{"type":"ScholarlyArticle","title":"The Power of Media Agencies in Ad Auctions: Improving Utility through Coordinated Bidding","authors":[{"name":"Giulia Romano","slug":"giulia-romano","given":"Giulia","family":"Romano","affiliation":"Politecnico di Milano , Piazza Leonardo da Vinci 32 , I-20133 , Milan , Italy"},{"name":"Matteo Castiglioni","slug":"matteo-castiglioni","given":"Matteo","family":"Castiglioni","affiliation":"Politecnico di Milano , Piazza Leonardo da Vinci 32 , I-20133 , Milan , Italy"},{"name":"Alberto Marchesi","slug":"alberto-marchesi","given":"Alberto","family":"Marchesi","affiliation":"Politecnico di Milano , Piazza Leonardo da Vinci 32 , I-20133 , Milan , Italy"},{"name":"Nicola Gatti","slug":"nicola-gatti","given":"Nicola","family":"Gatti","affiliation":"Politecnico di Milano , Piazza Leonardo da Vinci 32 , I-20133 , Milan , Italy"}],"abstract":"The increasing competition in digital advertising induced a proliferation of media agencies playing the role of intermediaries between advertisers and platforms selling ad slots. When a group of competing advertisers is managed by a common agency, many forms of collusion, such as bid rigging, can be implemented by coordinating bidding strategies, dramatically increasing advertisers' value. We study the problem of finding bids and monetary transfers maximizing the utility of a group of colluders, under GSP and VCG mechanisms. First, we introduce an abstract bid optimization problem---called weighted utility problem (WUP)---, which is useful in proving our results. We show that the utilities of bidding strategies are related to the length of paths in a directed acyclic weighted graph, whose structure and weights depend on the mechanism under study. This allows us to solve WUP in polynomial time by finding 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 they can be enforced by implementing monetary transfers between the agency and the advertisers. In particular, we study the arbitrary transfers setting, where any kind of monetary transfer to and from the advertisers is allowed, and the more realistic limited liability setting, in which no advertiser can be paid by the agency.\r\n In the former, we cast the problem as a WUP instance and solve it by our graph-based algorithm, while, in the latter, we formulate it as a linear program with exponentially-many variables efficiently solvable by applying the ellipsoid algorithm to its dual. This requires to solve a suitable separation problem in polynomial time, which can be done by reducing it to the weighted utility problem a WUP instance.","doi":"10.24963/ijcai.2022/66","url":"https://ijcai.org/proceedings/2022/66","pdf":"https://ijcai.org/proceedings/2022/0066.pdf","markdown":"https://ijcai.org/proceedings/2022/66.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/66","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":66,"pages":{"first":461,"last":467},"keywords":["Agent-based and Multi-agent Systems: Mechanism Design","Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986904","length_sec":95,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985047","length_sec":359,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Ashlagi et al., 2009] Itai Ashlagi, Dov Monderer, and Moshe Tennenholtz. 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