We consider the allocation of indivisible objects when agents have preferences over their own allocations, but share the ownership of the resources to be distributed. Examples might include seats in public schools, faculty offices, and time slots in public tennis courts. Given an allocation, groups of agents who would prefer an alternative allocation might challenge it. An assignment is popular if it is not challenged by another one. By assuming that agents' ability to challenge allocations can be represented by weighted votes, we characterize the conditions under which popular allocations might exist and when these can be implemented via strategy-proof mechanisms. Serial dictatorships that use orderings consistent with the agents' weights are not only strategy-proof and Pareto efficient, but also popular, whenever these assignments exist. We also provide a new characterization for serial dictatorships as the only mechanisms that are popular, strategy-proof, non-wasteful, and satisfy a consistency condition.
A strictly strategy-proof mechanism is one that asks agents to use strictly dominant strategies. In the canonical one-dimensional mechanism design setting with private values, we show that strict strategy-proofness is equivalent to strict monotonicity plus the envelope formula, echoing a well-known characterisation of (weak) strategy-proofness. A consequence is that strategy-proofness can be made strict by an arbitrarily small modification, so that strictness is 'essentially for free'.
Strategy-proof mechanisms are widely used in market design. In an abstract allocation framework where outside options are available to agents, we obtain two results for strategy-proof mechanisms. They provide a unified foundation for several existing results in distinct models and imply new results in some models. The first result proves that, for individually rational and strategy-proof mechanisms, pinning down every agent's probability of choosing his outside option is equivalent to pinning down a mechanism. The second result provides a sufficient condition for two strategy-proof mechanisms …
School of Economics and Management, East China Normal University（华东师范大学经济与管理学院）；School of Economics, Shanghai University of Finance and Economics（上海财经大学经济学院）
We consider the problem of allocating indivisible objects to agents when agents have strict preferences over objects. There are inherent trade-offs between competing notions of efficiency, fairness and incentives in assignment mechanisms. It is, therefore, natural to consider mechanisms that satisfy two of these three properties in their strongest notions, while trying to improve on the third dimension. In this paper, we are motivated by the following question: Is there a strategy-proof and envy-free random assignment mechanism more efficient than equal division? Our contributions in this pape…
We give a structure theorem for all coalitionally strategy-proof social choice functions whose range is a subset of cardinality two of a given larger set of alternatives. We provide this in the case where the voters/agents are allowed to express indifference and the domain consists of profiles of preferences over a society of arbitrary cardinality. The theorem, that takes the form of a representation formula, can be used to construct all functions under consideration.
Strategy-Proof Probabilistic Social Choice Correspondences under Conditional Expected Utility
Indian Institute of Management Calcutta（印度管理学院加尔各答分校）；Hausdorff Center for Mathematics and Institute for Microeconomics, University of Bonn（波恩大学豪斯多夫数学中心与微观经济学研究所）；Indian Institute of Technology Kanpur（坎普尔印度理工学院）
Two characterizations of the whole class of strategy-proof aggregation rules on rich domains of locally unimodal preorders in finite median join-semilattices are provided. In particular, it is shown that such a class consists precisely of generalized weak sponsorship rules induced by certain families of order filters of the coalition poset. It follows that the co-majority rule and many other inclusive aggregation rules belong to that class. The co-majority rule for an odd number of agents is characterized and shown to be equivalent to a Condorcet-Kemeny median rule. Applications to preference …
We present a polynomial-time algorithm that determines, given some choice rule, whether there exists an obviously strategy-proof mechanism for that choice rule.
We provide novel simple representations of strategy-proof voting rules when voters have uni-dimensional single-peaked preferences (as well as multi-dimensional separable preferences). The analysis recovers, links and unifies existing results in the literature such as Moulin's classic characterization in terms of phantom voters and Barberà, Gul and Stacchetti's in terms of winning coalitions ("generalized median voter schemes"). First, we compare the computational properties of the various representations and show that the grading curve representation is superior in terms of computational compl…
Coalition strategy-proof anonymous binary social choice in a countably infinite society
Dipartimento di Scienze Economiche e Statistiche, Università Federico II（那不勒斯费德里科二世大学）；Department of Computer Information Systems, Indiana University Northwest（印第安纳大学西北分校）；School of Business and Economics, Indiana University Northwest（印第安纳大学西北分校）
In this paper, we study efficiency in truthful auctions via a social network, where a seller can only spread the information of an auction to the buyers through the buyers' network. In single-item auctions, we show that no mechanism is strategy-proof, individually rational, efficient, and weakly budget balanced. In addition, we propose $α$-APG mechanisms, a class of mechanisms which operate a trade-off between efficiency and weakly budget balancedness. In multi-item auctions, there already exists a strategy-proof mechanism when all buyers need only one item. However, we indicate a counter-exam…
A preference domain is called a non-dictatorial domain if it allows the design of unanimous social choice functions (henceforth, rules) that are non-dictatorial and strategy-proof. We study a class of preference domains called unidimensional domains and establish that the unique seconds property (introduced by Aswal, Chatterji, and Sen (2003)) characterizes all non-dictatorial domains. The principal contribution is the subsequent exhaustive classification of all non-dictatorial, unidimensional domains and canonical strategy-proof rules on these domains, based on a simple property of two-voter …
Let $V$ be society whose members express preferences about two alternatives, indifference included. Identifying anonymous binary social choice functions with binary functions $f=f(k,m)$ defined over the integer triangular grid $G=\{(k,m)\in \mathbb{N}_0\times\mathbb{N}_0 : k+m\le |V|\} $, we show that every strategy-proof, anonymous social choice function can be described geometrically by listing, in a sequential manner, groups of segments of G, of equal (maximum possible) length, alternately horizontal and vertical, representative of preference profiles that determine the collective choice of…
Auctions via social network, pioneered by Li et al. (2017), have been attracting considerable attention in the literature of mechanism design for auctions. However, no known mechanism has satisfied strategy-proofness, non-deficit, non-wastefulness, and individual rationality for the multi-unit unit-demand auction, except for some naive ones. In this paper, we first propose a mechanism that satisfies all the above properties. We then make a comprehensive comparison with two naive mechanisms, showing that the proposed mechanism dominates them in social surplus, seller's revenue, and incentive of…
