Learning in Repeated Auctions with Budgets: Regret Minimization and Equilibrium

70 Pages Posted: 23 Feb 2017 Last revised: 2 Jan 2020

See all articles by Santiago Balseiro

Santiago Balseiro

Columbia Business School - Decision Risk and Operations

Yonatan Gur

Stanford Graduate School of Business

Date Written: September 2019


In online advertising markets, advertisers often purchase ad placements through bidding in repeated auctions based on realized viewer information. We study how budget-constrained advertisers may compete in such sequential auctions in the presence of uncertainty about future bidding opportunities and competition. We formulate this problem as a sequential game of incomplete information, where bidders know neither their own valuation distribution, nor the budgets and valuation distributions of their competitors. We introduce a family of practical bidding strategies we refer to as adaptive pacing strategies, in which advertisers adjust their bids according to the sample path of expenditures they exhibit, and analyze the performance of these strategies in different competitive settings. We establish the asymptotic optimality of these strategies when competitors' bids are independent and identically distributed over auctions, but also when competing bids are arbitrary. When all the bidders adopt these strategies, we establish the convergence of the induced dynamics and characterize a regime (motivated in the context of online advertising markets) under which these strategies constitute an approximate Nash equilibrium in dynamic strategies: the bene fit from unilaterally deviating to other strategies, including ones with access to complete information, becomes negligible as the number of auctions and competitors grows large. This establishes a connection between regret minimization and market stability, by which advertisers can essentially follow approximate equilibrium bidding strategies that also ensure the best performance that can be guaranteed off equilibrium.

Keywords: Sequential auctions, online advertising, online learning, stochastic optimization, stochastic approximation, incomplete information, regret analysis, dynamic games

Suggested Citation

Balseiro, Santiago and Gur, Yonatan, Learning in Repeated Auctions with Budgets: Regret Minimization and Equilibrium (September 2019). Management Science 65 (9), 3952-3968, Available at SSRN: https://ssrn.com/abstract=2921446 or http://dx.doi.org/10.2139/ssrn.2921446

Santiago Balseiro

Columbia Business School - Decision Risk and Operations ( email )

3022 Broadway
New York, NY 10027
United States

Yonatan Gur (Contact Author)

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

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