Heavy Tails Make Happy Buyers

Approximating the Revenue Maximization Problem with Sharp Demands

We consider the revenue maximization problem with sharp multi-demand, in which $m$ indivisible items have to be sold to $n$ potential buyers. Each buyer $i$ is interested in getting exactly $d_i$ items, and each item $j$ gives a benefit $v_{ij}$ to buyer $i$. We distinguish between unrelated and related valuations. In the former case, the benefit $v_{ij}$ is completely arbitrary, while, in the latter, each item $j$ has a quality $q_j$, each buyer $i$ has a value $v_i$ and the benefit $v_{ij}$ is defined as the product $v_i q_j$. The problem asks to determine a price for each item and an alloca…

Simple Mechanisms for a Subadditive Buyer and Applications to Revenue Monotonicity

We study the revenue maximization problem of a seller with n heterogeneous items for sale to a single buyer whose valuation function for sets of items is unknown and drawn from some distribution D. We show that if D is a distribution over subadditive valuations with independent items, then the better of pricing each item separately or pricing only the grand bundle achieves a constant-factor approximation to the revenue of the optimal mechanism. This includes buyers who are k-demand, additive up to a matroid constraint, or additive up to constraints of any downwards-closed set system (and whose…

Bulow-Klemperer-Style Results for Welfare Maximization in Two-Sided Markets

We consider the problem of welfare maximization in two-sided markets using simple mechanisms that are prior-independent. The Myerson-Satterthwaite impossibility theorem shows that even for bilateral trade, there is no feasible (IR, truthful, budget balanced) mechanism that has welfare as high as the optimal-yet-infeasible VCG mechanism, which attains maximal welfare but runs a deficit. On the other hand, the optimal feasible mechanism needs to be carefully tailored to the Bayesian prior, and is extremely complex, eluding a precise description. We present Bulow-Klemperer-style results to circum…

On the Competition Complexity of Dynamic Mechanism Design

The Competition Complexity of an auction measures how much competition is needed for the revenue of a simple auction to surpass the optimal revenue. A classic result from auction theory by Bulow and Klemperer [9], states that the Competition Complexity of VCG, in the case of n i.i.d. buyers and a single item, is 1, i.e., it is better to recruit one extra buyer and run a second price auction than to learn exactly the buyers' underlying distribution and run the revenue-maximizing auction tailored to this distribution. In this paper we study the Competition Complexity of dynamic auctions. Conside…

An equilibrium model for matching impatient demand and patient supply over time

We present a simple dynamic equilibrium model for an online exchange where both buyers and sellers arrive according to a exogenously defined stochastic process. The structure of this exchange is motivated by the limit order book mechanism used in stock markets. Both buyers and sellers are elastic in the price-quantity space; however, only the sellers are assumed to be patient, i.e. only the sellers have a price - time elasticity, whereas the buyers are assumed to be impatient. Sellers select their selling price as a best response to all the other sellers' strategies. We define and establish th…

双边贸易中随机报价机制的更紧边界

Tighter Bounds for the Random-Offerer Mechanism in Bilateral Trade

研究双边贸易中随机报价机制，设\(\rho_{\rm RO}\)为该机制贸易收益与最优贸易收益之比下确界。证明了\(\frac{1}{\pi}\leq\rho_{\rm RO}<0.460242308085529\)，改进了上下界，分别采用参数化拉格朗日边界和构造明确族的方法。