Coalitional Strategy-proofness Research Articles

Strategy-proof aggregation rules and single peakedness in bounded distributive lattices

It is shown that, under a very comprehensive notion of single peakedness, an aggregation rule on a bounded distributive lattice is strategy-proof on any rich domain of single peaked total preorders if and only if it admits one of three distinct and mutually equivalent representations by lattice-polynomials, namely whenever it can be represented as a generalized weak consensus rule, a generalized weak sponsorship rule , or an iterated medianrule. The equivalence of individual and coalitional strategy-proofness that is known to hold for single peaked domains in bounded linearly ordered sets and in finite trees typically fails in such an extended setting. A related impossibility result concerning non-trivial anonymous and coalitionally strategy-proof aggregation rules is also obtained.

Weakly unimodal domains, anti-exchange properties, and coalitional strategy-proofness of aggregation rules

It is shown that simple and coalitional strategy-proofness of an aggregation rule on any rich weakly unimodal domain of an idempotent interval space are equivalent properties if that space satisfies interval anti-exchange, a basic property also shared by a large class of convex geometries including–but not reducing to–trees and Euclidean convex spaces. Therefore, strategy-proof location problems in a vast class of networks fall under the scope of that proposition.It is also established that a much weaker minimalanti-exchangeproperty is necessary to ensure equivalence of simple and coalitional strategy-proofness in that setting. An immediate corollary to that result is that such equivalence fails to hold both in certain median interval spaces including those induced by bounded distributive lattices that are not chains, and in certain non-median interval spaces including those induced by partial cubes that are not trees.Thus, it turns out that anti-exchange properties of the relevant interval space provide a powerful general common principle that explains the varying relationship between simple and coalitional strategy-proofness of aggregation rules for rich weakly unimodal domains across different interval spaces, both median and non-median.

Coalitional unanimity versus strategy-proofness in coalition formation problems

This paper examines coalition formation problems from the viewpoint of mechanism design. We consider the case where (i) the list of feasible coalitions (those coalitions which are permitted to form) is given in advance; and (ii) each individual’s preference is a ranking over those feasible coalitions which include this individual. We are interested in requiring the mechanism to guarantee each coalition the “right” of forming that coalition at least when every member of the coalition ranks the coalition at the top. We name this property coalitional unanimity. We examine the compatibility between coalitional unanimity and incentive requirements, and prove that if the mechanism is strategy-proof and respects coalitional unanimity, then for each preference profile, there exists at most one strictly core stable partition, and the mechanism chooses such a partition whenever available. Further, the mechanism is coalition strategy-proof and respects coalitional unanimity if, and only if, the strictly core stable partition uniquely exists for every preference profile.

Euclidean preferences, option sets and strategyproofness

In this note, we use the technique of option sets to sort out the implications of coalitional strategyproofness in the spatial setting. We also discuss related issues and open problems.

Maskin monotonicity and infinite individuals

This paper examines the logical relationship among Maskin monotonicity, independent person-by-person monotonicity, independent weak monotonicity, strategy-proofness, and coalitional strategy-proofness in a society with infinite individuals.

Coalitionally Strategy-Proof Rules in Allotment Economies with Homogeneous Indivisible Goods

We consider the allotment problem of homogeneous indivisible goods among agents with single-peaked and risk-averse von Neumann-Morgenstern expected utility functions. We establish that a rule satisfies coalitional strategy-proofness, same-sideness, and strong symmetry if and only if it is the uniform probabilistic rule. By constructing an example, we show that if same-sideness is replaced by respect for unanimity, this statement does not hold even with the additional requirements of no-envy, anonymity, at most binary, peaks-onlyness and continuity.

Coalitionally strategy-proof rules in allotment economies with homogeneous indivisible goods

We consider the allotment problem of homogeneous indivisible goods among agents with single-peaked and risk-averse von Neumann–Morgenstern expected utility functions. We establish that a rule satisfies coalitional strategy-proofness, same-sideness, and strong symmetry if and only if it is the uniform probabilistic rule. By constructing an example, we show that if same-sideness is replaced by respect for unanimity, this statement does not hold even with the additional requirements of no-envy, anonymity, at most binary, peaks-onlyness and continuity.

On the equivalence of coalitional and individual strategy-proofness properties

In this paper, we introduce a sufficient condition on the domain of admissible preferences of a social choice mechanism under which the properties of individual and coalitional strategyproofness are equivalent. Then, we illustrate the usefulness of this general result in the case where a fixed budget has to be allocated among several pure public goods.

