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Auctions for Online Display Advertising Exchanges : Approximation Result Technical Report
| Content Provider | Semantic Scholar |
|---|---|
| Author | Balseiro, Santiago R. Besbes, Omar Weintraub, Gabriel Y. |
| Copyright Year | 2012 |
| Abstract | In this technical report we show that the FMFE provides a good approximation to the rational behavior of agents when the markets are large and the number of bidding opportunities per advertiser are also large. More specifically, we show that when all advertisers implement the FMFE strategy, the relative increase in payoff of any unilateral deviation to a strategy that keeps track of all information available to the advertiser in the market becomes negligible as the market scale increases. Hence, FMFE strategies become asymptotically optimal. Before stating the result, we proceed by formalizing the scaling under consideration. We consider a sequence of markets indexed by a positive parameter κ, referred to as the scaling; such that the higher the scaling, the larger the market “size”. On the demand side, a θ-type advertiser matching probability decreases as ακ θ ∝ κ−1, while the budget increases as bθ ∝ log κ. Additionally, the arrival rate of advertisers increases as λθ ∝ κ; and both the distribution of values and the length of the campaign are invariant to the scaling. On the supply side, the arrival rate of impressions increases as ηκ ∝ κ log κ. Hence, the mean number of auctions an advertiser participates in, ακ θηsθ ∝ log κ, grows at the same rate that the budget. The scaling is such that auctions occur more frequently, but the expected number of matching bidders in each auction, ακ θλ κ θsθ, remains constant. Additionally, the FMFE is invariant to the scaling, because advertisers aim to satisfy the budget constraints in expectation and strategies are state-independent (see Eq. (1) and (2) in the main paper). Thus, irrespectively of the scaling, the FMFE strategy is given by β = {β θ }θ∈Θ and is described by a vector of multipliers. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://faculty.fuqua.duke.edu/~srb43/papers/dyn-auctions-approx.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
