Low Revenue in Display Ad Auctions: Algorithmic Collusion vs. Non-Quasilinear Preferences

The transition of display ad exchanges from second-price to first-price auctions has raised questions about its impact on revenue. Evaluating this shift empirically proves challenging. One key factor that is often ignored is the behavior of automated bidding agents, who are unlikely to use static game-theoretical equilibrium strategies instead of favoring dynamic realms that continuously adapt and learn independently through the process of exploration and exploitation. Thus revenue equivalence between first- and second-price auctions might not hold. Research on algorithmic collusion in display ad auctions found revenue differences between second-price and first-price auctions. First-price auctions can induce Q-learning agents to tacitly collude below the Nash equilibrium in repeated complete-information auctions with payoff-maximizing agents (i.e., agents maximizing value minus price).  Our analysis explores wide-spread online learning algorithms' convergence behavior in both complete and incomplete information models, but does not find a systematic deviance from equilibrium behavior. Convergence for Q-learning depends on hyperparameters and initializations, and algorithmic collusion vanishes when competing against other learning algorithms. Apart from their learning behavior, the objectives reported in the literature extend payoff maximization, often focusing on return-on-investment or return-on-spend.  We derive equilibrium bid functions for such utility models, revealing that revenue equivalence doesn't hold. In low-competition scenarios, the first-price auction often yields lower revenue than the second-price counterpart.  These insights offer an alternative rationale for the potential revenue decrease in first-price auctions. Understanding the intricate interplay of auction rules, learning algorithms, and utility models is crucial in maximizing revenue in the ever-evolving world of display ad exchanges.

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