Coalitionally strategy-proof social choice correspondences and the Pareto rule

This paper studies coalitional strategy-proofness of social choice correspondences that map preference profiles into sets of alternatives. In particular, we focus on the Pareto rule, which associates the set of Pareto optimal alternatives with each preference profile, and examine whether or not there is a necessary connection between coalitional strategy-proofness and Pareto optimality. The definition of coalitional strategy-proofness is given on the basis of a max–min criterion. We show that the Pareto rule is coalitionally strategy-proof in this sense. Moreover, we prove that given an arbitrary social choice correspondence satisfying the coalitional strategy-proofness and nonimposition, all alternatives selected by the correspondence are Pareto optimal. These two results imply that the Pareto rule is the maximal correspondence in the class of coalitionally strategy-proof and nonimposed social choice correspondences.

Coalitional strategy-proofness and resource monotonicity for house allocation problems

We consider the problem of allocating houses to agents when monetary compensations are not allowed. We present a simple and independent proof of a result due to Ehlers and Klaus (Int J Game Theory 32:545–560, 2004) that characterizes the class of rules satisfying efficiency, strategy-proofness, resource monotonicity and nonbossiness.

Beyond Moulin mechanisms

The only known general technique for designing truthful and approximately budget-balanced cost-sharing mechanisms with good efficiency or computational complexity properties is due to Moulin [1999. Incremental cost sharing: Characterization by coalition strategy-proofness. Soc. Choice Welfare 16 (2), 279–320]. For many fundamental cost-sharing applications, however, Moulin mechanisms provably suffer from poor budget-balance, poor economic efficiency, or both. We propose acyclic mechanisms, a new framework for designing truthful and approximately budget-balanced cost-sharing mechanisms. Acyclic mechanisms strictly generalize Moulin mechanisms and offer three important advantages. First, it is easier to design acyclic mechanisms than Moulin mechanisms: many classical primal-dual algorithms naturally induce a non-Moulin acyclic mechanism with good performance guarantees. Second, for important classes of cost-sharing problems, acyclic mechanisms have exponentially better budget-balance and economic efficiency than Moulin mechanisms. Finally, while Moulin mechanisms have found application primarily in binary demand games, we extend acyclic mechanisms to general demand games, a multi-parameter setting in which each bidder can be allocated one of several levels of service.

Coalitional strategy-proofness and fairness

This paper considers the problem of assigning a finite number of indivisible objects, like jobs, houses, positions, etc., to the same number of individuals. There is also a divisible good (money) and the individuals consume money and one object each. The class of fair allocation rules that are strategy-proof in the strong sense that no coalition of individuals can improve the allocation for all of its members, by misrepresenting their preferences, is characterized. It turns out that given a regularity condition, the outcome of a fair and coalitionally strategy-proof allocation rule must maximize the use of money subject to upper quantity bounds determined by the allocation rule. If available money is nonnegative, objects may be jobs and the distribution of money a wage structure. If available money is negative, the formal model may reflect a multi-object auction. In both cases fairness means equilibrium, i.e., that each individual receives a most demanded object.

The Gibbard–Satterthwaite theorem of social choice theory in an infinite society and LPO (limited principle of omniscience)

This paper is an attempt to examine the main theorems of social choice theory from the viewpoint of constructive mathematics. We examine the Gibbard–Satterthwaite theorem [A.F. Gibbard, Manipulation of voting schemes: a general result, Econometrica 41 (1973) 587–601; M.A. Satterthwaite, Strategyproofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions, Journal of Economic Theory 10 (1975) 187–217] in a society with an infinite number of individuals (infinite society). We will show that the theorem that any coalitionally strategy-proof social choice function may have a dictator or has no dictator in an infinite society is equivalent to LPO (limited principle of omniscience). Therefore, it is non-constructive. A dictator of a social choice function is an individual such that if he strictly prefers an alternative (denoted by x) to another alternative (denoted by y), then the social choice function chooses an alternative other than y. Coalitional strategy-proofness is an extension of the ordinary strategy-proofness. It requires non-manipulability for coalitions of individuals as well as for a single individual.

