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2022, arXiv (Cornell University)
We study mechanism design with predictions for the obnoxious facility location problem. We present deterministic strategyproof mechanisms that display tradeoffs between robustness and consistency on segments, squares, circles and trees. All these mechanisms are actually group strategyproof, with the exception of the case of squares, where manipulations from coalitions of two agents exist. We prove that these tradeoffs are optimal in the 1-dimensional case.
2010
We study Facility Location games, where a number of facilities are placed in a metric space based on locations reported by strategic agents. A mechanism maps the agents’ locations to a set of facilities. The agents seek to minimize their connection cost, namely the distance of their true location to the nearest facility, and may misreport their location. We are interested in mechanisms that are strategyproof, i.e., ensure that no agent can benefit from misreporting her location, do not resort to monetary transfers, and approximate the optimal social cost. We focus on the closely related problems of k-Facility Location and Facility Location with a uniform facility opening cost, and mostly study winner-imposing mechanisms, which allocate facilities to the agents and require that each agent allocated a facility should connect to it. We show that the winner-imposing version of the Proportional Mechanism (Lu et al., EC ’10) is stategyproof and 4k-approximate for the k-Facility Location game. For the Facility Location game, we show that the winner-imposing version of the randomized algorithm of (Meyerson, FOCS ’01), which has an approximation ratio of 8, is strategyproof. Furthermore, we present a deterministic non-imposing group strategyproof O(logn)-approximate mechanism for the Facility Location game on the line.
2011
We study strategyproof (SP) mechanisms for the location of a facility on a discrete graph. We give a full characterization of SP mechanisms on lines and on sufficiently large cycles. Interestingly, the characterization deviates from the one given by Schummer and Vohra [21] for the continuous case. In particular, it is shown that an SP mechanism on a cycle is close to dictatorial, but all agents can affect the outcome, in contrast to the continuous case. Our characterization is also used to derive a lower bound on the approximation ratio with respect to the social cost that can be achieved by an SP mechanism on certain graphs. Finally, we show how the representation of such graphs as subsets of the binary cube reveals common properties of SP mechanisms and enables one to extend the lower bound to related domains. This property is a very basic requirement (usually justified as society sovereignty), and as such we will restrict attention to mechanisms satisfying this condition. We are also interested in the following properties, which are stronger. Definition 2. A mechanism f is unanimous if for every x ∈ V , f (x, x,. .. , x) = x. def:pareto Definition 3. A location y ∈ V is said to Pareto dominate x ∈ V if all the agents strictly prefer y over x (i.e. d(y, a j) < d(x, a j) for every j ∈ N). A mechanism f is Pareto if for all a ∈ V n , there is no location y ∈ V that Pareto dominates f (a). 4 It is easy to verify that Pareto entails unanimity, which in turn entails onto. An agent j is said to be a dictator in f if for every location profile a ∈ V n , it holds that f (a) = a j. Consider the following relaxation of the dictatorship notion. Definition 4. An agent j is said to be an m-dictator in f , if for every a ∈ V n , it holds that d(f (a), a j) ≤ m. A mechanism f is m-dictatorial if there exists an agent j that is an m-dictator in f. Note that a 0-dictator is essentially a dictator. It is argued that dictatorial mechanisms are "unfair" in the sense that the agent's name plays a major role in the decision of the facility location. Mechanisms that ignore agents' names altogether are said to be anonymous. Definition 5. A mechanism f is anonymous, if for every profile a and every permutation of agents π : N → N , it holds that f (a 1 ,. .. , a n) = f (a π(1) ,. .. , a π(n)). Our main interest is in strategyproof mechanisms, defined as follows.
Proceedings of the 23rd ACM Conference on Economics and Computation
In this work we introduce an alternative model for the design and analysis of strategyproof mechanisms that is motivated by the recent surge of work in "learning-augmented algorithms". Aiming to complement the traditional approach in computer science, which analyzes the performance of algorithms based on worst-case instances, this line of work has focused on the design and analysis of algorithms that are enhanced with machine-learned predictions regarding the optimal solution. The algorithms can use the predictions as a guide to inform their decisions, and the goal is to achieve much stronger performance guarantees when these predictions are accurate (consistency), while also maintaining near-optimal worst-case guarantees, even if these predictions are very inaccurate (robustness). So far, these results have been limited to algorithms, but in this work we argue that another fertile ground for this framework is in mechanism design. We initiate the design and analysis of strategyproof mechanisms that are augmented with predictions regarding the private information of the participating agents. To exhibit the important benefits of this approach, we revisit the canonical problem of facility location with strategic agents in the two-dimensional Euclidean space. We study both the egalitarian and utilitarian social cost functions, and we propose new strategyproof mechanisms that leverage predictions to guarantee an optimal trade-off between consistency and robustness guarantees. This provides the designer with a menu of mechanism options to choose from, depending on her confidence regarding the prediction accuracy. Furthermore, we also prove parameterized approximation results as a function of the prediction error, showing that our mechanisms perform well even when the predictions are not fully accurate. CCS Concepts: • Theory of computation → Algorithmic mechanism design.
