Bribeproof mechanisms for two-values domains

Schummer (Journal of Economic Theory 2000) introduced the concept of bribeproof mechanism which, in a context where monetary transfer between agents is possible, requires that manipulations through bribes are ruled out. Unfortunately, in many domains, the only bribeproof mechanisms are the trivial ones which return a fixed outcome. This work presents one of the few constructions of non-trivial bribeproof mechanisms for these quasi-linear environments. Though the suggested construction applies to rather restricted domains, the results obtained are tight: For several natural problems, the method yields the only possible bribeproof mechanism and no such mechanism is possible on more general domains.Comment: Extended abstract accepted to SAGT 2016. This ArXiv version corrects typos in the proofs of Theorem 7 and Claims 28-29 of prior ArXiv versio

Generalized Incremental Mechanisms for Scheduling Games

We study the problem of devising truthful mechanisms for cooperative cost sharing games that realize (approximate) budget balance and social cost. Recent negative results show that group-strategyproof mechanisms can only achieve very poor approximation guarantees for several fundamental cost sharing games. Driven by these limitations, we consider cost sharing mechanisms that realize the weaker notion of weak groupstrategyproofness. Mehta et al. [Games and Economic Behavior, 67:125–155, 2009] recently introduced the broad class of weakly group-strategyproof acyclic mechanisms and show that several primal-dual approximation algorithms naturally give rise to such mechanisms with attractive approximation guarantees. In this paper, we provide a simple yet powerful approach that enables us to turn any r-approximation algorithm into a r-budget balanced acyclic mechanism. We demonstrate the applicability of our approach by deriving weakly group-strategyproof mechanisms for several fundamental scheduling problems that outperform the best possible approximation guarantees of Moulin mechanisms. The mechanisms that we develop for completion time scheduling problems are the first mechanisms that achieve constant budget balance and social cost approximation factors. Interestingly, our mechanisms belong to the class of generalized incremental mechanisms proposed by Moulin [Social Choice and Welfare, 16:279–320, 1999]

Computing with strategic agents

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 179-189).This dissertation studies mechanism design for various combinatorial problems in the presence of strategic agents. A mechanism is an algorithm for allocating a resource among a group of participants, each of which has a privately-known value for any particular allocation. A mechanism is truthful if it is in each participant's best interest to reveal his private information truthfully regardless of the strategies of the other participants. First, we explore a competitive auction framework for truthful mechanism design in the setting of multi-unit auctions, or auctions which sell multiple identical copies of a good. In this framework, the goal is to design a truthful auction whose revenue approximates that of an omniscient auction for any set of bids. We focus on two natural settings - the limited demand setting where bidders desire at most a fixed number of copies and the limited budget setting where bidders can spend at most a fixed amount of money. In the limit demand setting, all prior auctions employed the use of randomization in the computation of the allocation and prices.(cont.) Randomization in truthful mechanism design is undesirable because, in arguing the truthfulness of the mechanism, we employ an underlying assumption that the bidders trust the random coin flips of the auctioneer. Despite conjectures to the contrary, we are able to design a technique to derandomize any multi-unit auction in the limited demand case without losing much of the revenue guarantees. We then consider the limited budget case and provide the first competitive auction for this setting, although our auction is randomized. Next, we consider abandoning truthfulness in order to improve the revenue properties of procurement auctions, or auctions that are used to hire a team of agents to complete a task. We study first-price procurement auctions and their variants and argue that in certain settings the payment is never significantly more than, and sometimes much less than, truthful mechanisms. Then we consider the setting of cost-sharing auctions. In a cost-sharing auction, agents bid to receive some service, such as connectivity to the Internet. A subset of agents is then selected for service and charged prices to approximately recover the cost of servicing them.(cont.) We ask what can be achieved by cost -sharing auctions satisfying a strengthening of truthfulness called group-strategyproofness. Group-strategyproofness requires that even coalitions of agents do not have an incentive to report bids other than their true values in the absence of side-payments. For a particular class of such mechanisms, we develop a novel technique based on the probabilistic method for proving bounds on their revenue and use this technique to derive tight or nearly-tight bounds for several combinatorial optimization games. Our results are quite pessimistic, suggesting that for many problems group-strategyproofness is incompatible with revenue goals. Finally, we study centralized two-sided markets, or markets that form a matching between participants based on preference lists. We consider mechanisms that output matching which are stable with respect to the submitted preferences. A matching is stable if no two participants can jointly benefit by breaking away from the assigned matching to form a pair.(cont.) For such mechanisms, we are able to prove that in a certain probabilistic setting each participant's best strategy is truthfulness with high probability (assuming other participants are truthful as well) even though in such markets in general there are provably no truthful mechanisms.by Nicole Immorlica.Ph.D

