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Added by
Benjamin Heymann
Publication date
2018
fields
Informatics Engineering
and research's language is
English
Authors
Benjamin Heymann
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A standard result from auction theory is that bidding truthfully in a second price auction is a weakly dominant strategy. The result, however, does not apply in the presence of Cost Per Action (CPA) constraints. Such constraints exist, for instance, in digital advertising, as some buyer may try to maximize the total number of clicks while keeping the empirical Cost Per Click (CPC) below a threshold. More generally the CPA constraint implies that the buyer has a maximal average cost per unit of value in mind. We discuss how such constraints change some traditional results from auction theory. Following the usual textbook narrative on auction theory, we focus specifically on the symmetric setting, We formalize the notion of CPA constrained auctions and derive a Nash equilibrium for second price auctions. We then extend this result to combinations of first and second price auctions. Further, we expose a revenue equivalence property and show that the sellers revenue-maximizing reserve price is zero. In practice, CPA-constrained buyers may target an empirical CPA on a given time horizon, as the auction is repeated many times. Thus his bidding behavior depends on past realization. We show that the resulting buyer dynamic optimization problem can be formalized with stochastic control tools and solved numerically with available solvers.
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Taobao, as the largest online retail platform in the world, provides billions of online display advertising impressions for millions of advertisers every day. For commercial purposes, the advertisers bid for specific spots and target crowds to compete for business traffic. The platform chooses the most suitable ads to display in tens of milliseconds. Common pricing methods include cost per mille (CPM) and cost per click (CPC). Traditional advertising systems target certain traits of users and ad placements with fixed bids, essentially regarded as coarse-grained matching of bid and traffic quality. However, the fixed bids set by the advertisers competing for different quality requests cannot fully optimize the advertisers key requirements. Moreover, the platform has to be responsible for the business revenue and user experience. Thus, we proposed a bid optimizing strategy called optimized cost per click (OCPC) which automatically adjusts the bid to achieve finer matching of bid and traffic quality of page view (PV) request granularity. Our approach optimizes advertisers demands, platform business revenue and user experience and as a whole improves traffic allocation efficiency. We have validated our approach in Taobao display advertising system in production. The online A/B test shows our algorithm yields substantially better results than previous fixed bid manner.
We present a deterministic exploration mechanism for sponsored search auctions, which enables the auctioneer to learn the relevance scores of advertisers, and allows advertisers to estimate the true value of clicks generated at the auction site. This exploratory mechanism deviates only minimally from the mechanism being currently used by Google and Yahoo! in the sense that it retains the same pricing rule, similar ranking scheme, as well as, similar mathematical structure of payoffs. In particular, the estimations of the relevance scores and true-values are achieved by providing a chance to lower ranked advertisers to obtain better slots. This allows the search engine to potentially test a new pool of advertisers, and correspondingly, enables new advertisers to estimate the value of clicks/leads generated via the auction. Both these quantities are unknown a priori, and their knowledge is necessary for the auction to operate efficiently. We show that such an exploration policy can be incorporated without any significant loss in revenue for the auctioneer. We compare the revenue of the new mechanism to that of the standard mechanism at their corresponding symmetric Nash equilibria and compute the cost of uncertainty, which is defined as the relative loss in expected revenue per impression. We also bound the loss in efficiency, as well as, in user experience due to exploration, under the same solution concept (i.e. SNE). Thus the proposed exploration mechanism learns the relevance scores while incorporating the incentive constraints from the advertisers who are selfish and are trying to maximize their own profits, and therefore, the exploration is essentially achieved via mechanism design. We also discuss variations of the new mechanism such as truthful implementations.
Our paper concerns the computation of Nash equilibria of first-price auctions with correlated values. While there exist several equilibrium computation methods for auctions with independent values, the correlation of the bidders values introduces significant complications that render existing methods unsatisfactory in practice. Our contribution is a step towards filling this gap: inspired by the seminal fictitious play process of Brown and Robinson, we present a learning heuristic-that we call fictitious bidding (FB)-for estimating Bayes-Nash equilibria of first-price auctions with correlated values, and we assess the performance of this heuristic on several relevant examples.
We address Bayesian persuasion between a sender and a receiver with state-dependent quadratic cost measures for general classes of distributions. The receiver seeks to make mean-square-error estimate of a state based on a signal sent by the sender while the sender signals strategically in order to control the receivers estimate in a certain way. Such a scheme could model, e.g., deception and privacy, problems in multi-agent systems. Existing solution concepts are not viable since here the receiver has continuous action space. We show that for finite state spaces, optimal signaling strategies can be computed through an equivalent linear optimization problem over the cone of completely positive matrices. We then establish its strong duality to a copositive program. To exemplify the effectiveness of this equivalence result, we adopt sequential polyhedral approximation of completely-positive cones and analyze its performance numerically. We also quantify the approximation error for a quantized version of a continuous distribution and show that a semi-definite program relaxation of the equivalent problem could be a benchmark lower bound for the senders cost for large state spaces.
We study single-good auctions in a setting where each player knows his own valuation only within a constant multiplicative factor delta{} in (0,1), and the mechanism designer knows delta. The classical notions of implementation in dominant strategies and implementation in undominated strategies are naturally extended to this setting, but their power is vastly different. On the negative side, we prove that no dominant-strategy mechanism can guarantee social welfare that is significantly better than that achievable by assigning the good to a random player. On the positive side, we provide tight upper and lower bounds for the fraction of the maximum social welfare achievable in undominated strategies, whether deterministically or probabilistically.
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