Economics: Research Guide

The paradigm of best-of-both-worlds advocates an approach that achieves desirable properties both ex-ante and ex-post. We initiate a best-of-both-worlds fairness perspective for the important social choice setting of approval-based committee voting. To this end, we formalize a hierarchy of ex-ante properties including Individual Fair Share (IFS) and its strengthening Group Fair Share (GFS). We establish their relations with well-studied ex-post concepts such as extended justified representation (EJR) and proportional justified representation (PJR). Our central result is a polynomial-time algorithm that simultaneously satisfies ex-post EJR and ex-ante GFS. Our algorithm uses as a subroutine t..

I consider a repeated auction setting with colluding buyers and a seller who adjusts reserve prices over time without long-term commitment. To model the seller’s concern for collusion, I introduce a new equilibrium concept: collusive public perfect equilibrium (cPPE). For every strategy of the seller I define the corresponding “buyer-game†in which the seller is replaced by Nature who chooses the reserve prices for the buyers in accordance with the seller’s strategy. A public perfect equilibrium is collusive if the buyers cannot achieve a higher symmetric public perfect equilibrium payoff in the corresponding buyer-game. In a setting with symmetric buyers with private..

We study the costs and benefits of selling data to a competitor. Although selling all consumers' data may decrease total firm profits, there exist other selling mechanisms -- in which only some consumers' data is sold -- that render both firms better off. We identify the profit-maximizing mechanism, and show that the benefit to firms comes at a cost to consumers. We then construct Pareto-improving mechanisms, in which each consumers' welfare, as well as both firms' profits, increase. Finally, we show that consumer opt-in can serve as an instrument to induce firms to choose a Pareto-improving mechanism over a profit-maximizing one.

Agents may form coalitions. Each coalition shares its endowment among its agents by applying a sharing rule. The sharing rule induces a coalition formation problem by assuming that agents rank coalitions according to the allocation they obtain in the corresponding sharing problem. We characterize the sharing rules that induce a class of stable coalition formation problems as those that satisfy a natural axiom that formalizes the principle of solidarity. Thus, solidarity becomes a sufficient condition to achieve stability.

A powerful feature in mechanism design is the ability to irrevocably commit to the rules of a mechanism. Commitment is achieved by public declaration, which enables players to verify incentive properties in advance and the outcome in retrospect. However, public declaration can reveal superfluous information that the mechanism designer might prefer not to disclose, such as her target function or private costs. Avoiding this may be possible via a trusted mediator; however, the availability of a trusted mediator, especially if mechanism secrecy must be maintained for years, might be unrealistic. We propose a new approach to commitment, and show how to commit to, and run, any given mechanism wit..

We design a mechanism, Majority voting with random checks, that fully implements the majority rule for binary social decisions. After a simultaneous vote over the two options, the winner must be confirmed by at least one agent from a random sample of agents voting sequentially. The mechanism incentivizes agents to act truthfully as a lottery is held if no agent confirms the outcome. Our mechanism also reduces by almost half the number of stages required for implementation. Furthermore, we extend our results to incomplete information and abstention and introduce additional implementation mechanisms based on the concept of network formation

We study the distribution of multiple homogeneous items to multiple agents with unit demand. Monetary transfer is not allowed and the allocation of the items can only depend on the informative signals that are manipulable by costly and wasteful efforts. Examples of such scenarios include grant allocation, college admission, lobbying and affordable housing. We show that the welfare-maximizing mechanism takes the form of a contest and characterize it. We apply our characterizations to study large contests. When the number of agents is large compared to item(s), the format of the optimal contest converges to winner-takes-all, but principal's payoff does not. When both the number of items and ag..

Approval-based committee (ABC) voting rules elect a fixed size subset of the candidates, a so-called committee, based on the voters' approval ballots over the candidates. While these rules have recently attracted significant attention, axiomatic characterizations are largely missing so far. We address this problem by characterizing ABC voting rules within the broad and intuitive class of sequential valuation rules. These rules compute the winning committees by sequentially adding candidates that increase the score of the chosen committee the most. In more detail, we first characterize almost the full class of sequential valuation rules based on mild standard conditions and a new axiom called..

We study the partial and full set-asides and their implication for changes in bidding behavior in first-price sealed-bid auctions in the context of United States Department of Agriculture (USDA) food procurement auctions. Using five years of bid data on different beef products, we implement weighted least squares regression models to show that partial set-aside predicts decreases in both offer prices and winning prices among large and small business bidders. Full set-aside predicts a small increase in offer prices and winning prices among small businesses. With these predictions, we infer that net profit of small businesses is unlikely to increase when set-asides are present.

