Group Strategy-proof Research Articles

The Role of Domain Restrictions in Mechanism Design: Ex Post Incentive Compatibility and Pareto Efficiency

We study the possibility of designing satisfactory ex post incentive compatible single valued direct mechanisms in interdependent values environments, characterized by the set of agents’ type profiles and by their induced preference profiles. For environments that we call knit and strict, only constant mechanisms can be ex post (or interim) incentive compatible. For those called partially knit, ex post incentive compatibility extends to groups, and strategy-proofnes implies strong group strategy-proofness in private values environments. The results extend to mechanisms operating on non-strict domains under an additional requirement of respectfulness. We discuss voting, assignment and auctions environments where our theorems apply.

Multi-Unit Assignment Under Dichotomous Preferences

I study the problem of allocating objects among agents without using money. Agents can receive several objects and have dichotomous preferences, meaning that they either consider objects to be acceptable or not. In this setup, the egalitarian solution is more appealing than the competitive equilibrium with equal incomes because it is Lorenz dominant, unique in utilities, and group strategy-proof. Moreover, it can be adapted to satisfy a new fairness axiom that arises naturally in this context. Both solutions are disjoint.

On Stable and Efficient Mechanisms for Priority-Based Allocation Problems

For school choice (priority-based allocation) problems, when the priority structure is acyclic, the associated student-proposing deferred acceptance algorithm is Pareto efficient and group strategy-proof (Ergin, 2002). We reveal a hidden iterative removal structure behind such deferred acceptance algorithms. A nonempty set of students is called a top fair set (TFS) if when all students apply to their most preferred schools and all schools accept the best applicants up to their quotas, students in the set are always accepted, regardless of other students’ preferences. We provide an elimination process to find the maximal TFS, if any TFS exists. We show that for any priority structure, iterative removal of TFS is equivalent to the associated deferred acceptance algorithm if and only if the latter is a Pareto efficient mechanism.

Constrained Allocation of Projects to Heterogeneous Workers with Preferences over Peers

AbstractWe study the problem of allocating projects to heterogeneous workers. The simultaneous execution of multiple projects imposes constraints across project teams. Each worker has preferences over the combinations of projects in which he can potentially participate and his team members in any of these projects. We propose a revelation mechanism that is Pareto-efficient and group strategy-proof (Theorem 1). We also identify two preference domains on which the mechanism is strongly group strategy-proof (Theorem 2). Our results subsume results by Monte and Tumennasan (2013) and Kamiyama (2013) .

Group Strategy-Proof Stable Mechanisms in Priority-Based Resource Allocation Under Multi-Unit Demand: A Note

We prove that group strategy-proofness and strategy-proofness are equivalent requirements on stable mechanisms in priority-based resource allocation problems with multi-unit demand. The result extends to the model with contracts.

Groupstrategyproofness of the egalitarian mechanism for constrained rationing problems

Motivated by applications in many economic environments, Bochet et al. (2010) generalize the classic rationing model (Sprumont 1991) as follows: there is a moneyless market, in which a non-storable, homogeneous commodity is reallocated between agents with single-peaked preferences. Agents are either suppliers or demanders. Transfers between a supplier and a demander are feasible only if they are linked, and the links form an arbitrary bipartite graph. Information about individual preferences is private, and so is information about feasible links: an agent may unilaterally close one of her links if it is in her interest to do so. For this problem they propose the egalitarian transfer solution, which equalizes the net transfers of rationed agents as much as permitted by the bilateral constraints. Furthermore, they show that the egalitarian mechanism elicits a truthful report of both preferences and links. In the variant where demanders are not strategic but demands need to be exactly met Bochet et al. (2013), they propose a similar mechanism for which truthfully reporting the peaks is a dominant strategy, but truthful reporting of links is not.The key contribution of the paper is a comprehensive study of the egalitarian mechanism with respect to manipulation by a coalition of agents. Our main result is that the egalitarian mechanism is group strategyproof : no coalition of agents can (weakly) benefit from jointly misreporting their peaks. Furthermore, we show that the egalitarian mechanism cannot be manipulated – by misreporting links or by misreporting peaks – by any coalition of suppliers (or any coalition of demanders) in the model where both the suppliers and demanders are agents. Our proofs shed light on the structure of the two models and simplify some of the earlier proofs of strategyproofness. An implication of our results is that the well known algorithm of Megiddo (1977) to compute a lexicographically optimal flow in a network is group strategyproof with respect to the source capacities and sink capacities.

