Two-sided matching platforms provide users with menus of match recommendations. To maximize the number of realized matches between the two sides (referred here as customers and suppliers), the platform must balance the inherent tension between recommending customers more potential suppliers to match with and avoiding potential collisions. We introduce a stylized model to study the above trade-off. The platform offers each customer a menu of suppliers, and customers choose, simultaneously and independently, either a supplier from their menu or to remain unmatched. Suppliers then see the set of customers that have selected them, and choose to either match with one of these customers or to remain unmatched. A match occurs if a customer and a supplier choose each other (in sequence). Agents' choices are probabilistic, and proportional to public scores of agents in their menu and a score that is associated with remaining unmatched. The platform's problem is to construct menus for costumers to maximize the number of matches. This problem is shown to be strongly NP-hard via a reduction from 3-partition. We provide an efficient algorithm that achieves a constant-factor approximation to the expected number of matches.
We consider an online assortment problem with $[n]:=\{1,2,\ldots,n\}$ sellers, each holding exactly one item $i\in[n]$ with initial inventory $c_i\in \mathbb{Z}_+$, and a sequence of homogeneous buyers arriving over a finite time horizon $t=1,2,\ldots,m$. There is an online platform whose goal is to offer a subset $S_t\subseteq [n]$ of sellers to the arriving buyer at time $t$ to maximize the expected revenue derived over the entire horizon while respecting the inventory constraints. Given an assortment $S_t$ at time $t$, it is assumed that the buyer will select an item from $S_t$ based on the…
We study how to maximize the broker's (expected) profit in a two-sided market, where she buys items from a set of sellers and resells them to a set of buyers. Each seller has a single item to sell and holds a private value on her item, and each buyer has a valuation function over the bundles of the sellers' items. We consider the Bayesian setting where the agents' values are independently drawn from prior distributions, and aim at designing dominant-strategy incentive-compatible (DSIC) mechanisms that are approximately optimal. Production-cost markets, where each item has a publicly-known cost…
Motivated by the emergence of popular service-based two-sided markets where sellers can serve multiple buyers at the same time, we formulate and study the {\em two-sided cost sharing} problem. In two-sided cost sharing, sellers incur different costs for serving different subsets of buyers and buyers have different values for being served by different sellers. Both buyers and sellers are self-interested agents whose values and costs are private information. We study the problem from the perspective of an intermediary platform that matches buyers to sellers and assigns prices and wages in an eff…
We consider two sided matching markets consisting of agents with non-transferable utilities; agents from the opposite sides form matching pairs (e.g., buyers-sellers) and negotiate the terms of their math which may include a monetary transfer. Competitive equilibria are the elements of the core of this game. We present the first combinatorial characterization of competitive equilibria that relates the utility of each agent at equilibrium to the equilibrium utilities of other agents in a strictly smaller market excluding that agent; thus automatically providing a constructive proof of existence…
Strategic behavior in two-sided matching markets has been traditionally studied in a "one-sided" manipulation setting where the agent who misreports is also the intended beneficiary. Our work investigates "two-sided" manipulation of the deferred acceptance algorithm where the misreporting agent and the manipulator (or beneficiary) are on different sides. Specifically, we generalize the recently proposed accomplice manipulation model (where a man misreports on behalf of a woman) along two complementary dimensions: (a) the two for one model, with a pair of misreporting agents (man and woman) and…
We design simple mechanisms to approximate the Gains from Trade (GFT) in two-sided markets with multiple unit-supply sellers and multiple unit-demand buyers. A classical impossibility result by Myerson and Satterthwaite showed that even with only one seller and one buyer, no Individually Rational (IR), Bayesian Incentive Compatible (BIC) and Budget-Balanced (BB) mechanism can achieve full GFT (trade whenever buyer's value is higher than the seller's cost). On the other hand, they proposed the "second-best" mechanism that maximizes the GFT subject to IR, BIC and BB constraints, which is unfortu…
We study the problem of allocating indivisible objects to a set of rational agents where each agent's final utility depends on the intrinsic valuation of the allocated item as well as the allocation within the agent's local neighbourhood. We specify agents' local neighbourhood in terms of a weighted graph. This extends the model of one-sided markets to incorporate neighbourhood externalities. We consider the solution concept of stability and show that, unlike in the case of one-sided markets, stable allocations may not always exist. When the underlying local neighbourhood graph is symmetric, a…
"Net neutrality" often refers to the policy dictating that an Internet service provider (ISP) cannot charge content providers (CPs) for delivering their content to consumers. Many past quantitative models designed to determine whether net neutrality is a good idea have been rather equivocal in their conclusions. Here we propose a very simple two-sided market model, in which the types of the consumers and the CPs are {\em power-law distributed} --- a kind of distribution known to often arise precisely in connection with Internet-related phenomena. We derive mostly analytical, closed-form result…