LP-duality theory has played a central role in the study of the core, right from its early days to the present time. The 1971 paper of Shapley and Shubik, which gave a characterization of the core of the assignment game, has been a paradigm-setting work in this regard. However, despite extensive follow-up work, basic gaps still remain. We address these gaps using the following building blocks from LP-duality theory: 1). Total unimodularity (TUM). 2). Complementary slackness conditions and strict complementarity. TUM plays a vital role in the Shapley-Shubik theorem. We define several generalizations of the assignment game whose LP-formulations admit TUM; using the latter, we characterize thei..

We study matching with couples problems where hospitals have one vacant position. We introduce a constraint on couples’ preferences over pairs of hospitals called restricted complementarity, which is a “translation” of bilateral substitutability in matching with contracts. Next, we extend Klaus and Klijn’s (2007) path to stability result by showing that if couples’ preferences satisfy restricted complementarity, then from any arbitrary matching, there exists a finite path of matchings where each matching on the path is obtained by “satisfying” a blocking coalition for the previous one and the final matching is stable.

The conditions of strong Condorcet winner consistency and strong Condorcet loser consistency are, in essence, universally accepted. However, there are many situations in which they are silent. The weak counterparts of these properties suffer from the fatal flaw that a weak Condorcet winner can be a weak Condorcet loser at the same time. We propose a new notion of Condorcet-type winners and losers that is intermediate in strength between these two extremes. A feasible candidate is an intermediate Condorcet winner if this candidate wins against or ties with each other feasible candidate in a pairwise contest, with at least one instance of a win. Likewise, a feasible candidate is an intermediat..

This paper formalizes the lattice structure of the ballot voters cast in a ranked-choice election and the preferences that this structure induces. These preferences are shown to be counter to previous assumptions about the preferences of voters, which indicate that ranked-choice elections require different considerations for voters and candidates alike. While this model assumes that voters vote sincerely, the model of ranked-choice elections this paper presents allows for considerations of strategic voting in future work.

In the allocation of indivisible goods, the maximum Nash welfare rule has recently been characterized as the only rule within the class of additive welfarist rules that satisfies envy-freeness up to one good. We extend this characterization to the class of all welfarist rules.

We consider the obnoxious facility location problem (in which agents prefer the facility location to be far from them) and propose a hierarchy of distance-based proportional fairness concepts for the problem. These fairness axioms ensure that groups of agents at the same location are guaranteed to be a distance from the facility proportional to their group size. We consider deterministic and randomized mechanisms, and compute tight bounds on the price of proportional fairness. In the deterministic setting, not only are our proportional fairness axioms incompatible with strategyproofness, the Nash equilibria may not guarantee welfare within a constant factor of the optimal welfare. On the oth..

How transparent are informational institutions if their founders have to agree on the design? We analyze a model where several agents bargain over persuasion of a single receiver. We characterize the existence of anagreement that is beneficial for all agents relative to some fixed benchmark information structure, when the preferences of agents are state-independent, and provide sufficient conditions for general preferences. We further show that a beneficial agreement exists if, for every coalition of a fixed size, there is a belief that generates enough surplus for its members. Next, we concentrate on agent-partitional environments, where for each agent there is a state where the informed de..

We introduce a generalization of the concept of sufficientarianism, intended (but not limited) to study multiple consumption goods. We discuss three properties that uniquely pin down our family and, up to continuity requirements, endogenize the sufficientarian threshold. Two, anonymity and reinforcement, are standard. The third, sufficientarian monotonicity, generalizes classical monotonicity and requires that for any two lists of bundles in which individuals are ordered similarly by how much they receive, the worse of the two is indifferent to the new list of bundles considered by taking the componentwise minimum of the two bundles for each agent.

How much does it hurt seller revenue if some bidders know that others are colluding? Using a simple model of first and second price Independent Private Value auctions with uniformly distributed values where a single bidder knows privately of the existence of collusion by others, we show that this knowledge leads him to bid shading (weakly) in the first price auction compared to what he would have bid otherwise. This in turn yields the result that the second price auction dominates the first price auction in terms of seller revenue. This contrasts results from the literature showing that under our framework, when bidding is done while the presence of colluding bidders is common knowledge, the..

We study the problem of allocating packages of different objects to a group of bidders. A rule is overbidding-proof if no bidder has incentives to bid above his actual valuations. We prove that if an efficient rule is overbidding-proof, then each winning bidder pays a price between his winning bid and what he would pay in a Vickrey auction for the same package. In counterpart, the set of rules that satisfy underbidding-proofness always charge a price below the corresponding Vickrey price. A new characterization of the Vickrey allocation rule is provided with a weak form of strategy-proofness. The Vickrey rule is the only rule that satisfies efficiency, individual rationality, overbidding-pro..

