Sequential Posted-Price Mechanisms with Correlated Valuations

Abstract

We study the revenue performance of sequential posted-price mechanisms and some natural extensions for a setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted-price mechanisms are conceptually simple mechanisms that work by proposing a "take-it-or-leave-it" offer to each buyer. We apply sequential posted-price mechanisms to single-parameter multiunit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers.For standard sequential posted-price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted-price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the case of a continuous valuation distribution when various standard assumptions hold simultaneously (i.e., everywhere-supported, continuous, symmetric, and normalized (conditional) distributions that satisfy regularity, the MHR condition, and affiliation). In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted-price mechanism is proportional to the ratio of the highest and lowest possible valuation.We prove that a simple generalization of these mechanisms achieves a better revenue performance; namely, if the sequential posted-price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a Ω(1/ max{1, d }) fraction of the optimal revenue can be extracted, where d denotes the degree of dependence of the valuations, ranging from complete independence (d = 0) to arbitrary dependence (d = n − 1).

Posted Price Mechanisms and Optimal Threshold Strategies for Random Arrivals

“…In terms of upper bounds Correa et al [15] (in the full version of their paper) establish that no stopping rule can achieve a ratio better than √ 3 − 1 ≈ 0.732 for the prophet secretary problem. 2 This latter upper bound together with the fact that we show that the impossibility for nonadaptive stopping rules to beat 1 − 1/e holds even if the random variables are i.i.d., lead us to study adaptive stopping rules in this simpler setting. Of course, in the i.i.d.…”

“…In recent years there has been a significant effort to understand the expected revenue of the outcome generated by different posted price mechanisms when compared to that of the optimal auction [21,9,2,7,10,42]. Interestingly, first Hajiaghayi et al [21] and then Chawla et al [10] noted a close connection between online mechanisms in general and posted price mechanisms in particular and prophet inequalities.…”

Approximation Guarantee of OSP Mechanisms: The Case of Machine Scheduling and Facility Location

“…For example, a mechanism can force a machine that in her declaration has augmented her running time to work that long by keeping her idle for the difference between real and reported running time. 1 We first prove that, no matter the algorithm at hand, there exists an OSP mechanism with monitoring that always compensates the agents their costs. This reimbursement mechanism, introduced in the context of mechanisms with monitoring by Serafino et al [40] (with the name of first-price mechanisms), yields a couple of interesting observations in the context of OSP mechanisms.…”

“…Recent research has come up with different approaches to deal with this question. Some authors [1,5,9,39] suggest to focus on "simple" mechanisms; e.g., in postedprice mechanisms one's own bid is immaterial for the price paid to get some goods of interest-this should immediately suggest that trying to play the mechanism is worthless no matter the cognitive abilities of the agents. However, in such a body of work, this property remains unsatisfactorily vague.…”

Designing Cost-Sharing Methods for Bayesian Games

“…Dynamic pricing schemes has been used by Cohen, Eden, Fiat and Jez [31] in several online settings to induce the same performance as the best online algorithm, and by Cohen-Addad, Eden, Feldman and Fiat [32] in matching markets in order to achieve the optimal social welfare, for any tie breaking rule. For maximizing the revenue with posted price mechanisms see [3,6,8,14,[18][19][20].…”