arXiv subjects

Michal Feldman

Publications and source records attributed to Michal Feldman.

At least 73 records · Page 4Linked to original sources

arXiv2020

Long-Term Care Facilities as a Risk Factor for Death Due to COVID-19

A large percentage of the deaths from COVID-19 occur among residents of long-term care facilities. There are two possible reasons for this phenomenon. First, the structural features of such settings may lead to death. Alternatively, it is possible that individuals in these facilities are in poorer health than those living elsewhere, and that these individuals would have died even if they had not been in these facilities. Our findings show that, controlling for the population density and the percentage of older adults in the population, there is a significant positive association between the number of long-term care beds per capita and COVID-19 mortality rates. This finding provides support for the claim that long-term care living arrangements (of older people) are a significant risk factor for dying from COVID-19.

physics.soc-ph↗

arXiv2020

The Efficiency of Best-Response Dynamics

Best response (BR) dynamics is a natural method by which players proceed toward a pure Nash equilibrium via a local search method. The quality of the equilibrium reached may depend heavily on the order by which players are chosen to perform their best response moves. A {\em deviator rule} $S$ is a method for selecting the next deviating player. We provide a measure for quantifying the performance of different deviator rules. The {\em inefficiency} of a deviator rule $S$ is the maximum ratio, over all initial profiles $p$, between the social cost of the worst equilibrium reachable by $S$ from $p$ and the social cost of the best equilibrium reachable from $p$. This inefficiency always lies between $1$ and the {\em price of anarchy}. We study the inefficiency of various deviator rules in network formation games and job scheduling games (both are congestion games, where BR dynamics always converges to a pure NE). For some classes of games, we compute optimal deviator rules. Furthermore, we define and study a new class of deviator rules, called {\em local} deviator rules. Such rules choose the next deviator as a function of a restricted set of parameters, and satisfy a natural condition called {\em independence of irrelevant players}. We present upper bounds on the inefficiency of some local deviator rules, and also show that for some classes of games, no local deviator rule can guarantee inefficiency lower than the price of anarchy.

cs.GT↗

arXiv2020

Online Stochastic Max-Weight Matching: prophet inequality for vertex and edge arrival models

We provide prophet inequality algorithms for online weighted matching in general (non-bipartite) graphs, under two well-studied arrival models, namely edge arrival and vertex arrival. The weight of each edge is drawn independently from an a-priori known probability distribution. Under edge arrival, the weight of each edge is revealed upon arrival, and the algorithm decides whether to include it in the matching or not. Under vertex arrival, the weights of all edges from the newly arriving vertex to all previously arrived vertices are revealed, and the algorithm decides which of these edges, if any, to include in the matching. To study these settings, we introduce a novel unified framework of batched prophet inequalities that captures online settings where elements arrive in batches; in particular it captures matching under the two aforementioned arrival models. Our algorithms rely on the construction of suitable online contention resolution scheme (OCRS). We first extend the framework of OCRS to batched-OCRS, we then establish a reduction from batched prophet inequality to batched OCRS, and finally we construct batched OCRSs with selectable ratios of 0.337 and 0.5 for edge and vertex arrival models, respectively. Both results improve the state of the art for the corresponding settings. For the vertex arrival, our result is tight. Interestingly, a pricing-based prophet inequality with comparable competitive ratios is unknown.