The study of mechanisms for multi-sided markets has received an increasingly growing attention from the research community, and is motivated by the numerous examples of such markets on the web and in electronic commerce. Many of these examples represent dynamic and uncertain environments, and thus, require, in fact, online mechanisms. Unfortunately, as far as we know, no previously published online mechanism for a multi-sided market (or even for a double-sided market) has managed to (approximately) maximize the gain from trade, while guaranteeing desirable economic properties such as incentivi…
We consider mechanisms for markets that are double-sided and have players with multi-dimensional strategic spaces on at least one side. The players of the market are strategic, and act to optimize their own utilities. The mechanism designer, on the other hand, aims to optimize a social goal, i.e., the gain from trade. We focus on one example of this setting which is motivated by the foreseeable future form of online advertising. Online advertising currently supports some of the most important Internet services, including: search, social media and user generated content sites. To overcome priva…
Mechanism design for one-sided markets has been investigated for several decades in economics and in computer science. More recently, there has been an increased attention on mechanisms for two-sided markets, in which buyers and sellers act strategically. For two-sided markets, an impossibility result of Myerson and Satterthwaite states that no mechanism can simultaneously satisfy individual rationality (IR), incentive compatibility (IC), strong budget-balance (SBB), and be efficient. On the other hand, important applications to web advertisement, stock exchange, and frequency spectrum allocat…
In this paper, we present a new model and two mechanisms for auctions in two-sided markets of buyers and sellers, where budget constraints are imposed on buyers. Our model incorporates polymatroidal environments, and is applicable to a wide variety of models that include multiunit auctions, matching markets and reservation exchange markets. Our mechanisms are build on polymatroidal network flow model by Lawler and Martel, and enjoy various nice properties such as incentive compatibility of buyers, individual rationality, pareto optimality, strong budget balance. The first mechanism is a simple…
Double sided auctions are widely used in financial markets to match demand and supply. Prior works on double sided auctions have focused primarily on single quantity trade requests. We extend various notions of double sided auctions to incorporate multiple quantity trade requests and provide fully formalized matching algorithms for double sided auctions with their correctness proofs. We establish new uniqueness theorems that enable automatic detection of violations in an exchange program by comparing its output with that of a verified program. All proofs are formalized in the Coq proof assista…
A two-sided market consists of two sets of agents, each of whom have preferences over the other (Airbnb, Upwork, Lyft, Uber, etc.). We propose and analyze a repeated matching problem, where some set of matches occur on each time step, and our goal is to ensure fairness with respect to the cumulative allocations over an infinite time horizon. Our main result is a polynomial-time algorithm for additive, symmetric (v_i(j) = v_j(i)), and binary (v_i(j) \in \{a,1\}) valuations that both (1) guarantees "envy-freeness up to a single match" (EF1) and (2) selects a maximum weight matching on each time …
We study gains from trade in multi-dimensional two-sided markets. Specifically, we focus on a setting with $n$ heterogeneous items, where each item is owned by a different seller $i$, and there is a constrained-additive buyer with feasibility constraint $\mathcal{F}$. Multi-dimensional settings in one-sided markets, e.g. where a seller owns multiple heterogeneous items but also is the mechanism designer, are well-understood. In addition, single-dimensional settings in two-sided markets, e.g. where a buyer and seller each seek or own a single item, are also well-understood. Multi-dimensional tw…
Hong Kong University of Science and Technology（香港科技大学）；Central China Normal University（华中师范大学）；Shanghai University of Finance and Economics（上海财经大学）；Great Bay University（大湾区大学）
本文研究了双边市场中在线定价问题，提出双价格和分段价格机制，分别在利润和GFT最大化中取得O(n² log log T)和O(n² log log T + n³)的后悔界。
In two-sided markets, Myerson and Satterthwaite's impossibility theorem states that one can not maximize the gain-from-trade while also satisfying truthfulness, individual-rationality and no deficit. Attempts have been made to circumvent Myerson and Satterthwaite's result by attaining approximately-maximum gain-from-trade: the double-sided auctions of McAfee (1992) is truthful and has no deficit, and the one by Segal-Halevi et al. (2016) additionally has no surplus --- it is strongly-budget-balanced. They consider two categories of agents --- buyers and sellers, where each trade set is compose…
We study social welfare in one-sided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent's utility linearly decreases down his preference lists, and measures th…