The paper uses bids submitted by primary dealer banks at auctions of sovereign bonds to quantify the price elasticity of demand. The price elasticity of demand correlates strongly with the volatility of returns of the same bonds traded in the secondary market but only weakly with their bid-ask spread. The price elasticity of demand predicts same-bond post-auction returns in the secondary market, even after controlling for pre-auction volatility. The evidence suggests that the price elasticity of demand is associated with the magnitude of price pressure in the secondary market around auction days, and proxies for primary dealer risk-bearing capacity.

This paper analyses the properties of (strong) core allocations in a two-period asymmetric information economy that also involves both negligible and non-negligible agents as well as an infinite dimensional commodity space. Within this setup, we allow the consumption set of each agent to be an arbitrary subset of the commodity space that may not have any lower bound. Our first result deals with the robustness of the core and the strong core allocations with respect to the restrictions imposed on the size of the blocking coalitions in an economy with only non-negligible agents. The second result is a generalization of the first result to an economy that allows the simultaneous presence of neg..

We describe a two-stage mechanism that fully implements the set of efficient outcomes in two-agent environments with quasi-linear utilities. The mechanism asks one agent to set prices for each outcome, and the other agent to make a choice, paying the corresponding price: Price \& Choose. We extend our implementation result in three main directions: an arbitrary number of players, non-quasi linear utilities, and robustness to max-min behavior. Finally, we discuss how to reduce the payoff inequality between players while still achieving efficiency.

We study various novel complexity measures for two-sided matching mechanisms, applied to the popular real-world school choice mechanisms of Deferred Acceptance (DA) and Top Trading Cycles (TTC). In contrast to typical bounds in computer science, our metrics are not aimed to capture how hard the mechanisms are to compute. Rather, they aim to capture certain aspects of the difficulty of understanding or explaining the mechanisms and their properties. First, we study a set of questions regarding the complexity of how one agent's report can affect other facets of the mechanism. We show that in both DA and TTC, one agent's report can have a structurally complex effect on the final matching. Consi..

Results from the communication complexity literature have demonstrated that stable matching requires communication: one cannot find or verify a stable match without having access to essentially all of the ordinal preference information held privately by the agents in the market. Stated differently, these results show that stable matching mechanisms are not robust to even a small number of labeled inaccuracies in the input preferences. In practice, these results indicate that agents must go through the time-intensive process of accurately ranking each and every potential match candidate if they wish for the resulting match to be guaranteedly stable. Thus, in large markets, communication requi..

It is well known that Sperner lemma is equivalent to Brouwer fixed-point theorem. Tanaka [12] proved that Brouwer theorem is equivalent to Arrow theorem, hence Arrow theorem is equivalent to Sperner lemma. In this paper we will prove this result directly. Moreover, we describe a number of other statements equivalent to Arrow theorem.

We study optimal bundling when consumers differ in one dimension. We introduce a partial order on the set of bundles defined by (i) set inclusion and (ii) sales volumes (if sold alone and priced optimally). We show that if the undominated bundles with respect to this partial order are nested, then nested bundling (tiered pricing) is optimal. We characterize which nested menu is optimal: Selling a given menu of nested bundles is optimal if a smaller bundle in (out of) the menu sells more (less) than a bigger bundle in the menu. We apply these insights to connect optimal bundling and quality design to price elasticities and cost structures: (i) when price elasticities are quasi-convex on the s..

Given a policy objective on the distribution of student types to schools, we study the existence of a mechanism that weakly improves the distributional objective and satisfies constrained efficiency, individual rationality, and strategy-proofness. We show that such a mechanism need not exist in general. We introduce a new notion of discrete concavity that we call pseudo M$^{\natural}$-concavity and construct a mechanism with the desirable properties when the distributional objective satisfies this notion. We show that several distributional objectives, that are natural in our setting, satisfy M$^{\natural}$-concavity.

Consider a population of agents whose choice behaviors are partially comparable according to given primitive orderings. A choice theory specifies the set of choice functions admissible in the population. A choice theory is self-progressive if any aggregate choice behavior consistent with the theory can uniquely be represented as a probability distribution over admissible choice functions that are comparable to each other. We establish an equivalence between self-progressive choice theories and (i) well-known algebraic structures called lattices; (ii) the maximizers of supermodular functions over choice functions. Keywords: Random choice, heterogeneity, identification, lattice, supermodular o..