arXiv subjects

Moshe Babaioff

Publications and source records attributed to Moshe Babaioff.

At least 37 records · Page 2Linked to original sources

arXiv2022

Optimal Collaterals in Multi-Enterprise Investment Networks

We study a market of investments on networks, where each agent (vertex) can invest in any enterprise linked to her, and at the same time, raise capital for her firm's enterprise from other agents she is linked to. Failing to raise sufficient capital results with the firm defaulting, being unable to invest in others. Our main objective is to examine the role of collateral contracts in handling the strategic risk that can propagate to a systemic risk throughout the network in a cascade of defaults. We take a mechanism-design approach and solve for the optimal scheme of collateral contracts that capital raisers offer their investors. These contracts aim at sustaining the efficient level of investment as a unique Nash equilibrium, while minimizing the total collateral. Our main results contrast the network environment with its non-network counterpart (where the sets of investors and capital raisers are disjoint). We show that for acyclic investment networks, the network environment does not necessitate any additional collaterals, and systemic risk can be fully handled by optimal bilateral collateral contracts between capital raisers and their investors. This is, unfortunately, not the case for cyclic investment networks. We show that bilateral contracting will not suffice to resolve systemic risk, and the market will need an external entity to design a global collateral scheme for all capital raisers. Furthermore, the minimum total collateral that will sustain the efficient level of investment as a unique equilibrium may be arbitrarily higher, even in simple cyclic investment networks, compared with its corresponding non-network environment. Additionally, we prove computational-complexity results, both for a single enterprise and for networks.

cs.GT↗

arXiv2022

Truthful Online Scheduling of Cloud Workloads under Uncertainty

Cloud computing customers often submit repeating jobs and computation pipelines on \emph{approximately} regular schedules, with arrival and running times that exhibit variance. This pattern, typical of training tasks in machine learning, allows customers to partially predict future job requirements. We develop a model of cloud computing platforms that receive statements of work (SoWs) in an online fashion. The SoWs describe future jobs whose arrival times and durations are probabilistic, and whose utility to the submitting agents declines with completion time. The arrival and duration distributions, as well as the utility functions, are considered private customer information and are reported by strategic agents to a scheduler that is optimizing for social welfare. We design pricing, scheduling, and eviction mechanisms that incentivize truthful reporting of SoWs. An important challenge is maintaining incentives despite the possibility of the platform becoming saturated. We introduce a framework to reduce scheduling under uncertainty to a relaxed scheduling problem without uncertainty. Using this framework, we tackle both adversarial and stochastic submissions of statements of work, and obtain logarithmic and constant competitive mechanisms, respectively.

cs.GT↗

arXiv2021

Fair-Share Allocations for Agents with Arbitrary Entitlements

We consider the problem of fair allocation of indivisible goods to $n$ agents, with no transfers. When agents have equal entitlements, the well established notion of the maximin share (MMS) serves as an attractive fairness criterion, where to qualify as fair, an allocation needs to give every agent at least a substantial fraction of her MMS. In this paper we consider the case of arbitrary (unequal) entitlements. We explain shortcomings in previous attempts that extend the MMS to unequal entitlements. Our conceptual contribution is the introduction of a new notion of a share, the AnyPrice share (APS), that is appropriate for settings with arbitrary entitlements. Even for the equal entitlements case, this notion is new, and satisfies $APS \ge MMS$, where the inequality is sometimes strict. We present two equivalent definitions for the APS (one as a minimization problem, the other as a maximization problem), and provide comparisons between the APS and previous notions of fairness. Our main result concerns additive valuations and arbitrary entitlements, for which we provide a polynomial-time algorithm that gives every agent at least a $\frac{3}{5}$-fraction of her APS. This algorithm can also be viewed as providing strategies in a certain natural bidding game, and these strategies secure each agent at least a $\frac{3}{5}$-fraction of her APS.

