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Sponsored search advertising has grown rapidly since the last decade and is now a significant revenue source for search engines. To ameliorate revenues, search engines often set fixed or variable reserve price to in influence advertisers’ bidding. This paper studies and compares two pricing mechanisms: the generalized second-price auction (GSP) where the winner at the last ad position pays the larger value between the highest losing bid and reserve price, and the GSP with a posted reserve price (APR) where the winner at the last position pays the reserve price. We show that if advertisers’ per-click value has an increasing generalized failure rate, the search engine’s revenue rate is quasi-concave and hence there exists an optimal reserve price under both mechanisms. While the number of advertisers and the number of ad positions have no effect on the selection of reserve price in GSP, the optimal reserve price is affected by both factors in APR and it should be set higher than GSP.

In sponsored search advertising each advertiser bids for keywords and purchases sponsored links relevant to his business from Google, Yahoo!, MSN, and their partners. When an internet user searches a specific term or keyword in a search engine, sponsored links may be displayed in the front page in addition to search result links. Whenever a sponsored link is clicked, its sponsor or advertiser will pay the search engine a fee, called cost per-click (CPC), for the service of leading consumers to his web site. Many corporations and small businesses take advantage of this affordable, targeted advertising method. Google reported an annual revenue of $37.91 billion in 2011, and 96% of it came from its advertising business (Google Investor Relations [

Sponsored links associated with a particular keyword are sold through auction where each advertiser submits a bid to the search engine for his willingness to pay for a CPC. In 2002 Google introduced AdWords, which stipulates that an advertiser in position

To screen advertisers and improve the quality of sponsored links, search engines set up reserve price called minimum bid to each keyword auction. Advertisers must pay at least the minimum bid per click to maintain the active status of their ad links. Since early 2008 Yahoo! has no longer fixed its minimum bid at $0.10 and started imposing variable minimum bids for some keywords (Yahoo! Search Marketing Blog [

Motivated by the economy in sponsored search advertising and intrigued by the opaqueness of its practice, we study and compare two pricing mechanisms for selling multiple heterogeneous ad positions. The first is the GSP auction defined by Edelman et al. [

Although GSP has been widely used in the literature to analyze sponsored search advertising, it is based on a static game that ignores the dynamic nature of the auction. The search engine determines a reserve price before the auction starts while no ad position has been sold. In the reality, however, the search engine may review periodically as to whether the current reserve price needs to be revised given part of or all ad positions have been occupied. In a separate paper (Yang

The rest of the paper is organized as follows.

Reserve price for auctions has been studied long before sponsored search advertising came into practice. Myerson [

A complication of sponsored search advertising is the heterogeneity of auction items or ad positions. As the click-through rate is descending with positions, each advertiser chooses a position (or none) to maximize his payoff, and equilibrium becomes a natural issue. Since GSP auctions are infinitely repeated games, the sets of equilibria can be very large and analysis of possible equilibrium strategies becomes intractable. Edelman

While research on sponsored search auction has been popular, study on its reserve price is sporadic. Edelman and Schwarz [

In this article we study two pricing mechanisms, GSP and APR, in selling multiple heterogeneous ad positions. In both mechanisms advertiser at position

The keywords auctions in Yahoo! and Google are repeated games in which bidders gradually learn the value of their competitors and adjust their bids accordingly. The set of equilibria in repeated games can be very large and the strategies leading to such equilibria are complex. As Edelman

In practice, Google ranks advertisers based on the product of each advertiser’s bid and his “quality score”. The quality score is determined by a number of factors including the CTR, the keyword’s relevancy to the advertiser’s business and the quality of his web site. Varian [

An exogenously given

Since the advertiser in position

Note that any

It is easy to see that the bidding strategy at the lower bound belongs to the locally envy-free equilibrium (Edelman

Questions that follow naturally are why advertisers are destined to the lower bound of SNE and how their bids converge to this particular point? Varian [

In the rest of the paper we use the term of (lowest-revenue) envy-free equilibrium and lower bound of the SNE interchangeably. Any equilibrium strategy examined will satisfy the lower bound constraint (

We consider

Let

For a qualified bidder

Let

When there are

In a GSP, the revenue contributions from

The standard regularity condition in the auction literature requires an increasing failure rate (IFR) (Maskin and Riley [

In auctions of selling a single item or multiple homogeneous items, the optimal reserve price solves Equation (

Although English auctions with multiple heterogeneous items and endogenous entries have been studied in the literature, to our knowledge, there has not been theoretical development for an analytical solution of the optimal reserve price. The significance of Theorem 1, hence, is twofold. It provides the optimal reserve price for a static generalized English auction where the payment schedule for the last winning bidder is dependent on the number of bidders; second, it shows that heterogeneity among objects alone does not necessarily lead to a varied optimal reserve price.

