
on Economic Design 
By:  Haris Aziz; Florian Brandl 
Abstract:  We consider the problem of probabilistic allocation of objects under ordinal preferences. Our main contribution is an allocation mechanism, called the vigilant eating rule (VER), that applies to nearly arbitrary feasibility constraints. It is constrained ordinally efficient, can be computed efficiently for a large class of constraints, and treats agents equally if they have the same preferences and are subject to the same constraints. When the set of feasible allocations is convex, we also present a characterization of our rule based on ordinal egalitarianism. Our general results concerning VER do not just apply to allocation problems but to any collective choice problem in which agents have ordinal preferences over discrete outcomes. As a case study, we assume objects have priorities for agents and apply VER to sets of probabilistic allocations that are constrained by stability. VER coincides with the (extended) probabilistic serial rule when priorities are flat and the agent proposing deterministic deferred acceptance algorithm when preferences and priorities are strict. While VER always returns a stable and constrained efficient allocation, it fails to be strategyproof, unconstrained efficient, and envyfree. We show, however, that each of these three properties is incompatible with stability and constrained efficiency. 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2008.08991&r=all 
By:  Ce Liu 
Abstract:  This paper develops a framework for repeated matching markets. The model departs from the GaleShapley matching model by having a fixed set of longlived hospitals match with a new generation of shortlived residents in every period. I show that there are two kinds of hospitals in this repeated environment: some hospitals can be motivated dynamically to voluntarily reduce their hiring capacity, potentially making more residents available to rural hospitals; the others, however, are untouchable even with repeated interaction and must obtain the same match as they do in a static matching. In large matching markets with correlated preferences, at most a vanishingly small fraction of the hospitals are untouchable. The vast majority of hospitals can be motivated using dynamic incentives. 
Date:  2020–07 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2007.03794&r=all 
By:  Haitian Xie 
Abstract:  The paper studies the problem of auction design in a setting where the auctioneer accesses the knowledge of the valuation distribution only through statistical samples. A new framework is established that combines the statistical decision theory with mechanism design. Two optimality criteria, maxmin, and equivariance, are studied along with their implications on the form of auctions. The simplest form of the equivariant auction is the average bid auction, which set individual reservation prices proportional to the average of other bids and historical samples. This form of auction can be motivated by the Gamma distribution, and it sheds new light on the estimation of the optimal price, an irregular parameter. Theoretical results show that it is often possible to use the regular parameter population mean to approximate the optimal price. An adaptive average bid estimator is developed under this idea, and it has the same asymptotic properties as the empirical Myerson estimator. The new proposed estimator has a significantly better performance in terms of value at risk and expected shortfall when the sample size is small. 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2008.10217&r=all 
By:  Meng Zhang; Deepanshu Vasal 
Abstract:  In this paper, we consider infinite number of non atomic selfinterested agents with private valuation of a divisible good. We design a pricing mechanism that is easy to implement, is individually rational, weakly budget balanced and incentive compatible. In this mechanism, agents send reports of their types, based on which, the designer solves a constrained optimization problem through Lagrange's mechanism. The resulting optimal allocation and Lagrange's multiplier is sent as the allocation and prices to the respective agent. We show that reporting one's type truthfully is a dominant strategy of the players in this mechanism. We then extend this idea to the dynamic case, when player's types are dynamically evolving as a controlled Markov process. In this case, in each time period, reporting one's type is a dominant strategy of the players. 
Date:  2020–03 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2003.04263&r=all 
By:  Dominik Peters; Grzegorz Pierczy\'nski; Piotr Skowron 
Abstract:  We study voting rules for participatory budgeting, where a group of voters collectively decides which projects should be funded using a common budget. We allow the projects to have arbitrary costs, and the voters to have arbitrary additive valuations over the projects. We formulate two axioms that guarantee proportional representation to groups of voters with common interests. To the best of our knowledge, all known rules for participatory budgeting do not satisfy either of the two axioms; in addition we show that the most prominent proportional rules for committee elections (such as Proportional Approval Voting) cannot be adapted to arbitrary costs nor to additive valuations so that they would satisfy our axioms of proportionality. We construct a simple and attractive voting rule that satisfies one of our axioms (for arbitrary costs and arbitrary additive valuations), and that can be evaluated in polynomial time. We prove that our other stronger axiom is also satisfiable, though by a computationally more expensive and less natural voting rule. 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2008.13276&r=all 
By:  Alessandra Casella (Columbia University [New York]); Antonin Macé (PSE  Paris School of Economics, PJSE  Paris Jourdan Sciences Economiques  UP1  Université PanthéonSorbonne  ENS Paris  École normale supérieure  Paris  EHESS  École des hautes études en sciences sociales  ENPC  École des Ponts ParisTech  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  Voters have strong incentives to increase their inuence by trading votes, a practice indeed believed to be common. But is vote trading welfareimproving or welfaredecreasing? We review the theoretical literature and, when available, its related experimental tests. We begin with the analysis of logrolling { the exchange of votes for votes, considering both explicit vote exchanges and implicit vote trades engineered by bundling issues in a single bill. We then focus on vote markets, where votes can be traded against a numeraire. We cover competitive markets, strategic market games, decentralized bargaining, and more centralized mechanisms, such as quadratic voting, where votes can be bought at a quadratic cost. We conclude with procedures allowing voters to shift votes across decisions { to trade votes with oneself only { such as storable votes or a modi_ed form of quadratic voting. We _nd that vote trading and vote markets are typically ine_cient; more encouraging results are obtained by allowing voters to allocate votes across decisions. 
Keywords:  logrolling,vote trading,storable votes,quadratic voting,bundling,vote markets 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:halshs02922012&r=all 
By:  Christina Luxen; Tobias Rachidi 
Abstract:  This paper studies committee search where members either assess candidates “one at a time”, i.e., on a rolling basis, or they simultaneously review a set of candidates of fixed size in each time period. We compare both search procedures in terms of acceptance standards and welfare. There is a tradeoff between the expected value of a candidate conditional on stopping and the expected search costs. The resolution of this tradeoff depends on the voting rule and the specification of search costs associated with the simultaneous evaluation of multiple candidates. The adoption of a qualified majority rule changes the evaluation of search procedures compared to the unanimity rule, revealing that the presence of a search committee alters the search design problem in comparison with the single decisionmaker case. This is the main qualitative insight of this paper and we discuss its implications for committee search in practice. 
Keywords:  Committee search, sequential search, multiple options 
JEL:  D71 D83 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2020_203&r=all 