Proceedings of the 13th ACM Conference on Electronic Commerce - EC '12, 2012
We study strategyproof (SP) mechanisms for the location of a facility on a discrete graph. We give a full characterization of SP mechanisms on lines and on sufficiently large cycles. Interestingly, the characterization deviates from the one given by Schummer and Vohra [2004] for the continuous case. In particular, it is shown that an SP mechanism on a cycle is close to dictatorial, but all agents can affect the outcome, in contrast to the continuous case. Our characterization is also used to derive a lower bound on the approximation ratio with respect to the social cost that can be achieved by an SP mechanism on certain graphs. Finally, we show how the representation of such graphs as subsets of the binary cube reveals common properties of SP mechanisms and enables one to extend the lower bound to related domains.
2009
We consider the problem of locating a facility on a network, represented by a graph. A set of strategic agents have different ideal locations for the facility; the cost of an agent is the distance between its ideal location and the facility. A mechanism maps the locations reported by the agents to the location of the facility. Specifically, we are interested in social choice mechanisms that do not utilize payments. We wish to design mechanisms that are strategyproof, in the sense that agents can never benefit by lying, or, even better, group strategyproof, in the sense that a coalition of agents cannot all benefit by lying. At the same time, our mechanisms must provide a small approximation ratio with respect to one of two optimization targets: the social cost or the maximum cost. We give an almost complete characterization of the feasible truthful approximation ratio under both target functions, deterministic and randomized mechanisms, and with respect to different network topologies. Our main results are: We show that a simple randomized mechanism is group strategyproof and gives a (2 − 2/n)-approximation for the social cost, where n is the number of agents, when the network is a circle (known as a ring in the case of computer networks); we design a novel "hybrid" strategyproof randomized mechanism that provides a tight approximation ratio of 3/2 for the maximum cost when the network is a circle; and we show that no randomized SP mechanism can provide an approximation ratio better than 2 − o(1) to the maximum cost even when the network is a tree, thereby matching a trivial upper bound of two.
Proceedings of the AAAI Conference on Artificial Intelligence
Facility location is the problem of locating a public facility based on the preferences of multiple agents. In the classic framework, where each agent holds a single location on a line and can misreport it, strategyproof mechanisms for choosing the location of the facility are well-understood.We revisit this problem in a more general framework. We assume that each agent may hold several locations on the line with different degrees of importance to the agent. We study mechanisms which elicit the locations of the agents and different levels of information about their importance. Further, in addition to the classic manipulation of misreporting locations, we introduce and study a new manipulation, whereby agents may hide some of their locations. We argue for its novelty in facility location and applicability in practice. Our results provide a complete picture of the power of strategyproof mechanisms eliciting different levels of information and with respect to each type of manipulation....
We study the problem of designing group-strategyproof cost-sharing mechanisms. The players report their bids for getting serviced and the mechanism decides a set of players that are going to be serviced and how much each one of them is going to pay. We determine three conditions: Fence Monotonicity, Stability of the allocation and Validity of the tie-breaking rule that are necessary and sufficient for group-strategyproofness, regardless of the cost function. Consequently, Fence Monotonicity characterizes group-strategyproof cost-sharing schemes closing an important open problem. Finally, we use our results to prove that there exist families of cost functions, where any groupstrategyproof mechanism has arbitrarily poor budget balance.
Proceedings of the 4th ACM conference on Electronic commerce - EC '03, 2003
Strategyproof cost-sharing mechanisms, lying in the core, that recover 1/a fraction of the cost, are presented for the set cover and facility location games: a=O(log n) for the former and 1:861 for the latter. Our mechanisms utilize approximation algorithms for these problems based on the method of dual-fitting. D
ECAI 2014
The study of facility location in the presence of selfinterested agents has recently emerged as the benchmark problem in the research on mechanism design without money. Here we study the related problem of heterogeneous 2-facility location, that features more realistic assumptions such as: (i) multiple heterogeneous facilities have to be located, (ii) agents' locations are common knowledge and (iii) agents bid for the set of facilities they are interested in. We study the approximation ratio of both deterministic and randomized truthful algorithms when the underlying network is a line. We devise an (n − 1)-approximate deterministic truthful mechanism and prove a constant approximation lower bound. Furthermore, we devise an optimal and truthful (in expectation) randomized algorithm.
Springer Proceedings in Mathematics & Statistics, 2014
In a facility game one or more facilities are placed in a metric space to serve a set of selfish agents whose addresses are their private information. In a classical facility game, each agent wants to be as close to a facility as possible, and the cost of an agent can be defined as the distance between her location and the closest facility. In an obnoxious facility game, each agent wants to be far away from all facilities, and her utility is the distance from her location to the facility set. The objective of each agent is to minimize her cost or maximize her utility. An agent may lie if, by doing so, more benefit can be obtained. We are interested in social choice mechanisms that do not utilize payments. The game designer aims at a mechanism that is strategy-proof, in the sense that any agent cannot benefit by misreporting her address, or, even better, group strategy-proof, in the sense that any coalition of agents cannot all benefit by lying. Meanwhile, it is desirable to have the mechanism to be approximately optimal with respect to a chosen objective function. Several models for such approximation mechanism design without money for facility games have been proposed. In this paper we briefly review these models and related results for both deterministic and randomized mechanisms, and meanwhile we present a general framework for approximation mechanism design without money for facility games.
