To Broad-Match or Not to Broad-Match : An Auctioneers Dilemma ?

We initiate the study of an interesting aspect of sponsored search advertising, namely the consequences of broad match-a feature where an ad of an advertiser can be mapped to a broader range of relevant queries, and not necessarily to the particular keyword(s) that ad is associated with. Starting with a very natural setting for strategies available to the advertisers, and via a careful look through the algorithmic lens, we first propose solution concepts for the game originating from the strategic behavior of advertisers as they try to optimize their budget allocation across various keywords. Next, we consider two broad match scenarios based on factors such as information asymmetry between advertisers and the auctioneer, and the extent of auctioneers control on the budget splitting. In the first scenario, the advertisers have the full information about broad match and relevant parameters, and can reapportion their own budgets to utilize the extra information; in particular, the auctioneer has no direct control over budget splitting. We show that, the same broad match may lead to different equilibria, one leading to a revenue improvement, whereas another to a revenue loss. This leaves the auctioneer in a dilemma - whether to broad-match or not. This motivates us to consider another broad match scenario, where the advertisers have information only about the current scenario, and the allocation of the budgets unspent in the current scenario is in the control of the auctioneer. We observe that the auctioneer can always improve his revenue by judiciously using broad match. Thus, information seems to be a double-edged sword for the auctioneer.

Capacity as a Fundamental Metric for Mechanism Design in the Information Economy

The auction theory literature has so far focused mostly on the design of mechanisms that takes the revenue or the efficiency as a yardstick. However, scenarios where the {it capacity}, which we define as textit{``the number of bidders the auctioneer wants to have a positive probability of getting the item}, is a fundamental concern are ubiquitous in the information economy. For instance, in sponsored search auctions (SSAs) or in online ad-exchanges, the true value of an ad-slot for an advertiser is inherently derived from the conversion-rate, which in turn depends on whether the advertiser actually obtained the ad-slot or not; thus, unless the capacity of the underlying auction is large, key parameters, such as true valuations and advertiser-specific conversion rates, will remain unknown or uncertain leading to inherent inefficiencies in the system. In general, the same holds true for all information goods/digital goods. We initiate a study of mechanisms, which take capacity as a yardstick, in addition to revenue/efficiency. We show that in the case of a single indivisible item one simple way to incorporate capacity constraints is via designing mechanisms to sell probability distributions, and that under certain conditions, such optimal probability distributions could be identified using a Linear programming approach. We define a quantity called {it price of capacity} to capture the tradeoff between capacity and revenue/efficiency. We also study the case of sponsored search auctions. Finally, we discuss how general such an approach via probability spikes can be made, and potential directions for future investigations.

Diversification in the Internet Economy:The Role of For-Profit Mediators

We investigate market forces that would lead to the emergence of new classes of players in the sponsored search market. We report a 3-fold diversification triggered by two inherent features of the sponsored search market, namely, capacity constraints and collusion-vulnerability of current mechanisms. In the first scenario, we present a comparative study of two models motivated by capacity constraints - one where the additional capacity is provided by for-profit agents, who compete for slots in the original auction, draw traffic, and run their own sub-auctions, and the other, where the additional capacity is provided by the auctioneer herself, by essentially acting as a mediator and running a single combined auction. This study was initiated by us in cite{SRGR07}, where the mediator-based model was studied. In the present work, we study the auctioneer-based model and show that this model seems inferior to the mediator-based model in terms of revenue or efficiency guarantee due to added capacity. In the second scenario, we initiate a game theoretic study of current sponsored search auctions, involving incentive driven mediators who exploit the fact that these mechanisms are not collusion-resistant. In particular, we show that advertisers can improve their payoffs by using the services of the mediator compared to directly participating in the auction, and that the mediator can also obtain monetary benefit, without violating incentive constraints from the advertisers who do not use its services. We also point out that the auctioneer can not do very much via mechanism design to avoid such for-profit mediation without losing badly in terms of revenue, and therefore, the mediators are likely to prevail.

Exploration via design and the cost of uncertainty in keyword auctions

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.

For-profit mediators in sponsored search advertising

A mediator is a well-known construct in game theory, and is an entity that plays on behalf of some of the agents who choose to use its services, while the rest of the agents participate in the game directly. We initiate a game theoretic study of sponsored search auctions, such as those used by Google and Yahoo!, involving {em incentive driven} mediators. We refer to such mediators as {em for-profit} mediators, so as to distinguish them from mediators introduced in prior work, who have no monetary incentives, and are driven by the altruistic goal of implementing certain desired outcomes. We show that in our model, (i) players/advertisers can improve their payoffs by choosing to use the services of the mediator, compared to directly participating in the auction; (ii) the mediator can obtain monetary benefit by managing the advertising burden of its group of advertisers; and (iii) the payoffs of the mediator and the advertisers it plays for are compatible with the incentive constraints from the advertisers who do dot use its services. A simple intuition behind the above result comes from the observation that the mediator has more information about and more control over the bid profile than any individual advertiser, allowing her to reduce the payments made to the auctioneer, while still maintaining incentive constraints. Further, our results indicate that there are significant opportunities for diversification in the internet economy and we should expect it to continue to develop richer structure, with room for different types of agents to coexist.

Capacity constraints and the inevitability of mediators in adword auctions

One natural constraint in the sponsored search advertising framework arises from the fact that there is a limit on the number of available slots, especially for the popular keywords, and as a result, a significant pool of advertisers are left out. We study the emergence of diversification in the adword market triggered by such capacity constraints in the sense that new market mechanisms, as well as, new for-profit agents are likely to emerge to combat or to make profit from the opportunities created by shortages in ad-space inventory. We propose a model where the additional capacity is provided by for-profit agents (or, mediators), who compete for slots in the original auction, draw traffic, and run their own sub-auctions. The quality of the additional capacity provided by a mediator is measured by its {it fitness} factor. We compute revenues and payoffs for all the different parties at a {it symmetric Nash equilibrium} (SNE) when the mediator-based model is operated by a mechanism currently being used by Google and Yahoo!, and then compare these numbers with those obtained at a corresponding SNE for the same mechanism, but without any mediators involved in the auctions. Such calculations allow us to determine the value of the additional capacity. Our results show that the revenue of the auctioneer, as well as the social value (i.e. efficiency), always increase when mediators are involved; moreover even the payoffs of {em all} the bidders will increase if the mediator has a high enough fitness. Thus, our analysis indicates that there are significant opportunities for diversification in the internet economy and we should expect it to continue to develop richer structure, with room for different types of agents and mechanisms to coexist.