Weak Strategy-proofness Research Articles

Strategy-Proof Spectrum Allocation Among Multiple Operators in Wireless Networks

The exponentially increasing demand for data necessitates efficient spectrum allocation among operators in wireless networks. In this paper, we address the spectrum allocation problem among non-cooperative operators via auctions. The classical Vickrey-Clarke-Groves (VCG) approach provides the framework for a strategy-proof and social welfare maximizing auction. However, the VCG mechanism has high computational complexity, which makes it infeasible for practical implementation. In this work, we propose sealed bid auction mechanisms for spectrum allocation, which are computationally tractable. These can be used for spectrum allocation by performing auctions at shorter intervals to cater to the dynamic load variation in the network. We establish that the proposed algorithm is strategy-proof for the uniform demand scenario. Furthermore, for non-uniform demand, we propose an algorithm that satisfies weak strategy-proofness. Here, we also consider non-linear increase in the marginal valuations with demand. Simulation results are also presented to exhibit the performance comparison of the proposed algorithms with VCG and other existing mechanisms.

Stepwise ordinal efficiency for the random assignment problem

We introduce a notion of efficiency, called Stepwise Ordinal Efficiency (SOE), and prove that it coincides with a fairness notion of interim favoring ranks, in the sense of Harless (2018). We also prove that SOE implies ordinal efficiency, while it is not compatible with rank efficiency. Then, we provide an impossibility result which states that no mechanism meets SOE, weak strategy-proof, and strong equal treatment of equals. Finally, we show that a modified eating algorithm satisfies SOE.

Short trading cycles: Paired kidney exchange with strict ordinal preferences

I study kidney exchange with strict ordinal preferences and with constraints on the lengths of the exchange cycles. Efficient deterministic mechanisms have poor fairness properties in this environment. Instead, I propose an individually rational, ordinally efficient and anonymous random mechanism for two-way kidney exchange based on Bogomolnaia and Moulin’s (2001) Probabilistic Serial mechanism. Individual rationality incentivizes patient–donor pairs who are compatible with each other to participate in the exchange, thus increasing the overall transplantation rate. Finally, individual rationality, ex-post efficiency and weak strategyproofness are incompatible for any mechanism.

An impossibility result for housing markets with fractional endowments

The housing market setting constitutes a fundamental model of exchange economies of goods. House allocation with fractional endowments of houses was considered by Athanassoglou and Sethuraman (2011) who posed the open problem whether individual rationality, efficiency, and weak strategyproofness are compatible for the setting. We show that the three axioms are incompatible.

Incompatibility of efficiency and strategyproofness in the random assignment setting with indifferences

A fundamental resource allocation setting is the random assignment problem in which agents express preferences over objects that are then randomly allocated to the agents. In 2001, Bogomolnaia and Moulin presented the probabilistic serial (PS) mechanism that is an anonymous, Pareto optimal, and weak strategyproof mechanism when the preferences are considered with respect to stochastic dominance. The result holds when agents have strict preferences over individual objects. It has been an open problem whether there exists a mechanism that satisfies the same properties when agents may have indifference among the objects. We show that for this more general domain, there exists no extension of PS that is ex post efficient and weak strategyproof. The result is surprising because it does not even require additional symmetry or fairness conditions such as anonymity, neutrality, or equal treatment of equals. Our result further demonstrates that the lack of weak SD-strategyproofness of the extended PS mechanism of Katta and Sethuraman (2006) is not a design flaw but is due to an inherent incompatibility of efficiency and strategyproofness of PS in the full preference domain.

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.

On characterizations of the probabilistic serial mechanism involving incentive and invariance properties

This paper studies the problem of assigning n indivisible objects to n agents when each agent consumes one object and monetary transfers are not allowed. Bogomolnaia and Moulin (2001) proved that for n=3, the probabilistic serial mechanism is characterized by the three axioms of ordinal efficiency, envy-freeness, and weak strategy-proofness. We show that this characterization does not extend to problems of arbitrary size; in particular, it does not hold for any n≥5. A number of general characterizations of the probabilistic serial mechanism have been obtained in the recent literature by replacing weak strategy-proofness with various invariance axioms while retaining ordinal efficiency and envy-freeness. We show that weak strategy-proofness is in fact logically independent of all invariance axioms used in these characterizations.