Strategyproof Profit Sharing: A Two-Agent Characterization

Two agents jointly operate a decreasing marginal returns technology to produce a private good. We characterize the class of output-sharing rules for which the labor-supply game has a unique Nash equilibrium. It consists of two families: rules of the serial type which protect a small user from the negative externality imposed by a large user, and rules of the reverse serial type, where one agent effectively employs the other agent's labor. Exactly two rules satisfy symmetry; a result in sharp contrast with Moulin and Shenker's (Econometrica, 1992) characterization of their serial mechanism as the unique cost -sharing rule satisfying the same incentives property. We also show that the familiar stand alone test characterizes the class of fixed-path methods (Friedman, Economic Theory, 2002) under our incentives criterion.

Sharing the cost of multicast transmissions in wireless networks

AbstractA crucial issue in non-cooperative wireless networks is that of sharing the cost of multicast transmissions to different users residing at the stations of the network. Each station acts as a selfish agent that may misreport its utility (i.e., the maximum cost it is willing to incur to receive the service, in terms of power consumption) in order to maximize its individual welfare, defined as the difference between its true utility and its charged cost. A provider can discourage such deceptions by using a strategyproof cost sharing mechanism, that is a particular public algorithm that, by forcing the agents to truthfully reveal their utility, starting from the reported utilities, decides who gets the service (the receivers) and at what price. A mechanism is said budget balanced (BB) if the receivers pay exactly the (possibly minimum) cost of the transmission, and β-approximate budget balanced (β-BB) if the total cost charged to the receivers covers the overall cost and is at most β times the optimal one, while it is efficient if it maximizes the sum of the receivers’ utilities minus the total cost over all receivers’ sets. In this paper, we first investigate cost sharing strategyproof mechanisms for symmetric wireless networks, in which the powers necessary for exchanging messages between stations may be arbitrary and we provide mechanisms that are either efficient or BB when the power assignments are induced by a fixed universal spanning tree, or (3ln(k+1))-BB (k is the number of receivers), otherwise. Then we consider the case in which the stations lay in a d-dimensional Euclidean space and the powers fall as 1/dα, and provide strategyproof mechanisms that are either 1-BB or efficient for α=1 or d=1. Finally, we show the existence of 2(3d-1)-BB strategyproof mechanisms in any d-dimensional space for every α⩾d. For the special case of d=2 such a result can be improved to achieve 12-BB mechanisms

On Proportionate and Truthful International Alliance Contributions: An Analysis of Incentive Compatible Cost Sharing Mechanisms to Burden Sharing

Burden sharing within an international alliance is a contentious topic, especially in the current geopolitical environment, that in practice is generally imposed by a central authority\u27s perception of its members\u27 abilities to contribute. Instead, we propose a cost sharing mechanism such that burden shares are allocated to nations based on their honest declarations of the alliance\u27s worth. Specifically, we develop a set of multiobjective nonlinear optimization problem formulations that respectively impose Bayesian Incentive Compatible (BIC), Strategyproof (SP), and Group Strategyproof (GSP) mechanisms based on probabilistic inspection efforts and deception penalties that are budget balanced and in the core. Any feasible solution to these problems corresponds to a single stage Bayesian stochastic game wherein a collectively honest declaration is a Bayes-Nash equilibrium, a Nash Equilibrium in dominant strategies, or a collusion resistant Nash equilibrium, respectively, but the optimal solution considers the alliance\u27s central authority preferences. Each formulation is shown to be a nonconvex optimization problem. The solution quality and computational effort required for three heuristic algorithms as well as the BARON global solver are analyzed to determine the superlative solution methodology for each problem. The Pareto fronts associated with each multiobjective optimization problem are examined to determine the tradeoff between inspection frequency and penalty severity required to obtain truthfulness under stronger assumptions. Memory limitations are examined to ascertain the size of alliances for which the proposed methodology can be utilized. Finally, a full block design experiment considering the clustering of available alliance valuations and the member nations\u27 probability distributions therein is executed on an intermediate-sized alliance motivated by the South American alliance UNASUR