cs.GT↗

arXiv2021

A Note on the Gains from Trade of the Random-Offerer Mechanism

We study the classic bilateral trade setting. Myerson and Satterthwaite show that there is no Bayesian incentive compatible and budget-balanced mechanism that obtains the gains from trade of the first-best mechanism. Consider the random-offerer mechanism: with probability $\frac{1}{2}$ run the \emph{seller-offering} mechanism, in which the seller offers the buyer a take-it-or-leave-it price that maximizes the expected profit of the seller, and with probability $\frac{1}{2}$ run the \emph{buyer-offering} mechanism. Very recently, Deng, Mao, Sivan, and Wang showed that the gains from trade of the random-offerer mechanism is at least a constant factor of $\frac 1 {8.23}\approx 0.121$ of the gains from trade of the first best mechanism. Perhaps a natural conjecture is that the gains-from-trade of the random-offerer mechanism, which is known to be at least half of the gains-from-trade of the second-best mechanism, is also at least half of the gains-from-trade of the first-best mechanism. However, in this note we exhibit distributions such as the gains-from trade of the random-offerer mechanism is smaller than a $0.495$-fraction of the gains-from-trade of the first-best mechanism.

cs.GT↗

arXiv2021

Beyond Pigouvian Taxes: A Worst Case Analysis

In the early $20^{th}$ century, Pigou observed that imposing a marginal cost tax on the usage of a public good induces a socially efficient level of use as an equilibrium. Unfortunately, such a "Pigouvian" tax may also induce other, socially inefficient, equilibria. We observe that this social inefficiency may be unbounded, and study whether alternative tax structures may lead to milder losses in the worst case, i.e. to a lower price of anarchy. We show that no tax structure leads to bounded losses in the worst case. However, we do find a tax scheme that has a lower price of anarchy than the Pigouvian tax, obtaining tight lower and upper bounds in terms of a crucial parameter that we identify. We generalize our results to various scenarios that each offers an alternative to the use of a public road by private cars, such as ride sharing, or using a bus or a train.

econ.TH↗

arXiv2021

The Menu-Size Complexity of Revenue Approximation

Consider a monopolist selling $n$ items to an additive buyer whose item values are drawn from independent distributions $F_1,F_2,\ldots,F_n$ possibly having unbounded support. Unlike in the single-item case, it is well known that the revenue-optimal selling mechanism (a pricing scheme) may be complex, sometimes requiring a continuum of menu entries. Also known is that simple mechanisms with a bounded number of menu entries can extract a constant fraction of the optimal revenue. Nonetheless, whether an arbitrarily high fraction of the optimal revenue can be extracted via a bounded menu size remained open. We give an affirmative answer: for every $n$ and $\varepsilon>0$, there exists $C=C(n,\varepsilon)$ s.t. mechanisms of menu size at most $C$ suffice for obtaining $(1-\varepsilon)$ of the optimal revenue from any $F_1,\ldots,F_n$. We prove upper and lower bounds on the revenue-approximation complexity $C(n,\varepsilon)$ and on the deterministic communication complexity required to run a mechanism achieving such an approximation.

cs.GT↗

arXiv2020

Fair and Truthful Mechanisms for Dichotomous Valuations

We consider the problem of allocating a set on indivisible items to players with private preferences in an efficient and fair way. We focus on valuations that have dichotomous marginals, in which the added value of any item to a set is either 0 or 1, and aim to design truthful allocation mechanisms (without money) that maximize welfare and are fair. For the case that players have submodular valuations with dichotomous marginals, we design such a deterministic truthful allocation mechanism. The allocation output by our mechanism is Lorenz dominating, and consequently satisfies many desired fairness properties, such as being envy-free up to any item (EFX), and maximizing the Nash Social Welfare (NSW). We then show that our mechanism with random priorities is envy-free ex-ante, while having all the above properties ex-post. Furthermore, we present several impossibility results precluding similar results for the larger class of XOS valuations. To gauge the robustness of our positive results, we also study $ε$-dichotomous valuations, in which the added value of any item to a set is either non-positive, or in the range $[1, 1 + ε]$. We show several impossibility results in this setting, and also a positive result: for players that have additive $ε$-dichotomous valuations with sufficiently small $ε$, we design a randomized truthful mechanism with strong ex-post guarantees. For $ρ= \frac{1}{1 + ε}$, the allocations that it produces generate at least a $ρ$-fraction of the maximum welfare, and enjoy $ρ$-approximations for various fairness properties, such as being envy-free up to one item (EF1), and giving each player at least her maximin share.