cs.DS↗

arXiv2019

A General Framework for Endowment Effects in Combinatorial Markets

The endowment effect, coined by Nobel Laureate Richard Thaler, posits that people tend to inflate the value of items they own. This bias was studied, both theoretically and empirically, with respect to a single item. Babaioff et al. [EC'18] took a first step at extending this study beyond a single item. They proposed a specific formulation of the endowment effect in combinatorial settings, and showed that equilibrium existence with respect to the endowed valuations extends from gross substitutes to submodular valuations, but provably fails to extend to XOS valuations. Extending the endowment effect to combinatorial settings can take different forms. In this work, we devise a framework that captures a space of endowment effects, upon which we impose a partial order, which preserves endowment equilibrium existence. Within this framework, we provide existence and welfare guarantees for endowment equilibria corresponding to various endowment effects. Our main results are the following: (1) For markets with XOS valuations, we introduce an endowment effect that is stronger than that of Babaioff et al., for which an endowment equilibrium is guaranteed to exist and gives at least half of the optimal welfare. Moreover, this equilibrium can be reached via a variant of the flexible ascent auction. (2) For markets with arbitrary valuations, we show that bundling leads to a sweeping positive result. In particular, if items can be prepacked into indivisible bundles, there always exists an endowment equilibrium with optimal welfare. Moreover, we provide a polynomial algorithm that given an arbitrary allocation $S$, computes an endowment equilibrium with the same welfare guarantee as in $S$.

cs.GT↗

arXiv2019

Prophets and Secretaries with Overbooking

The prophet and secretary problems demonstrate online scenarios involving the optimal stopping theory. In a typical prophet or secretary problem, selection decisions are assumed to be immediate and irrevocable. However, many online settings accommodate some degree of revocability. To study such scenarios, we introduce the $\ell-out-of-k$ setting, where the decision maker can select up to $k$ elements immediately and irrevocably, but her performance is measured by the top $\ell$ elements in the selected set. Equivalently, the decision makes can hold up to $\ell$ elements at any given point in time, but can make up to $k-\ell$ returns as new elements arrive. We give upper and lower bounds on the competitive ratio of $\ell$-out-of-$k$ prophet and secretary scenarios. These include a single-sample prophet algorithm that gives a competitive ratio of $1-\ell\cdot e^{-Θ\left(\frac{\left(k-\ell\right)^2}{k}\right)}$, which is asymptotically tight for $k-\ell=Θ(\ell)$. For secretary settings, we devise an algorithm that obtains a competitive ratio of $1-\ell e^{-\frac{k-8\ell}{2+2\ln \ell}} - e^{-k/6}$, and show that no secretary algorithm obtains a better ratio than $1-e^{-k}$ (up to negligible terms). In passing, our results lead to an improvement of the results of Assaf et al. [2000] for $1-out-of-k$ prophet scenarios. Beyond the contribution to online algorithms and optimal stopping theory, our results have implications to mechanism design. In particular, we use our prophet algorithms to derive {\em overbooking} mechanisms with good welfare and revenue guarantees; these are mechanisms that sell more items than the seller's capacity, then allocate to the agents with the highest values among the selected agents.

cs.GT↗

arXiv2019

Combinatorial Auctions with Interdependent Valuations: SOS to the Rescue

We study combinatorial auctions with interdependent valuations. In such settings, each agent $i$ has a private signal $s_i$ that captures her private information, and the valuation function of every agent depends on the entire signal profile, ${\bf s}=(s_1,\ldots,s_n)$. The literature in economics shows that the interdependent model gives rise to strong impossibility results, and identifies assumptions under which optimal solutions can be attained. The computer science literature provides approximation results for simple single-parameter settings (mostly single item auctions, or matroid feasibility constraints). Both bodies of literature focus largely on valuations satisfying a technical condition termed {\em single crossing} (or variants thereof). We consider the class of {\em submodular over signals} (SOS) valuations (without imposing any single-crossing type assumption), and provide the first welfare approximation guarantees for multi-dimensional combinatorial auctions, achieved by universally ex-post IC-IR mechanisms. Our main results are: $(i)$ 4-approximation for any single-parameter downward-closed setting with single-dimensional signals and SOS valuations; $(ii)$ 4-approximation for any combinatorial auction with multi-dimensional signals and {\em separable}-SOS valuations; and $(iii)$ $(k+3)$- and $(2\log(k)+4)$-approximation for any combinatorial auction with single-dimensional signals, with $k$-sized signal space, for SOS and strong-SOS valuations, respectively. All of our results extend to a parameterized version of SOS, $d$-SOS, while losing a factor that depends on $d$.