Domains of social choice functions on which coalition strategy-proofness and Maskin monotonicity are equivalent

It is known that on some social choice and economic domains, a social choice function is coalition strategy-proof if and only if it is Maskin monotonic (e.g. Muller, E., and Satterthwaite, M., (1977). The equivalence of strong positive association and strategy-proofness. J. Econ. Theory, 14 pp412–18.). This paper studies the foundation of those results. I provide a set of conditions which is sufficient for the equivalence between coalition strategy-proofness and Maskin monotonicity. This generalizes some known results.

Domains of Social Choice Functions on Which Coalition Strategy-Proofness and Maskin Monotonicity are Equivalent

It is known that on some social choice and economic domains, a social choice function is coalition strategy-proof if and only if it is Maskin monotonic (e.g. Muller and Satterthwaite, 1977). This paper studies the foundation of those results. I provide a set of conditions which is sufficient for the equivalence between coalition strategy-proofness and Maskin monotonicity. This generalizes some known results.

Serial cost sharing of an excludable public good available in multiple units

This paper characterizes serial mechanisms for the cost sharing of an excludable public good that is available in multiple units. We show that serial mechanisms are the only voluntary mechanisms that satisfy coalition strategy-proofness and consumer sovereignty.

Type two computability of social choice functions and the Gibbard–Satterthwaite theorem in an infinite society

This paper investigates the computability problem of the Gibbard–Satterthwaite theorem [A.F. Gibbard, Manipulation of voting schemes: a general result, Econometrica 41 (1973) 587–601; M.A. Satterthwaite, Strategyproofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions, Journal of Economic Theory 10 (1975) 187–217] of social choice theory in a society with an infinite number of individuals (infinite society) based on Type two computability by Weihrauch [K. Weihrauch, A Simple Introduction to Computable Analysis, Informatik Berichte, vol. 171, second ed., Fern Universität Hagen, Hagen, 1995; K. Weihrauch, Computable Analysis, Springer-Verlag, 2000]. There exists a dictator or there exists no dictator for any coalitionally strategy-proof social choice function in an infinite society. We will show that if there exists a dictator for a social choice function, it is computable in the sense of Type two computability, but if there exists no dictator it is not computable. A dictator of a social choice function is an individual such that if he strictly prefers an alternative (denoted by x) to another alternative (denoted by y), then it does not choose y, and his most preferred alternative is always chosen. Coalitional strategy-proofness is an extension of the ordinary strategy-proofness. It requires non-manipulability by coalitions of individuals as well as by a single individual.

On strategy-proofness and essentially single-valued cores: A converse result

In a general model of indivisible good allocation, Sonmez (1999) established that, whenever the core is nonempty for each preference profile, if an allocation rule is strategy-proof, individually rational and Pareto optimal, then the rule is a selection from the core correspondence, and the core correspondence must be essentially single-valued. This paper studies the converse claim of this result. I demonstrate that whenever the preference domain satisfies a certain condition of `richness', if the core correspondence is essentially single-valued, then any selection from the core correspondence is strategy-proof (even weakly coalition strategy-proof, in fact). In particular, on the domain of preferences in which each individual has strict preferences over his own assignments and there is no consumption externality, such an allocation rule is coalition strategy-proof. And on this domain, coalition strategy-proofness is equivalent to Maskin monotonicity, an important property in implementation theory.

Coalitional Strategy-Proof House Allocation

We consider house allocation without endowments. We show that there is a unique maximal domain including all strict preferences on which efficiency and coalitional strategy-proofness are compatible. A preference relation belongs to the unique maximal domain if it is a strict descending ranking of houses to a certain house and indifference holds over it and the remaining houses. We also show that on this domain mixed dictator-pairwise-exchange rules are the only rules satisfying efficiency and coalitional strategy-proofness. Journal of Economic Literature Classification Numbers: C78, D63, D71.

Coalitional Strategy-Proofness in Economies with Single-Dipped Preferences and the Assignment of an Indivisible Object

We study two allocation models. In the first model, we consider the problem of allocating an infinitely divisible commodity among agents with single-dipped preferences. In the second model, a degenerate case of the first one, we study the allocation of an indivisible object to a group of agents. Our main result is the characterization of the class of Pareto optimal and coalitionally strategy-proof allocation rules. Alternatively, this class of rules, which largely consists of serially dictatorial components, can be characterized by Pareto optimality, strategy-proofness, and weak non-bossiness (in terms of welfare). Furthermore, we study properties of fairness such as anonymity and no-envy. Journal of Economic Literature Classification Numbers: D63, D71.