Strategy-proof Allocation Mechanisms Research Articles

Locally efficient and strategy-proof allocation mechanisms in exchange economies

In this paper, we investigate whether efficiency and strategy-proofness of allocation mechanisms defined on a “local” preference set imply dictatorship. Although there is an extensive literature on the characterization of efficient and strategy-proof allocation mechanisms defined on the whole preference set, little attention has been given to a local characterization even in two-agent economies. This paper presents three results. First, we point out that locally efficient, strategy-proof, and nondictatorial allocation mechanisms exists even in two-agent economies, when boundary allocations can be efficient. Second, excluding such exceptional cases, we show that in economies where the number of goods equals or exceeds the number of agents, any efficient and strategy-proof allocation mechanism defined on any local preference domain is alternately dictatorial, that is, it always allocates the total amount of goods to some single agent, even if the receivers vary. Third, we clarify that the local characterization is generally an open question even with allocation conditions such as the minimum consumption guarantee, and show that efficiency and strategy-proofness are incompatible with allocation conditions when all agents have the same local preference set.

Strategyproof Allocation Mechanisms with Endowments and M-convex Distributional Constraints

We consider an allocation problem of multiple types of objects to agents, where each type of object has multiple copies (e.g., multiple seats in a school), each agent is endowed with an object, and some distributional constraints are imposed on the allocation (e.g., minimum/maximum quotas). We develop two mechanisms that are strategyproof, feasible (they always satisfy distributional constraints), and individually rational, assuming the distributional constraints are represented by an M-convex set. One mechanism, based on Top Trading Cycles, is Pareto efficient; the other, which belongs to the mechanism class specified by Kojima et al. [1], satisfies a relaxed fairness requirement. The class of distributional constraints we consider contains many situations raised from realistic matching problems, including individual minimum/maximum quotas, regional maximum quotas, type-specific quotas, and distance constraints. Finally, we experimentally evaluate the performance of these mechanisms by a computer simulation.

Pair Auction and Matching for Resource Allocation in Full-Duplex Cellular Systems

Full-duplex techniques improve spectral efficiency in cellular networks by allowing a transceiver to simultaneously transmit and receive data with the same radio resource. To minimize self-interference and inter-node interference due to the deployment of full-duplex radio, users have to feed back their measurements of interference to allow the base station to effectively allocate resources and form transmission pairs. Considering that the interference measurements are private information, users may not report the true values and may try to gain their own benefits. To solve this problem, we propose a strategy-proof resource allocation mechanism for full-duplex cellular networks. The proposed scheme, which is based on auction and matching theories, guarantees that users report true values of their channel quality and utilities, and therefore guarantees the correctness of feedback information and the efficiency of resource allocation. Moreover, the proposed matching-based mechanism is theoretically proved to be stable and Pareto efficient. Simulation results confirm that, compared to a centralized scheme with non-truthful information from users, the proposed scheme can achieve an 11 $\%$ gain.

Efficient and strategy-proof allocation mechanisms in many-agent economies

In this paper, we show that in pure exchange economies, any Pareto-efficient and strategy-proof allocation mechanism is alternately dictatorial; that is, it always allocates the total endowment to a single agent even if the receivers vary. While many studies have shown that such an allocation mechanism is dictatorial in two-agent economies, it has long remained an open question whether such a characterization can be obtained in many-agent economies.

Secure implementability under Pareto-efficient rules in linear production economies with classical preferences

This paper studies secure implementability (Saijo et al. (2007) “Secure Implementation,” Theoretical Economics 2, pp.203–229) in linear production economies with classical preferences. Although secure implementability is in general stronger than the combination of strategy-proofness and non-bossiness (Satterthwaite and Sonnenschein (1981) “Strategy-Proof Allocation Mechanisms at Differentiable Points,” Review of Economic Studies 48, pp.587–597), this paper shows that both properties are equivalent under Pareto-efficient rules in the economies. In addition, this paper characterizes securely implementable and Pareto-efficient rules in the economies when the number of agents is two.

Sequential rules for house allocation with price restrictions

This paper considers a housing market with price restrictions. On such market, price equilibrium may be excluded for certain preference profiles. However, the existence of a unique minimal rationing price equilibrium has previously been established on a general preference domain that contains “almost all” preference profiles. This type of equilibrium has been demonstrated to be an important ingredient in a direct and strategy-proof allocation mechanism for housing markets with price restrictions. The main contribution of this paper is to provide a finite ascending price sequence that terminates to a minimal rationing price equilibrium. This sequence is demonstrated to play a key-role in an Iterative English Auction Rule for housing markets with price restrictions.

Efficient and strategy-proof allocation mechanisms in economies with many goods

In this paper, we show that in pure exchange economies where the number of goods equals or exceeds the number of agents, any Pareto-efficient and strategy-proof allocation mechanism always allocates the total endowment to some single agent even if the receivers vary.