cs.GT↗

arXiv2018

Complement-Free Couples Must Communicate: A Hardness Result for Two-Player Combinatorial Auctions

We study the communication complexity of welfare maximization in combinatorial auctions with $m$ items and two subadditive bidders. A $\frac{1}{2}$-approximation can be guaranteed by a trivial randomized protocol with zero communication, or a trivial deterministic protocol with $O(1)$ communication. We show that outperforming these trivial protocols requires exponential communication, settling an open question of [DobzinskiNS10, Feige09]. Specifically, we show that any (randomized) protocol guaranteeing a $(\frac{1}{2}+\frac{6}{\log_2 m})$-approximation requires communication exponential in $m$. This is tight even up to lower-order terms: we further present a $(\frac{1}{2}+\frac{1}{O(\log m)})$-approximation in poly($m$) communication. To derive our results, we introduce a new class of subadditive functions that are "far from" fractionally subadditive functions, and may be of independent interest for future works. Beyond our main result, we consider the spectrum of valuations between fractionally-subadditive and subadditive via the MPH hierarchy. Finally, we discuss the implications of our results towards combinatorial auctions with strategic bidders.

cs.GT↗

arXiv2018

Interdependent Values without Single-Crossing

We consider a setting where an auctioneer sells a single item to $n$ potential agents with {\em interdependent values}. That is, each agent has her own private signal, and the valuation of each agent is a known function of all $n$ private signals. This captures settings such as valuations for artwork, oil drilling rights, broadcast rights, and many more. In the interdependent value setting, all previous work has assumed a so-called {\sl single-crossing condition}. Single-crossing means that the impact of agent $i$'s private signal, $s_i$, on her own valuation is greater than the impact of $s_i$ on the valuation of any other agent. It is known that without the single-crossing condition an efficient outcome cannot be obtained. We study welfare maximization for interdependent valuations through the lens of approximation. We show that, in general, without the single-crossing condition, one cannot hope to approximate the optimal social welfare any better than the approximation given by assigning the item to a random bidder. Consequently, we introduce a relaxed version of single-crossing, {\sl $c$-single-crossing}, parameterized by $c\geq 1$, which means that the impact of $s_i$ on the valuation of agent $i$ is at least $1/c$ times the impact of $s_i$ on the valuation of any other agent ($c=1$ is single-crossing). Using this parameterized notion, we obtain a host of positive results. We propose a prior-free deterministic mechanism that gives an $(n-1)c$-approximation guarantee to welfare. We then show that a random version of the proposed mechanism gives a prior-free universally truthful $2c$-approximation to the optimal welfare for any concave $c$-single crossing setting (and a $2\sqrt{n}c^{3/2}$-approximation in the absence of concavity). We extend this mechanism to a universally truthful mechanism that gives $O(c^2)$-approximation to the optimal revenue.

cs.GT↗

arXiv2018

The Invisible Hand of Dynamic Market Pricing

Walrasian prices, if they exist, have the property that one can assign every buyer some bundle in her demand set, such that the resulting assignment will maximize social welfare. Unfortunately, this assumes carefully breaking ties amongst different bundles in the buyer demand set. Presumably, the shopkeeper cleverly convinces the buyer to break ties in a manner consistent with maximizing social welfare. Lacking such a shopkeeper, if buyers arrive sequentially and simply choose some arbitrary bundle in their demand set, the social welfare may be arbitrarily bad. In the context of matching markets, we show how to compute dynamic prices, based upon the current inventory, that guarantee that social welfare is maximized. Such prices are set without knowing the identity of the next buyer to arrive. We also show that this is impossible in general (e.g., for coverage valuations), but consider other scenarios where this can be done. We further extend our results to Bayesian and bounded rationality models.

cs.GT↗

arXiv2018

Prompt Scheduling for Selfish Agents

We give a prompt online mechanism for minimizing the sum of [weighted] completion times. This is the first prompt online algorithm for the problem. When such jobs are strategic agents, delaying scheduling decisions makes little sense. Moreover, the mechanism has a particularly simple form of an anonymous menu of options.