cs.GT↗

arXiv2020

Non-quasi-linear Agents in Quasi-linear Mechanisms

Mechanisms with money are commonly designed under the assumption that agents are quasi-linear, meaning they have linear disutility for spending money. We study the implications when agents with non-linear (specifically, convex) disutility for payments participate in mechanisms designed for quasi-linear agents. We first show that any mechanism that is truthful for quasi-linear buyers has a simple best response function for buyers with non-linear disutility from payments, in which each bidder simply scales down her value for each potential outcome by a fixed factor, equal to her target return on investment (ROI). We call such a strategy ROI-optimal. We prove the existence of a Nash equilibrium in which agents use ROI-optimal strategies for a general class of allocation problems. Motivated by online marketplaces, we then focus on simultaneous second-price auctions for additive bidders and show that all ROI-optimal equilibria in this setting achieve constant-factor approximations to suitable welfare and revenue benchmarks.

cs.GT↗

arXiv2020

Escaping Cannibalization? Correlation-Robust Pricing for a Unit-Demand Buyer

We consider a robust version of the revenue maximization problem, where a single seller wishes to sell $n$ items to a single unit-demand buyer. In this robust version, the seller knows the buyer's marginal value distribution for each item separately, but not the joint distribution, and prices the items to maximize revenue in the worst case over all compatible correlation structures. We devise a computationally efficient (polynomial in the support size of the marginals) algorithm that computes the worst-case joint distribution for any choice of item prices. And yet, in sharp contrast to the additive buyer case (Carroll, 2017), we show that it is NP-hard to approximate the optimal choice of prices to within any factor better than $n^{1/2-ε}$. For the special case of marginal distributions that satisfy the monotone hazard rate property, we show how to guarantee a constant fraction of the optimal worst-case revenue using item pricing; this pricing equates revenue across all possible correlations and can be computed efficiently.

cs.GT↗

arXiv2020

A Simple and Approximately Optimal Mechanism for an Additive Buyer

We consider a monopolist seller with $n$ heterogeneous items, facing a single buyer. The buyer has a value for each item drawn independently according to (non-identical) distributions, and her value for a set of items is additive. The seller aims to maximize his revenue. We suggest using the a-priori better of two simple pricing methods: selling the items separately, each at its optimal price, and bundling together, in which the entire set of items is sold as one bundle at its optimal price. We show that for any distribution, this mechanism achieves a constant-factor approximation to the optimal revenue. Beyond its simplicity, this is the first computationally tractable mechanism to obtain a constant-factor approximation for this multi-parameter problem. We additionally discuss extensions to multiple buyers and to valuations that are correlated across items.

cs.GT↗

arXiv2020

Playing on a Level Field: Sincere and Sophisticated Players in the Boston Mechanism with a Coarse Priority Structure

Who gains and who loses from a manipulable school-choice mechanism? Studying the outcomes of sincere and sophisticated students under the manipulable Boston Mechanism as compared with the strategy-proof Deferred Acceptance, we provide robust "anything-goes" theorems for large random markets with coarse priority structures. I.e., there are many sincere and sophisticated students who prefer the Boston Mechanism to Deferred Acceptance, and vice versa. Some populations may even benefit from being sincere (if also perceived as such). Our findings reconcile qualitative differences between previous theory and known empirical results. We conclude by studying market forces that can influence the choice between these mechanisms.

