ROI constrained Auctions
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A standard result from auction theory is that bidding truthfully in a second price auction is a weakly dominant strategy, or, in the language of digital advertising, 'the cost per mille (eCPM) is equal to the click through rate (CTR) times the cost per clicks (CPC)'. However, such assertion is incorrect if the buyers are subject to ROI constraints. More generally, several predictions derived by the traditional auction theory literature fail to apply. This is what I propose to discuss in this article. I formalize the notion of ROI constrained auctions and derive a Nash equilibrium for second price auctions. I then extend this result to any combination of first and second price payment rules and do an asymptotic analysis of the equilibrium as the number of bidders increases. Further I expose a revenue equivalence property, and finish with a proposal for a dynamic extension of the bidder ROI constrained optimization problem.
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