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.
Deep Dive into 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 c
Sponsored search advertising is a significant growth market and is witnessing rapid growth and evolution. The analysis of the underlying models has so far primarily focused on the scenario, where advertisers/bidders interact directly with the auctioneers, i.e., the Search Engines and publishers. However, the market is already witnessing the spontaneous emergence of several categories of companies who are trying to mediate or facilitate the auction process. For example, a number of different AdNetworks have started proliferating, and so have companies who specialize in reselling ad inventories. Hence, there is a need for analyzing the impact of such incentive driven and for-profit agents, especially as they become more sophisticated in playing the game. In the present work, our focus is on the emergence of market mechanisms and for-profit agents motivated by capacity constraint inherent to the present models.
For instance, one natural constraint comes from the fact that there is a limit on the number of slots available for putting ads, especially for the popular keywords, and a significant pool of advertisers are left out due to this capacity constraint. We ask whether there are sustainable market constructs and mechanisms, where new players interact with the existing auction mechanisms to increase the overall capacity. In particular, lead-generation companies who bid for keywords, draw traffic from search pages and then redirect such traffic to service/product providers, have spontaneously emerged. However, the incentive and equilibria properties of paid-search auctions in the presence of such profit-driven players have not been explored. We investigate key questions, including what happens to the overall revenue of the auctioneers when such mediators participate, what is the payoff of a mediator and how does it dependent on her quality, how are the payoffs of the bidders affected, and is there an overall value that is generated by such mechanisms.
Formally, in the current models, there are K slots to be allocated among N (≥ K) bidders (i.e. the advertisers). A bidder i has a true valuation v i (known only to the bidder i) for the specific keyword and she bids b i . The expected click through rate (CTR) of an ad put by bidder i when allocated slot j has the form γ j e i i.e. separable in to a position effect and an advertiser effect. γ j ’s can be interpreted as the probability that an ad will be noticed when put in slot j and it is assumed that
. . γ N = 0. e i can be interpreted as the probability that an ad put by bidder i will be clicked on if noticed and is refered as the relevance of bidder i. The payoff/utility of bidder i when given slot j at a price of p per click is given by e i γ j (v ip) and they are assumed to be rational agents trying to maximize their payoffs. As of now, Google as well as Yahoo! uses schemes closely modeled as RBR(rank by revenue) with GSP(generalized second pricing). The bidders are ranked according to e i v i and the slots are allocated as per this ranks. For simplicity of notation, assume that the ith bidder is the one allocated slot i according to this ranking rule, then i is charged an amount equal to ei+1vi+1 ei . Formal analysis of such sponsored search advertising model has been done extensively in recent years, from algorithmic as well as from game theoretic perspective [2,6,3,1,7,4,5].
In the following section, we propose and study a model wherein the additional capacity is provided by a for-profit agent who competes for a slot in the original auction, draws traffic and runs its own sub-auction for the added slots. We discuss the cost or the value of capacity by analyzing the change in the revenues due to added capacity as compared to the ones without added capacity.
In this section, we discuss our model motivated by the capacity constraint, which can be formally described as follows:
-Primary Auction (p-auction) : Mediators participate in the original auction run by the search engine (called p-auction) and compete with advertisers for slots (called primary slots). For the ith agent (an advertiser or a mediator), let v p i and b p i denote her true valuation and the bid for the p-auction respectively. Further, let us denote v p i e p i by s p i where e p i is the relevance score of ith agent for p-auction. Let there are κ mediators and there indices are M 1 , M 2 , . . . , M κ respectively.
• Secondary slots: Suppose that in the primary auction, the slots assigned to the mediators are l 1 , l 2 , . . . , l κ respectively, then effectively, the additional slots are obtained by forking these primary slots in to L 1 , L 2 , . . . , L κ additional slots respectively, where L i ≤ K for all i = 1, 2, . . . , κ. By forking we mean the following: on the associated landing page the mediator puts some information relevant to the specific keyword associated with the p-auction along with the space for additional slots. Let us call these additional slots as secondary slot
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