Working papers

Feasible joint posterior beliefs (with Itai Arieli, Yakov Babichenko, and Omer Tamuz)
February 2020, arXiv:2002.11362
slides (Caltech, December 2019)
We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. Our main result is that, for the twoagent case, a quantitative version of Aumann's Agreement Theorem provides a necessary and sufficient condition for feasibility. We use our characterization to construct joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior. We also study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.

Can society learn without opinion leaders? (with Itai Arieli and Rann Smorodinsky)
June 2020
slides, video (CMID20, June 2020)
We are interested in the existence of socialnetwork topologies that aggregate information well even if 95% of agents are inactive and do not take part in the learning process. Agents are Bayesianrational, they take irrevocable decisions as in models of herding, and the arrival order is random. We derive new sufficient conditions for good information aggregation in terms of the topological properties of the network and find connections to the theory of expander graphs.

A polynomialtime algorithm for computing a Pareto optimal and almost proportional allocation (a short note with Haris Aziz and Herve Moulin)
R&R in Operations Research Letters
September 2019, arXiv:1909.00740
In this note, we show that Paretooptimal and almostfair (Proportional up to 1 item) allocations of a mixture of indivisible goods and bads always exist and can be computed in stronglypolynomial time.
The technique is based on the tradingcycle algorithm for finding divisible Paretoimprovements from the recent working paper "Fair division with minimal sharing" with Erel SegalHalevi and on an extension of BarmanKrishnamurthy rounding.

Fair Division with minimal sharing (with Erel SegalHalevi)
August 2019, arXiv:1908.01669
slides (De Aequa Divisione workshop on Fair Division, LUISS, Rome, May 2019)
Siblings inherited several apartments would not be satisfied by an allocation giving them an apartment with probability 50% or envyfree up to one apartment. We suggest a new approach to fair division with valuable items, which bridges the modern "divisible" and "indivisible" literature: sharing minimization. The problem of sharingminimization among fair Paretooptimal allocations turns out to be algorithmicallytractable for almost all instances.

Algorithms for Competitive Division of Chores (with Simina Branzei)
R&R in Mathematics of Operations Research
July 2019, arXiv:1907.01766
slides (Algorithms Seminar, TAU, March 2019)
This is the first explicit algorithm for computing market equilibria of "nonconvex" exchange economies that have disconnected equilibrium set. We avoid the "blackbox" of CellEnumeration technique, used in the literature, by the novel approach based on enumeration of all the faces of the Pareto frontier via a simple 2agent reduction.
The results are applied to approximately fair division of indivisible chores.

Protecting the Protected Group: Circumventing Harmful Fairness (with Omer BenPorat and Moshe Tennenholtz)
May 2019, arXiv:1905.10546
Fairness constraints used for Fair Machine Learning may harm the protected group because the "price of fairness" is reallocated to this group by selfinterested decision makers (e.g., a bank giving loans).

A simple online fair division problem (with Herve Moulin and Anna Bogomolnaia)
R&R in Management Science
March 2019, arXiv:1903.10361
slides with a different set of results including exact Price of Fairness for general bargaining (CompEcon seminar at HUJI, May 2019)
We propose a new family of allocation rules that, using minimal statistical information about the environment, achieve fairness and welfare guarantees. These are the first results on dynamic resource allocation that combine both fairness and efficiency design objectives.
Selected publications

Competitive division of a mixed manna (with Anna Bogomolnaia, Herve Moulin, and Elena Yanovskaya)
Econometrica, 2017, vol.85:6, p.18471871
preprint: arXiv:1702.00616
slides (CompEcon seminar, HUJI, November 2017)
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Dividing bads under additive utilities (with Anna Bogomolnaia, Herve Moulin, and Elena Yanovskaya)
Social Choice and Welfare, 2019, vol.52:3, p.395417
preprint: arXiv:1608.01540
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Dynamic Games and Applications, 2018, vol.8:1, p. 180198
preprint: arXiv:1509.01727
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