Impossibilities for probabilistic assignment

We consider the problem of assigning objects probabilistically among a group of agents who may have multi-unit demands. Each agent has linear preferences over the (set of) objects. The most commonly used extension of preferences to compare probabilistic assignments is by means of stochastic dominance, which leads to corresponding notions of envy-freeness, efficiency, and strategy-proofness. We show that equal treatment of equals, efficiency, and strategy-proofness are incompatible. Moreover, anonymity, neutrality, efficiency, and weak strategy-proofness are incompatible. If we strengthen weak strategy-proofness to weak group strategy-proofness, then when agents have single-unit demands, anonymity, neutrality, efficiency, and weak group strategy-proofness become incompatible.

Parameterization of Strategy-Proof Mechanisms in the Obnoxious Facility Game

In the obnoxious facility game, a location for an undesirable facility is to be determined based on votes cast by selfish agents. The design of group strategy proof mechanisms has been extensively studied, and it is known that choosing a facility location that maximizes the social benefit (i.e., the sum of individual benefits) may not be a strategy-proof decision, and vice-versa, the social benefit obtainable by a strategy-proof mechanism does not maximize the social benefit over all choices of facility locations; their ratio, called the benefit ratio, can be up to 3 in the line metric space. In this paper, we investigate a trade-off between the benefit ratio and a possible relaxation of group strategy proofness, taking $2$-candidate mechanisms for the obnoxious facility game in the line metric as an example. Given a real $\lambda \geq 1$ as a parameter, we introduce a new concept of strategy proofness, called "$\lambda$-group strategy-proofness," so that each coalition of agents has no incentive to lie unless every agent in the group can increase her benefit by strictly more than $\lambda$ times by doing so, where $1$-group strategy-proofness reduces to the standard concept of group strategy-proofness. We next introduce "masking zone mechanisms," a new notion on the structure of mechanisms, and prove that every $\lambda$ strategy-proof ($\lambda$-SP) mechanism is a masking zone mechanism. We then show that, for any $\lambda \geq 1$, there exists a $\lambda$-GSP mechanism whose benefit ratio is at most $1+\frac{2}{\lambda}$, which converges to 1 as $\lambda$ becomes infinitely large. Finally we prove that the bound is nearly tight: given $n \geq 1$ selfish agents, the benefit ratio of $\lambda$-GSP mechanisms cannot be better than $1+\frac{2}{\lambda}$ when $n$ is even, and $1 + \frac{2n-2}{\lambda n + 1}$ when $n$ is odd.

Incentive compatible allocation and exchange of discrete resources

The allocation and exchange of discrete resources, such as transplant organs, public housing, dormitory rooms, and many other resources for which agents have single-unit demand, is often conducted via direct mechanisms without monetary transfers. Incentive compatibility and efficiency are primary concerns when designing such mechanisms. We construct the full class of group strategy-proof and Pareto-efficient mechanisms and show that each of them can be implemented by endowing agents with control rights over resources. This new class, which we call trading cycles, contains new mechanisms as well as known mechanisms such as top trading cycles, serial dictatorships, and hierarchical exchange. We illustrate how one can use our construction to show what can and what cannot be achieved in a variety of allocation and exchange problems, and we provide an example in which the new trading-cycles mechanisms are more Lorenz equitable than all previously known mechanisms.

Immunity to credible deviations from the truth

We study a notion of non-manipulability by groups, based on the idea that only some agreements among potential manipulators may be credible. The derived notion of immunity to credible manipulations by groups is intermediate between individual and group strategy-proofness. Our main non-recursive definition turns out to be equivalent, in our context, to the requirement that truthful preference revelation should be a strong coalition-proof equilibrium, as recursively defined by Peleg and Sudhölter (1998, 1999). We provide characterizations of strategy-proof rules separating those that satisfy it from those that do not for a large family of public good decision problems.