When there are

The marginal revenue function can be verified as

The optimality condition (

The only difference between GSP and APR discussed in the preceding section is what the

As the reserve price increases from zero, both revenue rates go up while APR is affected more since

Although on average the GSP mechanism creates more revenue, APR has some practical appeals. First, the sponsored search auction is continuous and advertisers can update their bids over time. When a consumer clicks the

Classical auction theory shows that when selling identical items to a given number of bidders, the marginal revenue from a bidder with value

Intuitively

Search engine’s expected revenue rates from APR and GSP mechanisms

Each keyword for sale has its own market, whose demand is gauged by both the market size and depth. While market size represents the average number of potential buyers, market depth stands for the amount they each bid. The dynamic nature of advertising business is likely to influence the market size and depth over the course of time. Hence, it is necessary for the search engine to review the reserve price for each keyword when such changes in the market take place. The following proposition shows how the population of potential bidders affects the optimal reserve price.

Any additional demand is beneficial to the search engine because a new advertiser not only pays more for a sponsored link than the current reserve price, but also increases the competition and prompts other advertisers to raise the bids accordingly to secure their positions. Hence, given the limited space for displaying sponsored results on its front page, when the population of bidders for a keyword increases, the search engine should lift reserve price to create more revenue. Recognizing the importance of the market size, search engines make continuous efforts to recruit new advertisers. For instance, Yahoo! offers a $25 of signing credit for any new customer. In addition, no longer using the fixed $.10 minimum bid policy for sponsored search, Yahoo! now adjusts reserve price in a particular keyword market based on multiple factors including the number of bidders and the bid amounts (see Yahoo! Search Marketing Help [

In sponsored search advertising advertisers compete for ad links that appear in the front page of major search engines including Google and Yahoo! through auctions. Search engines often set variable reserve price to influence advertiser’s bidding and create more revenue. However, as advertising capacity is perishable, arbitrary thresholds may adversely affect revenues.

This paper compares two pricing mechanisms in sponsored search advertising—the generalized second-price auction (GSP) where the last winning position is charged the larger value between the reserve price and the highest losing bid, and an alternative GSP with posted reserve price (APR) where the last winning position pays the reserve price regardless how many positions are sold. Although the standard GSP is extensively studied in the literature to derive optimal reserve price, it fails to capture the dynamics of the auction. The continuous bidding game is unlikely to have the same number of unsold positions in each period and may require periodical reviews of the reserve price. The proposed APR mechanism is an attempt to remedy the problem. We assume that the number of eligible bidders is endogenously controlled by the reserve price. Focusing on the lower bound of the SNE our models maximize the long-term expected revenue rate. If the value per click of bidders has the property of IGFR, the expected revenue rates in both GSP and APR are quasi-concave of the reserve price and there exists a unique optimizer for each mechanism. In particular, the optimal reserve price in GSP is proved to be the same as the one in single-item auctions that is dependent on only the private value distribution. In contrast, the optimal reserve price in APR, depending on both the numbers of bidders and positions, should be set higher compared with the one in GSP.

Current research can be extended in several directions. First, in our model the CTR of each slot is exogenous. Although this is a standard assumption, it may not always be the case especially when not all slots are occupied. For instance, when it is only ad showing the link on the right of the first page may receive more clicks than when it has companies. Taking this situation into account will make our pricing model much more complex. On the other hand, it may facilitate the analysis on the optimal number of sponsored links a search engine should sell in the first page. Second, our model maximizes the expected revenue rate in a static auction with an endogenous number of bidders. It might be interesting to consider a dynamic model investigating how the search engine should update the reserve price at each period based on the incumbent and potential new entry. Third, it is worth exploring the Bayes–Nash equilibria of GSP and APR, and investigating whether the Revenue Equivalence Theorem (Myerson [

Obviously,

Let

Dividing both sides by

If advertisers’ willingness to pay has an increasing generalized failure rate (IGFR), then the ratio

Let