Expressiveness and Robustness of First-Price Position Auctions

Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized first-price mechanism with multi-dimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are one-dimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why first-price payments may be able to support equilibria in a wider range of circumstances than second-price payments

Expressiveness And Robustness of First-Price Position Auctions

Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized first-price mechanism with multi-dimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are one-dimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why first-price payments may be able to support equilibria in a wider range of circumstances than second-price payments.Engineering and Applied Science

Expressiveness and robustness of first-price position auctions

Ideally, the properties of an economic mechanism should hold in a robust way across multiple equilibria and under varying assumptions regarding the information available to participants. Focusing on the design of robust position auctions, we seek mechanisms that possess an efficient equilibrium and guarantee high revenue in every efficient equilibrium, under complete and incomplete information. A generalized first-price auction that is expressive in the sense of allowing multidimensional bids turns out to be the only standard design able to achieve this goal, even when valuations are one dimensional. The equilibria under complete information are obtained via Bernheim and Whinston’s profit target strategies, those under incomplete information via an appropriate generalization thereof. Particularly interesting from a technical perspective is the incomplete information case, where the standard technique for establishing equilibrium existence due to Myerson is generalized to a setting in which the bid space has higher dimension than the valuation space

Generalized Second Price Auction with Probabilistic Broad Match

Generalized Second Price (GSP) auctions are widely used by search engines today to sell their ad slots. Most search engines have supported broad match between queries and bid keywords when executing GSP auctions, however, it has been revealed that GSP auction with the standard broad-match mechanism they are currently using (denoted as SBM-GSP) has several theoretical drawbacks (e.g., its theoretical properties are known only for the single-slot case and full-information setting, and even in this simple setting, the corresponding worst-case social welfare can be rather bad). To address this issue, we propose a novel broad-match mechanism, which we call the Probabilistic Broad-Match (PBM) mechanism. Different from SBM that puts together the ads bidding on all the keywords matched to a given query for the GSP auction, the GSP with PBM (denoted as PBM-GSP) randomly samples a keyword according to a predefined probability distribution and only runs the GSP auction for the ads bidding on this sampled keyword. We perform a comprehensive study on the theoretical properties of the PBM-GSP. Specifically, we study its social welfare in the worst equilibrium, in both full-information and Bayesian settings. The results show that PBM-GSP can generate larger welfare than SBM-GSP under mild conditions. Furthermore, we also study the revenue guarantee for PBM-GSP in Bayesian setting. To the best of our knowledge, this is the first work on broad-match mechanisms for GSP that goes beyond the single-slot case and the full-information setting

Computational Challenges in E-Commerce

Economic and social sciences will drive Internet protocols and services into the future.Engineering and Applied Science

A note on the efficiency of position mechanisms with budget constraints

We study the social efficiency of several well-known mechanisms for the allocation of a set of available (advertising) positions to a set of competing budget-constrained users (advertisers). Specifically, we focus on the Generalized Second Price auction (GSP), the Vickrey–Clarke–Groves mechanism (VCG) and the Expressive Generalized First Price auction (EGFP). Using liquid welfare as our efficiency benchmark, we prove a tight bound of 2 on the liquid price of anarchy and stability of these mechanisms for pure Nash equilibria

Pacing Equilibrium in First-Price Auction Markets

In the isolated auction of a single item, second price often dominates first price in properties of theoretical interest. But, single items are rarely sold in true isolation, so considering the broader context is critical when adopting a pricing strategy. In this paper, we study a model centrally relevant to Internet advertising and show that when items (ad impressions) are individually auctioned within the context of a larger system that is managing budgets, theory offers surprising endorsement for using a first price auction to sell each individual item. In particular, first price auctions offer theoretical guarantees of equilibrium uniqueness, monotonicity, and other desirable properties, as well as efficient computability as the solution to the well-studied Eisenberg-Gale convex program. We also use simulations to demonstrate that a bidder's incentive to deviate vanishes in thick markets

The efficiency of resource allocation mechanisms for budget-constrained users

We study the effciency of mechanisms for allocating a divisible resource. Given scalar signals submitted by all users, such a mechanism decides the fraction of the resource that each user will receive and a payment that will be collected from her. Users are self-interested and aim to maximize their utility (defined as their value for the resource fraction they receive minus their payment). Starting with the seminal work of Johari and Tsitsiklis [Mathematics of Operations Research, 2004], a long list of papers studied the price of anarchy (in terms of the social welfare - the total users’ value) of resource allocation mechanisms for a variety of allocation and payment rules. Here, we further assume that each user has a budget constraint that invalidates strategies that yield a payment that is higher than the user’s budget. This subtle assumption, which is arguably more realistic, constitutes the traditional price of anarchy analysis meaningless as the set of equilibria may change drastically and their social welfare can be arbitrarily far from optimal. Instead, we study the price of anarchy using the liquid welfare benchmark that measures effciency taking budget constraints into account. We show a tight bound of 2 on the liquid price of anarchy of the well-known Kelly mechanism and prove that this result is essentially best possible among all multi-user resource allocation mechanisms. This comes in sharp contrast to the no-budget setting where there are mechanisms that considerably outperform Kelly in terms of social welfare and even achieve full effciency. In our proofs, we exploit the particular structure of worst-case games and equilibria, which also allows us to design (nearly) optimal two-player mechanisms by solving simple differential equations