Better redistribution with inefficient allocation in multi-unit auctions

For the problem of allocating one or more items among a group of competing agents, the Vickrey–Clarke–Groves (VCG) mechanism is strategy-proof and efficient. However, the VCG mechanism is not strongly budget balanced: in general, value flows out of the system of agents in the form of VCG payments, which reduces the agents' utilities. In many settings, the objective is to maximize the sum of the agents' utilities (taking payments into account). For this purpose, several VCG redistribution mechanisms have been proposed that redistribute a large fraction of the VCG payments back to the agents, in a way that maintains strategy-proofness and the non-deficit property. Unfortunately, sometimes even the best VCG redistribution mechanism fails to redistribute a substantial fraction of the VCG payments. This results in a low total utility for the agents, even though the items are allocated efficiently. In this paper, we study strategy-proof allocation mechanisms that do not always allocate the items efficiently. It turns out that by allocating inefficiently, more payment can sometimes be redistributed, so that the net effect is an increase in the sum of the agents' utilities.Our objective is to design mechanisms that are competitive against the first-best mechanism in terms of the agents' total utility. We first study multi-unit auctions with unit demand. We characterize the family of linear allocation mechanisms. We propose an optimization technique for simultaneously finding a linear allocation mechanism and a payment redistribution rule, which together are optimal. With the help of this technique, we also analytically characterize several competitive mechanisms, which are based on burning units and partitioning the agents into groups. Finally, we extend the definition of linear allocation mechanisms and the optimization technique to general multi-unit auctions.

Note on social choice allocation in exchange economies with many agents

Abstract We show that in pure exchange economies there exists no Pareto-efficient and strategy-proof allocation mechanism that ensures positive consumption for all agents. We also show that a Pareto-efficient, strategy-proof, and non-bossy allocation mechanism is dictatorial. We further show that in three-agent economies, the allocation given by a Pareto-efficient, strategy-proof, and non-dictatorial mechanism depends only on one agentʼs preference who is always allocated zero consumption. That is, in three-agent economies, Zhouʼs (1991) [14] conjecture is true and any Pareto-efficient and strategy-proof mechanism is of Satterthwaite and Sonnenscheinʼs (1981) [10] type.

Strategy-proof allocation mechanisms for economies with public goods

We show that strategy-proof allocation mechanisms for economies with public goods are dictatorial—i.e., they always select an allocation in their range that maximizes the welfare of the same single individual (the dictator). Further, strategy-proof and efficient allocation mechanisms are strongly dictatorial—i.e., they select the dictator’s preferred allocation on the entire feasible set. Thus, our results reveal the extent to which the conflict between individual incentives and other properties that may be deemed desirable (e.g., fairness, equal treatment, distributive justice) pervades resource allocation problems.

Strategy-proof allocation mechanisms for pure public goods economies when preferences are monotonic

A fundamental problem in public finance is that of allocating a␣given budget to financing the provision of public goods (education, transportation, police, etc.). In this paper it is established that when␣admissible preferences are those representable by continuous and increasing utility functions, then strategy-proof allocation mechanisms whose (undominated) range contains three or more outcomes are dictatorial on the set of profiles of strictly increasing utility functions, a dense subset of the domain in the topologies commonly used in this context. If admissible utility functions are further restricted to be strictly increasing, or if mechanisms are required to be non-wasteful, then strategy-profness leads to (full) dictatorship.

Strategy-proof allocation mechanisms for economies with an indivisible good

We consider economies with a single indivisible good and money. We characterize the set of mechanisms that satisfy strategy-proofness, individual rationality, equal compensation, and demand monotonicity. There are three types of mechanisms which have the following properties: (i) they determine the allocation of monetary compensation depending on who receives the indivisible good; (ii) they allocate the indivisible good to one of the pre-specified (one or two) agent(s); and (iii) they disregard preferences of agents other than the pre-specified agent(s). This result implies that the presence of an indivisible good induces serious asymmetry in mechanisms.

Asymptotically strategy-proof Walrasian exchange

In smooth exchange economies with a continuum of agents, any Walrasian mechanism is Pareto efficient, individually rational, anonymous, and strategy-proof. Barberà and Jackson's recent results imply that no such efficient mechanism is the limit of resource-balanced, individually rational, anonymous and non-bossy strategy-proof allocation mechanisms for an expanding sequence of finite economies. For a broad class of smooth random exchange economies, relaxing anonymity and non-bossiness admits mechanisms which, as the economy becomes infinitely large, are asymptotically Walrasian for all except one “balancing” agent, while being manipulable with generically vanishing probability. Also considered are some extensions to non-Walrasian mechanisms.

Procedural cum Endstate Justice: An Implementation Viewpoint

Means matter as well as ends. In the context of the microeconomic allocation of resources, the familiar statement corresponds to the duality of procedural versus endstate justice; the tension between these two approaches is highlighted by the strategic implementation approach. It is argued that the strong requirement of strategyproofness provides the only context where the two approaches coincide for strategyproof mechanisms, and only for those, the justice of the mechanism is equivalent to that of its endstate. The literature on strategyproof allocation mechanisms is briefly reviewed, and its recent revival is emphasized.

Inefficiency of strategy-proof allocation mechanisms in pure exchange economies

In this paper I prove that in the standard model of 2×n (n≧2) pure exchange economies there is no allocation mechanism that is efficient, non-inversely-dictatorial, and strategy-proof. This strengthens two previous results on this subject by Hurwicz and by Dasgupta, Hammond, and Maskin.

Strategy-Proof Allocation Mechanisms at Differentiable Points

Journal Article Strategy-Proof Allocation Mechanisms at Differentiable Points Get access Mark A. Satterthwaite, Mark A. Satterthwaite Northwestern University Search for other works by this author on: Oxford Academic Google Scholar Hugo Sonnenschein Hugo Sonnenschein Princeton University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 48, Issue 4, October 1981, Pages 587–597, https://doi.org/10.2307/2297198 Published: 01 October 1981 Article history Received: 01 October 1979 Accepted: 01 May 1981 Published: 01 October 1981