Convex strategyproofness with an application to the probabilistic serial mechanism

We consider two natural notions of strategyproofness in random object-assignment mechanisms based on ordinal preferences. The two notions are stronger than weak strategyproofness but weaker than strategyproofness. We demonstrate that the two notions are equivalent, provide a geometric characterization of the new intermediate property which we call convex strategyproofness, and then show that the (generalized) probabilistic serial mechanism is, in fact, convexly strategyproof. We finish by showing that the property of weak envy-freeness of the random serial dictatorship can be strengthened in an analogous manner.

Relaxing strategyproofness in one-sided matching

We consider the one-sided matching problem, where agents must be matched to indivisible objects. Our first result is a novel characterization of strategyproof mechanisms by three intuitive axioms. Furthermore, we introduce partial strategyproofness , a new relaxation of strategyproofness that bridges the gap between full and weak strategyproofness. Partial strategyproofness finds application in the incentive analysis of non-strategyproof mechanisms, such as Probabilistic Serial, different variants of the Boston mechanism, and hybrid mechanisms. In this letter, we summarize the main results from [Mennle and Seuken 2014a] and demonstrate how they can be used for the design and analysis of matching mechanisms.

House allocation with fractional endowments

This paper studies a generalization of the well known house allocation problem in which agents may own fractions of different houses summing to an arbitrary quantity, but have use for only the equivalent of one unit of a house. It departs from the classical model by assuming that arbitrary quantities of each house may be available to the market. Justified envy considerations arise when two agents have the same initial endowment, or when an agent is in some sense disproportionately rewarded in comparison to her peers. For this general model, an algorithm is designed to find a fractional allocation of houses to agents that satisfies ordinal efficiency, individual rationality, and no justified envy. The analysis extends to the full preference domain. Individual rationality, ordinal efficiency, and no justified envy conflict with weak strategyproofness. Moreover, individual rationality, ordinal efficiency and strategyproofness are shown to be incompatible. Finally, two reasonable notions of envy-freeness, no justified envy and equal-endowment no envy, conflict in the presence of ordinal efficiency and individual rationality. All of the impossibility results hold in the strict preference domain.

A solution to the random assignment problem on the full preference domain

We consider the problem of allocating a set of indivisible objects to agents in a fair and efficient manner. In a recent paper, Bogomolnaia and Moulin consider the case in which all agents have strict preferences, and propose the probabilistic serial (PS) mechanism; they define a new notion of efficiency, called ordinal efficiency, and prove that the probabilistic serial mechanism finds an envy-free ordinally efficient assignment. However, the restrictive assumption of strict preferences is critical to their algorithm. Our main contribution is an analogous algorithm for the full preference domain in which agents are allowed to be indifferent between objects. Our algorithm is based on a reinterpretation of the PS mechanism as an iterative algorithm to compute a “flow” in an associated network. In addition we show that on the full preference domain it is impossible for even a weak strategyproof mechanism to find a random assignment that is both ordinally efficient and envy-free.

Continuous selections from the Pareto correspondence and non-manipulability in exchange economies

In n-agent exchange economies, we show that all efficient and continuous rules are “diagonally dictatorial” over the restricted domain of linear preferences and, in the 2-good case, over the domain of homothetic preferences. The diagonal dictator receives the entire endowment whenever all agents have an identical preference. We show that (fully) dictatorial rules are the only rules satisfying, in addition, veto-proofness, the requirement that if truth-telling ever leads to the worst outcome for an agent, he should not be able to escape it, by misrepresenting his preference. The same conclusion holds replacing veto-proofness with stronger notions of non-manipulability, veto-proofness ∗ (no one can escape from the worst outcome or switch to the best outcome), weak strategy-proofness (no one can increase his bundle), and strategy-proofness. We extend these results to any larger domain imposing non-bossiness (no one can affect others’ bundles without affecting his own).

Weak strategy proofness: The case of nonbinary social choice functions

It is now well known that under some eminently acceptable behavioral rule in comparing various power sets every nonimposed, binary, multivalued social choice mechanism is strategy-proof or oligarchic. Various attempts have been made to resolve the paradox either by relaxing binariness or by weakening the notion of strategy-proofness. By relaxing both binariness and the notion of strategy-proofness this paper shows that the trade-off between weak strategy-proofness and various unacceptable power structures, such as oligarchy or dictatorship, would remain intact.