cs.GT↗

arXiv2019

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 circumvent these hurdles in double-auction markets. We suggest using the Buyer Trade Reduction (BTR) mechanism, a variant of McAfee's mechanism, which is feasible and simple (in particular, deterministic, truthful, prior-independent, anonymous). First, in the setting where buyers' and sellers' values are sampled i.i.d. from the same distribution, we show that for any such market of any size, BTR with one additional buyer whose value is sampled from the same distribution has expected welfare at least as high as the optimal in the original market. We then move to a more general setting where buyers' values are sampled from one distribution and sellers' from another, focusing on the case where the buyers' distribution first-order stochastically dominates the sellers'. We present bounds on the number of buyers that, when added, guarantees that BTR in the augmented market have welfare at least as high as the optimal in the original market. Our lower bounds extend to a large class of mechanisms, and all of our results extend to adding sellers instead of buyers. In addition, we present positive results about the usefulness of pricing at a sample for welfare maximization in two-sided markets under the above two settings, which to the best of our knowledge are the first sampling results in this context.

cs.GT↗

arXiv2019

Competitive Equilibrium with Generic Budgets: Beyond Additive

We study competitive equilibrium in the canonical Fisher market model, but with indivisible goods. In this model, every agent has a budget of artificial currency with which to purchase bundles of goods. Equilibrium prices match between demand and supply---at such prices, all agents simultaneously get their favorite within-budget bundle, and the market clears. Unfortunately, a competitive equilibrium may not exist when the goods are indivisible, even in extremely simple markets such as two agents with exactly the same budget and a single item. Yet in this example, once the budgets are slightly perturbed---i.e., made generic---a competitive equilibrium is guaranteed to exist. In this paper we explore the extent to which generic budgets can guarantee equilibrium existence (and thus related fairness guarantees) in markets with multiple items. We complement our results in [Babaioff et al., 2019] for additive preferences by exploring the case of general monotone preferences, establishing positive results for small numbers of items and mapping the limits of our approach. We then consider cardinal preferences, define a hierarchy of such preference classes and establish relations among them, and for some classes prove equilibrium existence under generic budgets.

cs.GT↗

arXiv2019

A New Approach to Fair Distribution of Welfare

We consider transferable-utility profit-sharing games that arise from settings in which agents need to jointly choose one of several alternatives, and may use transfers to redistribute the welfare generated by the chosen alternative. One such setting is the Shared-Rental problem, in which students jointly rent an apartment and need to decide which bedroom to allocate to each student, depending on the student's preferences. Many solution concepts have been proposed for such settings, ranging from mechanisms without transfers, such as Random Priority and the Eating mechanism, to mechanisms with transfers, such as envy free solutions, the Shapley value, and the Kalai-Smorodinsky bargaining solution. We seek a solution concept that satisfies three natural properties, concerning efficiency, fairness and decomposition. We observe that every solution concept known (to us) fails to satisfy at least one of the three properties. We present a new solution concept, designed so as to satisfy the three properties. A certain submodularity condition (which holds in interesting special cases such as the Shared-Rental setting) implies both existence and uniqueness of our solution concept.

econ.TH↗

arXiv2018

Incentives and Coordination in Bottleneck Models

We study a variant of Vickrey's classic bottleneck model. In our model there are $n$ agents and each agent strategically chooses when to join a first-come-first-served observable queue. Agents dislike standing in line and they take actions in discrete time steps: we assume that each agent has a cost of $1$ for every time step he waits before joining the queue and a cost of $w>1$ for every time step he waits in the queue. At each time step a single agent can be processed. Before each time step, every agent observes the queue and strategically decides whether or not to join, with the goal of minimizing his expected cost. In this paper we focus on symmetric strategies which are arguably more natural as they require less coordination. This brings up the following twist to the usual price of anarchy question: what is the main source for the inefficiency of symmetric equilibria? is it the players' strategic behavior or the lack of coordination? We present results for two different parameter regimes that are qualitatively very different: (i) when $w$ is fixed and $n$ grows, we prove a tight bound of $2$ and show that the entire loss is due to the players' selfish behavior (ii) when $n$ is fixed and $w$ grows, we prove a tight bound of $Θ\left(\sqrt{\frac{w}{n}}\right)$ and show that it is mainly due to lack of coordination: the same order of magnitude of loss is suffered by any symmetric profile.

