In this paper, we derive bounds for profit maximizing prior-free procurement auctions where a buyer wishes to procure multiple units of a homogeneous item from n sellers who are strategic about their per unit valuation. The buyer earns the profit by reselling these units in an external consumer market. The paper looks at three scenarios of increasing complexity. First, we look at unit capacity sellers where per unit valuation is private information of each seller and the revenue curve is concave. For this setting, we define two benchmarks. We show that no randomized prior free auction can be constant competitive against any of these two benchmarks. However, for a lightly constrained benchmark we design a prior-free auction PEPA (Profit Extracting Procurement Auction) which is 4-competitive and we show this bound is tight. Second, we study a setting where the sellers have non-unit capacities that are common knowledge and derive similar results. In particular, we propose a prior free auction PEPAC (Profit Extracting Procurement Auction with Capacity) which is truthful for any concave revenue curve. Third, we obtain results in the inherently harder bi-dimensional case where per unit valuation as well as capacities are private information of the sellers. We show that PEPAC is truthful and constant competitive for the specific case of linear revenue curves. We believe that this paper represents the first set of results on single dimensional and bi-dimensional profit maximizing prior-free multi-unit procurement auctions.
Although the design of prior-free auctions has generated wide interest in the research community ( @cite_12 , @cite_9 , @cite_1 , @cite_2 , @cite_3 , @cite_10 , @cite_13 , @cite_15 ) most of the works have considered the forward setting. The reverse auction setting is subtly different from forward auctions especially if the sellers are capacitated and the techniques used for forward auctions cannot be trivially extended to the case of procurement auctions. To the best of our knowledge, design of profit-maximizing prior-free multi-unit procurement auctions is yet unexplored.
@cite_13 @cite_9 @cite_1 @cite_3 @cite_2 @cite_15 @cite_10 @cite_12
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We consider prior-free auctions for revenue and welfare maximization when agents have a common budget. The abstract environments we consider are ones where there is a downward-closed and symmetric feasibility constraint on the probabilities of service of the agents. These environments include position auctions where slots with decreasing click-through rates are auctioned to advertisers. We generalize and characterize the envy-free benchmark from Hartline and Yan (2011) to settings with budgets and characterize the optimal envy-free outcomes for both welfare and revenue. We give prior-free mechanisms that approximate these benchmarks. A building block in our mechanism is a clinching auction for position auction environments. This auction is a generalization of the multi-unit clinching auction of (2008) and a special case of the polyhedral clinching auction of (2012). For welfare maximization, we show that this clinching auction is a good approximation to the envy-free optimal welfare for position auction environments. For profit maximization, we generalize the random sampling profit extraction auction from (2002) for digital goods to give a 10.0-approximation to the envy-free optimal revenue in symmetric, downward-closed environments. The profit maximization question is of interest even without budgets and our mechanism is a 7.5-approximation which improving on the 30.4 bound of Ha and Hartline (2012). We consider the problem of a single seller repeatedly selling a single item to a single buyer (specifically, the buyer has a value drawn fresh from known distribution D in every round). Prior work assumes that the buyer is fully rational and will perfectly reason about how their bids today affect the seller's decisions tomorrow. In this work we initiate a different direction: the buyer simply runs a no-regret learning algorithm over possible bids. We provide a fairly complete characterization of optimal auctions for the seller in this domain. Specifically: - If the buyer bids according to EXP3 (or any "mean-based" learning algorithm), then the seller can extract expected revenue arbitrarily close to the expected welfare. This auction is independent of the buyer's valuation D , but somewhat unnatural as it is sometimes in the buyer's interest to overbid. - There exists a learning algorithm A such that if the buyer bids according to A then the optimal strategy for the seller is simply to post the Myerson reserve for D every round. - If the buyer bids according to EXP3 (or any "mean-based" learning algorithm), but the seller is restricted to "natural" auction formats where overbidding is dominated (e.g. Generalized First-Price or Generalized Second-Price), then the optimal strategy for the seller is a pay-your-bid format with decreasing reserves over time. Moreover, the seller's optimal achievable revenue is characterized by a linear program, and can be unboundedly better than the best truthful auction yet simultaneously unboundedly worse than the expected welfare. We study the dynamic mechanism design problem of a seller who repeatedly sells independent items to a buyer with private values. In this setting, the seller could potentially extract the entire buyer surplus by running efficient auctions and charging an upfront participation fee at the beginning of the horizon. In some markets, such as internet advertising, participation fees are not practical since buyers expect to inspect items before purchasing them. This motivates us to study the design of dynamic mechanisms under successively more stringent requirements that capture the implicit business constraints of these markets. We first consider a periodic individual rationality constraint, which limits the mechanism to charge at most the buyer's value in each period. While this prevents large upfront participation fees, the seller can still design mechanisms that spread a participation fee across the first few auctions. These mechanisms have the unappealing feature that they provide close-to-zero buyer utility in earlier auctions in exchange for higher utility in later auctions. To address this problem, we introduce a martingale utility constraint, which imposes the requirement that from the perspective of the buyer, the next item's expected utility is equal to the present one's. Our main result is providing a dynamic auction satisfying martingale utility and periodic individual rationality whose loss in profit with respect to first-best (full extraction of buyer surplus) is optimal up to polylogarithmic factors. The proposed mechanism is a dynamic two-tier auction with a hard floor and a soft floor that allocates the item whenever the buyer's bid is above the hard floor and charges the minimum of the bid and the soft floor. We consider the problem of maximizing revenue in prior-free auctions for general single parameter settings. The setting is modeled by an arbitrary downward-closed set system, which captures many special cases such as single item, digital goods and single-minded combinatorial auctions. We relax the truthfulness requirement by the solution concept of Nash equilibria. Implementation by Nash equilibria is a natural and relevant framework in many applications of computer science, where auctions are run repeatedly and bidders can observe others’ strategies, but the auctioneer needs to design a mechanism in advance and cannot use any information on the bidders’ private valuations. We introduce a worst-case revenue benchmark which generalizes the second price of single item auction and the F2 benchmark, introduced by , for digital goods. We design a mechanism whose Nash equilibria obtains at least a constant factor of this benchmark and prove that no truthful mechanisms can achieve a constant approximation.