A necessary and sufficient condition for weak Maskin monotonicity in an allocation problem with indivisible goods

We consider an allocation problem with indivisible goods, and provide a necessary and sufficient condition for weak Maskin monotonic allocation rules under non-wastefulness. The condition is based on robustness to group manipulation. Specifically, we introduce a new condition called the no improvement property of unmatched agents which means that unmatched agents cannot be strictly better off through any group manipulation. We show that a non-wasteful allocation rule satisfies weak Maskin monotonicity if and only if it satisfies the no improvement property of unmatched agents and weak group strategy-proofness. In addition, together with our result and that of Kojima and Manea (Econometrica 78:633–653, 2010), the deferred acceptance (DA) rules with acceptant substitutable priorities are characterized based on the conditions related to robustness to group manipulation.

The blocking lemma and group incentive compatibility for matching with contracts

This paper considers a general class of two-sided many-to-one matching markets, so-called matching markets with contracts. We study the blocking lemma and group incentive compatibility for this class of matching markets. We first show that the blocking lemma for matching with contracts holds if hospitals’ choice functions satisfy substitutes and the law of aggregate demand. The blocking lemma for one-to-one matching (Gale and Sotomayor, 1985) and that for many-to-one matching (Martínez et al., 2010) are special cases of this result. Then, as an immediate consequence of the blocking lemma, we show that the doctor-optimal stable mechanism is group strategy-proof for doctors if hospitals’ choice functions satisfy substitutes and the law of aggregate demand. Hatfield and Kojima (2009) originally obtain this result by skillfully using the strategy-proofness of the doctor-optimal stable mechanism. In this paper we provide a different proof for the group incentive compatibility by applying the blocking lemma.

Immunity to Credible Deviations from the Truth

We introduce a new notion of non-manipulability by groups, based on the idea that some of the agreements among a set of potential manipulators may be credible, while others may not. The derived notion of immunity to credible manipulations by groups is intermediate between individual and group strategy-proofness. We show that our new concept has bite, by applying it to the analysis of a large family of public good decision problems in separable environments, where there exist many attractive strategy-proof rules that are, however, manipulable by groups. In these environments we show that some of these rules are indeed, immune to credible group manipulations, while others are not. We provide characterization results that separate these two classes.

Single-dipped preferences with satiation: strong group strategy-proofness and unanimity

We study the problem of the location of a public facility that generates negative externalities. We consider that agents have single-dipped preferences with satiation: each agent considers a location as the worst, the “dip”, and the farther the location is from the dip, the better for the agent. In addition, an agent might be indifferent between all the locations sufficiently far from his dip, reaching his highest level of satisfaction. We characterize the family of strongly group strategy-proof and unanimous rules. Opposite to previous results without satiation, the locations selected are not necessarily at the extremes of the alternatives’ space.

Strategyproof Facility Location for Concave Cost Functions

We consider k-Facility Location games, where n strategic agents report their locations on the real line and a mechanism maps them to k facilities. Each agent seeks to minimize his connection cost, given by a nonnegative increasing function of his distance to the nearest facility. Departing from previous work, that mostly considers the identity cost function, we are interested in mechanisms without payments that are (group) strategyproof for any given cost function, and achieve a good approximation ratio for the social cost and/or the maximum cost of the agents. We present a randomized mechanism, called Equal Cost, which is group strategyproof and achieves a bounded approximation ratio for all k and n, for any given concave cost function. The approximation ratio is at most 2 for Max Cost and at most n for Social Cost. To the best of our knowledge, this is the first mechanism with a bounded approximation ratio for instances with $$k \ge 3$$kź3 facilities and any number of agents. Our result implies an interesting separation between deterministic mechanisms, whose approximation ratio for Max Cost jumps from 2 to unbounded when k increases from 2 to 3, and randomized mechanisms, whose approximation ratio remains at most 2 for all k. On the negative side, we exclude the possibility of a mechanism with the properties of Equal Cost for strictly convex cost functions. We also present a randomized mechanism, called Pick the Loser, which applies to instances with k facilities and only $$n = k+1$$n=k+1 agents. For any given concave cost function, Pick the Loser is strongly group strategyproof and achieves an approximation ratio of 2 for Social Cost.