cs.GT↗

arXiv2018

Competitive Equilibrium with Indivisible Goods and Generic Budgets

Competitive equilibrium from equal incomes (CEEI) is a classic solution to the problem of fair and efficient allocation of goods [Foley'67, Varian'74]. Every agent receives an equal budget of artificial currency with which to purchase goods, and prices match demand and supply. However, a CEEI is not guaranteed to exist when the goods are indivisible, even in the simple two-agent, single-item market. Yet, it is easy to see that once the two budgets are slightly perturbed (made generic), a competitive equilibrium does exist. In this paper we aim to extend this approach beyond the single-item case, and study the existence of equilibria in markets with two agents and additive preferences over multiple items. We show that for agents with equal budgets, making the budgets generic -- by adding vanishingly small random perturbations -- ensures the existence of an equilibrium. We further consider agents with arbitrary non-equal budgets, representing non-equal entitlements for goods. We show that competitive equilibrium guarantees a new notion of fairness among non-equal agents, and that it exists in cases of interest (like when the agents have identical preferences) if budgets are perturbed. Our results open opportunities for future research on generic equilibrium existence and fair treatment of non-equals.

cs.GT↗

arXiv2018

Are Two (Samples) Really Better Than One? On the Non-Asymptotic Performance of Empirical Revenue Maximization

The literature on "mechanism design from samples," which has flourished in recent years at the interface of economics and computer science, offers a bridge between the classic computer-science approach of worst-case analysis (corresponding to "no samples") and the classic economic approach of average-case analysis for a given Bayesian prior (conceptually corresponding to the number of samples tending to infinity). Nonetheless, the two directions studied so far are two extreme and almost diametrically opposed directions: that of asymptotic results where the number of samples grows large, and that where only a single sample is available. In this paper, we take a first step toward understanding the middle ground that bridges these two approaches: that of a fixed number of samples greater than one. In a variety of contexts, we ask what is possibly the most fundamental question in this direction: "are two samples really better than one sample?". We present a few surprising negative results, and complement them with our main result: showing that the worst-case, over all regular distributions, expected-revenue guarantee of the Empirical Revenue Maximization algorithm given two samples is greater than that of this algorithm given one sample. The proof is technically challenging, and provides the first result that shows that some deterministic mechanism constructed using two samples can guarantee more than one half of the optimal revenue.

cs.GT↗

arXiv2018

Combinatorial Auctions with Endowment Effect

We study combinatorial auctions with bidders that exhibit endowment effect. In most of the previous work on cognitive biases in algorithmic game theory (e.g., [Kleinberg and Oren, EC'14] and its follow-ups) the focus was on analyzing the implications and mitigating their negative consequences. In contrast, in this paper we show how in some cases cognitive biases can be harnessed to obtain better outcomes. Specifically, we study Walrasian equilibria in combinatorial markets. It is well known that Walrasian equilibria exist only in limited settings, e.g., when all valuations are gross substitutes, but fails to exist in more general settings, e.g., when the valuations are submodular. We consider combinatorial settings in which bidders exhibit the endowment effect, that is, their value for items increases with ownership. Our main result shows that when the valuations are submodular, even a mild degree of endowment effect is sufficient to guarantee the existence of Walrasian equilibria. In fact, we show that in contrast to Walrasian equilibria with standard utility maximizing bidders -- in which the equilibrium allocation must be efficient -- when bidders exhibit endowment effect any local optimum can be an equilibrium allocation. Our techniques reveal interesting connections between the LP relaxation of combinatorial auctions and local maxima. We also provide lower bounds on the intensity of the endowment effect that the bidders must have in order to guarantee the existence of a Walrasian equilibrium in various settings.

cs.GT↗