cs.DS↗

arXiv2018

Approximate Modularity Revisited

Set functions with convenient properties (such as submodularity) appear in application areas of current interest, such as algorithmic game theory, and allow for improved optimization algorithms. It is natural to ask (e.g., in the context of data driven optimization) how robust such properties are, and whether small deviations from them can be tolerated. We consider two such questions in the important special case of linear set functions. One question that we address is whether any set function that approximately satisfies the modularity equation (linear functions satisfy the modularity equation exactly) is close to a linear function. The answer to this is positive (in a precise formal sense) as shown by Kalton and Roberts [1983] (and further improved by Bondarenko, Prymak, and Radchenko [2013]). We revisit their proof idea that is based on expander graphs, and provide significantly stronger upper bounds by combining it with new techniques. Furthermore, we provide improved lower bounds for this problem. Another question that we address is that of how to learn a linear function $h$ that is close to an approximately linear function $f$, while querying the value of $f$ on only a small number of sets. We present a deterministic algorithm that makes only linearly many (in the number of items) nonadaptive queries, by this improving over a previous algorithm of Chierichetti, Das, Dasgupta and Kumar [2015] that is randomized and makes more than a quadratic number of queries. Our learning algorithm is based on a Hadamard transform.

cs.DS↗

arXiv2018

Max-Min Greedy Matching

A bipartite graph $G(U,V;E)$ that admits a perfect matching is given. One player imposes a permutation $π$ over $V$, the other player imposes a permutation $σ$ over $U$. In the greedy matching algorithm, vertices of $U$ arrive in order $σ$ and each vertex is matched to the lowest (under $π$) yet unmatched neighbor in $V$ (or left unmatched, if all its neighbors are already matched). The obtained matching is maximal, thus matches at least a half of the vertices. The max-min greedy matching problem asks: suppose the first (max) player reveals $π$, and the second (min) player responds with the worst possible $σ$ for $π$, does there exist a permutation $π$ ensuring to match strictly more than a half of the vertices? Can such a permutation be computed in polynomial time? The main result of this paper is an affirmative answer for this question: we show that there exists a polytime algorithm to compute $π$ for which for every $σ$ at least $ρ> 0.51$ fraction of the vertices of $V$ are matched. We provide additional lower and upper bounds for special families of graphs, including regular and Hamiltonian. Interestingly, even for regular graphs with arbitrarily large degree (implying a large number of disjoint perfect matchings), there is no $π$ ensuring to match more than a fraction $8/9$ of the vertices. The max-min greedy matching problem solves an open problem regarding the welfare guarantees attainable by pricing in sequential markets with binary unit-demand valuations. In addition, it has implications for the size of the unique stable matching in markets with global preferences, subject to the graph structure.

cs.GT↗

arXiv2018

Pricing Multi-Unit Markets

We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer's information and agents' valuations. Our results provide insights about the relative power of uniform and non-uniform prices, the relative difficulty of different valuation classes, and the implications of different informational assumptions. Among other results, we prove constant-factor guarantees for agents with (symmetric) subadditive valuations, even in an incomplete-information setting and with uniform prices.

cs.GT↗

arXiv2018

99\% Revenue via Enhanced Competition

A sequence of recent studies show that even in the simple setting of a single seller and a single buyer with additive, independent valuations over $m$ items, the revenue-maximizing mechanism is prohibitively complex. This problem has been addressed using two main approaches: (i) Approximation: the best of two simple mechanisms (sell each item separately, or sell all the items as one bundle) gives $1/6$ of the optimal revenue [BILW14]. (ii) Enhanced competition: running the simple VCG mechanism with additional $m$ buyers extracts at least the optimal revenue in the original market [EFFTW17]. Both approaches, however, suffer from severe drawbacks: On the one hand, losing $83\%$ of the revenue is hardly acceptable in any application. On the other hand, attracting a linear number of new buyers may be prohibitive. Our main result is that by combining the two approaches one can achieve the best of both worlds. Specifically, for any constant $ε$ one can obtain a $(1-ε)$ fraction of the optimal revenue by running simple mechanisms --- either selling each item separately or selling all items as a single bundle --- with substantially fewer additional buyers: logarithmic, constant, or even none in some cases.