Nord. J. Comput., 2003
In this paper we consider several different problems of placing an obnoxious facility on geometric networks. In particular, our main results show how to obtain efficient polynomial time algorithms for locating an obnoxious facility on the given network under various distance functions such as maximizing the total sum of distances or maximizing the smallest of the distances from the facility to the nodes of the network. Our algorithms are obtained by applying concepts and techniques from Computational Geometry such as range searching, constructing spanners and other optimization schemes.
2008
Abstract. Multiagent planning methods are concerned with planning by and for a group of agents. If the agents are selfinterested, they may be tempted to lie in order to obtain an outcome that is more rewarding for them. We therefore study the multiagent planning problem from a mechanism design perspective, showing how to incentivise agents to be truthful. We prove that the well-known truthful VCG mechanism is not always truthful in the context of optimal planning, and present a modification to fix this.
Abstract We consider the mechanism design problem for agents with single-peaked preferences over multi-dimensional domains when multiple alternatives can be chosen. Facility location and committee selection are classic embodiments of this problem. We propose a class of percentile mechanisms, a form of generalized median mechanisms, that are (group) strategy-proof, and derive worst-case approximation ratios for social cost and maximum load for L1 and L2 cost models.
Operations Research Letters, 2007
A noncooperative game theoretical approach is considered for the multifacility location problem. It turns out that the facility location game is a potential game in the sense of Monderer and Shapley and some properties of the game are studied.
Autonomous Agents and Multi-Agent Systems, 2012
We present a functional framework for automated mechanism design based on a twostage game model of strategic interaction between the designer and the mechanism participants, and apply it to several classes of two-player infinite games of incomplete information. At the core of our framework is a black-box optimization algorithm which guides the selection process of candidate mechanisms. Our approach yields optimal or nearly optimal mechanisms in several application domains using various objective functions. By comparing our results with known optimal mechanisms, and in some cases improving on the best known mechanisms, we provide evidence that ours is a promising approach to parametric design of indirect mechanisms.
Proc. of the Int. Conf. on Uncertainty in AI
We introduce the notion of fault tolerant mechanism design, which extends the standard game theoretic framework of mechanism design to allow for uncertainty about execution. Specifically, we define the problem of task allocation in which the private information of the agents is not only their costs to attempt the tasks, but also their probabilities of failure. For several different instances of this setting we present technical results, including positive ones in the form of mechanisms that are incentive compatible, individually rational and efficient, and negative ones in the form of impossibility theorems.
Theoretical Computer Science, 2006
We study a general class of non-cooperative games coming from combinatorial covering and facility location problems. A game for k players is based on an integer programming formulation. Each player wants to satisfy a subset of the constraints. Variables represent resources, which are available in costly integer units and must be bought. The cost can be shared arbitrarily between players. Once a unit is bought, it can be used by all players to satisfy their constraints. In general the cost of pure-strategy Nash equilibria in this game can be prohibitively high, as both prices of anarchy and stability are in Θ(k). In addition, deciding the existence of pure Nash equilibria is NP-hard. These results extend to recently studied single-source connection games. Under certain conditions, however, cheap Nash equilibria exist: if the integrality gap of the underlying integer program is 1 and in the case of single constraint players. In addition, we present algorithms that compute cheap approximate Nash equilibria in polynomial time.
SSRN Electronic Journal, 2018
We develop a tool akin to the revelation principle for mechanism design with limited commitment. We identify a canonical class of mechanisms rich enough to replicate the payoffs of any equilibrium in a mechanism-selection game between an uninformed designer and a privately informed agent. A cornerstone of our methodology is the idea that a mechanism should encode not only the rules that determine the allocation, but also the information the designer obtains from the interaction with the agent. Therefore, how much the designer learns, which is the key tension in design with limited commitment, becomes an explicit part of the design. We show how this insight can be used to transform the designer's problem into a constrained optimization one: To the usual truthtelling and participation constraints, one must add the designer's sequential rationality constraint.
2009
We consider a way to evaluate mechanisms without assuming mutual knowledge of rationality among the agents. More specifically, we assume that each agent can take any undominated strategy under a mechanism, and the mechanism is evaluated by its worst-case scenario. First, we provide some characteristics of a mechanism that implements a “strongly monotonic ” social choice correspondence in an environment with “single-crossing ” preferences. Second, we show that if the mechanism designer is interested in implementation of “individually rational outcome mappings ” in a “random valuation ” model, any mechanism that is not dominant-strategy incentive compatible (DSIC) is outperformed by a DSIC mechanism. Key words: mechanism design, implementation
Econometrica, 2005
The mechanism design literature assumes too much common knowledge of the environment among the players and planner. We relax this assumption by studying implementation on richer type spaces.
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