaries between advertisers andplatforms selling ad slots. When a group of competing advertisers is managed bya common agency, many forms of collusion, such as bid rigging, can beimplemented by coordinating bidding strategies, dramatically increasingadvertisers' value. We study the problem of finding bids and monetary transfersmaximizing the utility of a group of colluders, under GSP and VCG mechanisms.First, we introduce an abstract bid optimization problem -- called weightedutility problem (WUP) -- , which is useful in proving our results. We show thatthe utilities of bidding strategies are related to the length of paths in adirected acyclic weighted graph, whose structure and weights depend on themechanism under study. This allows us to solve WUP in polynomial time byfinding a shortest path of the graph. Next, we switch to our original problem,focusing on two settings that differ for the incentives they allow for.Incentive constraints ensure that colluders do not leave the agency, and theycan be enforced by implementing monetary transfers between the agency and theadvertisers. In particular, we study the arbitrary transfers setting, where anykind of monetary transfer to and from the advertisers is allowed, and the morerealistic limited liability setting, in which no advertiser can be paid by theagency. In the former, we cast the problem as a WUP instance and solve it byour graph-based algorithm, while, in the latter, we formulate it as a linearprogram with exponentially-many variables efficiently solvable by applying theellipsoid algorithm to its dual. This requires to solve a suitable separationproblem in polynomial time, which can be done by reducing it to a WUP instance.

The Power of Media Agencies in Ad Auctions: Improving Utility through Coordinated Bidding