The Arrow-Debreu extension of the classic Hylland-Zeckhauser scheme for a one-sided matching market -- called ADHZ in this paper -- has natural applications but has instances which do not admit equilibria. By introducing approximation, we define the $ε$-approximate ADHZ model, and we give the following results. * Existence of equilibrium under linear utility functions. We prove that the equilibrium satisfies Pareto optimality, approximate envy-freeness, and approximate weak core stability. * A combinatorial polynomial-time algorithm for an $ε$-approximate ADHZ equilibrium for the case of dicho…
We study the welfare structure in two-sided large random matching markets. In the model, each agent has a latent personal score for every agent on the other side of the market and her preferences follow a logit model based on these scores. Under a contiguity condition, we provide a tight description of stable outcomes. First, we identify an intrinsic fitness for each agent that represents her relative competitiveness in the market, independent of the realized stable outcome. The intrinsic fitness values correspond to scaling coefficients needed to make a latent mutual matrix bi-stochastic, whe…
We design novel mechanisms for welfare-maximization in two-sided markets. That is, there are buyers willing to purchase items and sellers holding items initially, both acting rationally and strategically in order to maximize utility. Our mechanisms are designed based on a powerful correspondence between two-sided markets and prophet inequalities. They satisfy individual rationality, dominant-strategy incentive compatibility, budget-balance constraints and give constant-factor approximations to the optimal social welfare. We improve previous results in several settings: Our main focus is on mat…
Following up on purely theoretical work of Bredereck et al. [AAAI 2020], we contribute further theoretical insights into adapting stable two-sided matchings to change. Moreover, we perform extensive empirical studies hinting at numerous practically useful properties. Our theoretical extensions include the study of new problems (that is, incremental variants of Almost Stable Marriage and Hospital Residents), focusing on their (parameterized) computational complexity and the equivalence of various change types (thus simplifying algorithmic and complexity-theoretic studies for various natural cha…
We introduce a new algorithm for finding stable matchings in multi-sided matching markets. Our setting is motivated by a PhD market of students, advisors, and co-advisors, and can be generalized to supply chain networks viewed as $n$-sided markets. In the three-sided PhD market, students primarily care about advisors and then about co-advisors (consistent preferences), while advisors and co-advisors have preferences over students only (hence they are cooperative). A student must be matched to one advisor and one co-advisor, or not at all. In contrast to previous work, advisor-student and stude…
Mobility-as-a-Service (MaaS) is an emerging business model driven by the concept of "Everything-as-a-Service" and enabled through mobile internet technologies. In the context of economic deregulation, a MaaS system consists of a typical two-sided market, where travelers and transportation service providers (TSPs) are two groups of agents interacting with each other through a MaaS platform. In this study, we propose a modeling and optimization framework for the regulation of two-sided MaaS markets. We consider a name-your-own-price (NYOP)-auction mechanism where travelers submit purchase-bids t…
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…
Two-sided matching markets have long existed to pair agents in the absence of regulated exchanges. A common example is school choice, where a matching mechanism uses student and school preferences to assign students to schools. In such settings, forming preferences is both difficult and critical. Prior work has suggested various prediction mechanisms that help agents make decisions about their preferences. Although often deployed together, these matching and prediction mechanisms are almost always analyzed separately. The present work shows that at the intersection of the two lies a previously…
The ELLIS PhD program is a European initiative that supports excellent young researchers by connecting them to leading researchers in AI. In particular, PhD students are supervised by two advisors from different countries: an advisor and a co-advisor. In this work we summarize the procedure that, in its final step, matches students to advisors in the ELLIS 2020 PhD program. The steps of the procedure are based on the extensive literature of two-sided matching markets and the college admissions problem [Knuth and De Bruijn, 1997, Gale and Shapley, 1962, Rothand Sotomayor, 1992]. We introduce Po…
We study variants of the stable marriage and college admissions models in which the agents are allowed to express weak preferences over the set of agents on the other side of the market and the option of remaining unmatched. For the problems that we address, previous authors have presented polynomial-time algorithms for computing a "Pareto-stable" matching. In the case of college admissions, these algorithms require the preferences of the colleges over groups of students to satisfy a technical condition related to responsiveness. We design new polynomial-time Pareto-stable algorithms for stabl…
In 1979, Hylland and Zeckhauser \cite{hylland} gave a simple and general scheme for implementing a one-sided matching market using the power of a pricing mechanism. Their method has nice properties -- it is incentive compatible in the large and produces an allocation that is Pareto optimal -- and hence it provides an attractive, off-the-shelf method for running an application involving such a market. With matching markets becoming ever more prevalant and impactful, it is imperative to finally settle the computational complexity of this scheme. We present the following partial resolution: 1. A …