cs.GT↗

arXiv2017

Prophet Inequalities Made Easy: Stochastic Optimization by Pricing Non-Stochastic Inputs

We present a general framework for stochastic online maximization problems with combinatorial feasibility constraints. The framework establishes prophet inequalities by constructing price-based online approximation algorithms, a natural extension of threshold algorithms for settings beyond binary selection. Our analysis takes the form of an extension theorem: we derive sufficient conditions on prices when all weights are known in advance, then prove that the resulting approximation guarantees extend directly to stochastic settings. Our framework unifies and simplifies much of the existing literature on prophet inequalities and posted price mechanisms, and is used to derive new and improved results for combinatorial markets (with and without complements), multi-dimensional matroids, and sparse packing problems. Finally, we highlight a surprising connection between the smoothness framework for bounding the price of anarchy of mechanisms and our framework, and show that many smooth mechanisms can be recast as posted price mechanisms with comparable performance guarantees.

cs.GT↗

arXiv2017

Pricing Social Goods

Social goods are goods that grant value not only to their owners but also to the owners' surroundings, be it their families, friends or office mates. The benefit a non-owner derives from the good is affected by many factors, including the type of the good, its availability, and the social status of the non-owner. Depending on the magnitude of the benefit and on the price of the good, a potential buyer might stay away from purchasing the good, hoping to free ride on others' purchases. A revenue-maximizing seller who sells social goods must take these considerations into account when setting prices for the good. The literature on optimal pricing has advanced considerably over the last decade, but little is known about optimal pricing schemes for selling social goods. In this paper, we conduct a systematic study of revenue-maximizing pricing schemes for social goods: we introduce a Bayesian model for this scenario, and devise nearly-optimal pricing schemes for various types of externalities, both for simultaneous sales and for sequential sales.

cs.GT↗

arXiv2017

Makespan Minimization via Posted Prices

We consider job scheduling settings, with multiple machines, where jobs arrive online and choose a machine selfishly so as to minimize their cost. Our objective is the classic makespan minimization objective, which corresponds to the completion time of the last job to complete. The incentives of the selfish jobs may lead to poor performance. To reconcile the differing objectives, we introduce posted machine prices. The selfish job seeks to minimize the sum of its completion time on the machine and the posted price for the machine. Prices may be static (i.e., set once and for all before any arrival) or dynamic (i.e., change over time), but they are determined only by the past, assuming nothing about upcoming events. Obviously, such schemes are inherently truthful. We consider the competitive ratio: the ratio between the makespan achievable by the pricing scheme and that of the optimal algorithm. We give tight bounds on the competitive ratio for both dynamic and static pricing schemes for identical, restricted, related, and unrelated machine settings. Our main result is a dynamic pricing scheme for related machines that gives a constant competitive ratio, essentially matching the competitive ratio of online algorithms for this setting. In contrast, dynamic pricing gives poor performance for unrelated machines. This lower bound also exhibits a gap between what can be achieved by pricing versus what can be achieved by online algorithms.

cs.GT↗

arXiv2017

Stable Secretaries

We define and study a new variant of the secretary problem. Whereas in the classic setting multiple secretaries compete for a single position, we study the case where the secretaries arrive one at a time and are assigned, in an on-line fashion, to one of multiple positions. Secretaries are ranked according to talent, as in the original formulation, and in addition positions are ranked according to attractiveness. To evaluate an online matching mechanism, we use the notion of blocking pairs from stable matching theory: our goal is to maximize the number of positions (or secretaries) that do not take part in a blocking pair. This is compared with a stable matching in which no blocking pair exists. We consider the case where secretaries arrive randomly, as well as that of an adversarial arrival order, and provide corresponding upper and lower bounds.

cs.GT↗