Reaching consensus: solidarity and strategic properties in binary social choice

We study solidarity and strategic properties in binary social choice. We consider both the standard setting with strict preferences and the “full” preference domain which allows for indifference. Two solidarity properties drive our investigation: “Welfare dominance under preference replacement”, which says that when the preferences of one agent change, the other agents all weakly gain or all weakly lose; and “population monotonicity”, which requires the same conclusion when one agent leaves. We identify the families of rules satisfying these properties on each preference domain. Additionally requiring efficiency characterizes the “consensus” rules in each case. We also relate welfare dominance to other properties. Two results highlight the role of indifference: Welfare dominance implies “anonymity” when preferences are strict, but not otherwise; “group strategy-proofness” implies welfare dominance when indifference is allowed, but not otherwise. Finally, we introduce a “duality” operator which structures the space of rules and extends our results to a model in which rules may select neither alternative. Only in this case are our solidarity properties consistent with “neutrality”.

Strategy-Proof Location of Public Facilities

Agents frequently have different opinions on where to locate a public facility. While some agents consider the facility a good and prefer to have it nearby, others dislike it and would like to see it built far away from their own locations. To aggregate agents' preferences in these situations, we propose a new preference domain according to which each agent is allowed to have single-peaked or single-dipped preferences on the location of the facility, but in such a way that the peak or dip is situated in her own location. We characterize all strategy-proof rules in this general framework and show that they are also group strategy-proof. Finally, we characterize for some focal cases the rules that additionally satisfy Pareto efficiency.

Generalizing Deferred Acceptance Auctions to Allow Multiple Relinquishment Options

Introduction and the Statement of the Problem. Reallocation of spectrum from current licensees TV broadcasters to mobile uses to promote e cient use of spectrum has become a public policy agenda. The Congress authorized the FCC to conduct incentive auctions for reallocations of spectrum in the UHF band. In this paper, we focus on the design of reverse auctions where TV stations submit bids to voluntarily relinquish spectrum rights to FCC in exchange for payments. The state of the art of the design of reverse auctions is the framework given in Paul Milgrom, Lawrence Ausubel, Jon Levin, and Ilya Segal (2012) and deferred acceptance auctions proposed by Paul Milgrom and Ilya Segal (2014). In deferred acceptance auctions, each seller submits a single o er. At each round, an o er is evaluated with its scoring function. The buyer deletes the o er with the highest score. Then the set of frozen sellers (i.e., the set of sellers who will be assigned back to the band because the scores are too high) will be updated and o ers are re-evaluated. Auctions end when only o ers with the zero score remain. The payment rule is determined by the threshold price that is the maximum amount that the seller can o er to sell. When bidders are single-minded (that is, a bidder can make only one bid), then, the deferred acceptance auctions are strategy-proof, can be implemented in descending clock auctions, nearlyoptimal, group strategy-proofness, and equivalent to payas-bid auctions. But the Spectrum Act 6403(a)(2) stipulates that bidders shall have multiple relinquishment options such as going o the air, moving to the VHF band, and channel sharing. When the seller can make only one o er, the seller has to choose which auction to bid. Then the payment depends on the choice of auctions by other bidders. Therefore, the seller’s choice of auctions can depend on other sellers’ choices. Thus sincere bidding may not be an equilibrium.

Group Strategy-Proofness in Private Good Economies Without Money: Matching, Division and House Allocation

We observe that three salient solutions to matching, division and house allocation problems are not only (partially) strategy-proof, but (partially) group strategy-proof as well, in appropriate domains of definition. That is the case for the Gale-Shapley mechanism, the uniform rule and the top trading cycle solution, respectively. We embed these three types of problems into a general framework. We then notice that the three rules, as well as many others, do share a common set of properties, which together imply their (partial) group strategy-proofness. This proves that the equivalence between individual and group strategy-proofness in all these cases is not a fortuitous event, but results from the structure of the functions under consideration.

Joint misrepresentation with bribes

We study the problem of assigning objects to buyers. Monetary transfers are allowed. Each buyer’s preference space contains, but is not limited to, the linear additively separable preferences. A rule maps each preference profile to an allocation. We are concerned about the possibility that a group of buyers may engage in the following kind of manipulation: They make side payments internally and then carry out a joint misrepresentation. A rule is strongly group strategy-proof if no group can gain by engaging in such operations. We also consider several other appealing requirements. We find that the posted-price rules are the only one that satisfies non-triviality, non-imposition, envy-freeness, and strong group strategy-proofness.