Strategyproof approximation mechanisms for location on networks

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

Decision Making in Manufacturing and Services, 2012

This paper is concerned with a competitive or voting location problem on networks under a proportional choice rule that has previously been introduced by Bauer et al. (1993). We refine a discretization result of the authors by proving convexity and concavity properties of related expected payoff functions. Furthermore, we answer the long time open question whether 1-suboptimal points are always vertices by providing a counterexample on a tree network.

2011

There has been recent interest in showing that real networks, designed via optimization [7], may possess topological properties similar to those investigated by the Network Science community [2], [17], [6], [1]. This suggests that the Network Science community's view that topological properties such as scale-freeness are not the result of some immutable physical laws, but in fact intentional optimization.

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.

2010

Linial, London and Rabinovich [16] and Aumann and Rabani [3] proved that the min-cut max-flow ratio for general maximum concurrent flow problems (when there are k commodities) is O(log k). Here we attempt to derive a more general theory of Steiner cut and flow problems, and we prove bounds that are poly-logarithmic in k for a much broader class of multicommodity flow and cut problems. Our structural results are motivated by the meta question: Suppose we are given a poly(log n) approximation algorithm for a flow or cut problem-when can we give a poly(log k) approximation algorithm for a generalization of this problem to a Steiner cut or flow problem? Thus we require that these approximation guarantees be independent of the size of the graph, and only depend on the number of commodities (or the number of terminal nodes in a Steiner cut problem). For many natural applications (when k = n o(1)) this yields much stronger guarantees. We construct vertex-sparsifiers that approximately preserve the value of all terminal min-cuts. We prove such sparsifiers exist through zero-sum games and metric geometry, and we construct such sparsifiers through oblivious routing guarantees. These results let us reduce a broad class of multicommodity-type problems to a uniform case (on k nodes) at the cost of a loss of a poly(log k) in the approximation guarantee. We then give poly(log k) approximation algorithms for a number of problems for which such results were previously unknown, such as requirement cut, lmulticut, oblivious 0-extension, and natural Steiner generalizations of oblivious routing, min-cut linear arrangement and minimum linear arrangement.

Eprint Arxiv Cs 0701071, 2007

Motivated by applications in peer-to-peer and overlay networks we define and study the \emph{Bounded Degree Network Formation} (BDNF) game. In an $(n,k)$-BDNF game, we are given $n$ nodes, a bound $k$ on the out-degree of each node, and a weight $w_{vu}$ for each ordered pair $(v,u)$ representing the traffic rate from node $v$ to node $u$. Each node $v$ uses up to $k$ directed links to connect to other nodes with an objective to minimize its average distance, using weights $w_{vu}$, to all other destinations. We study the existence of pure Nash equilibria for $(n,k)$-BDNF games. We show that if the weights are arbitrary, then a pure Nash wiring may not exist. Furthermore, it is NP-hard to determine whether a pure Nash wiring exists for a given $(n,k)$-BDNF instance. A major focus of this paper is on uniform $(n,k)$-BDNF games, in which all weights are 1. We describe how to construct a pure Nash equilibrium wiring given any $n$ and $k$, and establish that in all pure Nash wirings the cost of individual nodes cannot differ by more than a factor of nearly 2, whereas the diameter cannot exceed $O(\sqrt{n \log_k n})$. We also analyze best-response walks on the configuration space defined by the uniform game, and show that starting from any initial configuration, strong connectivity is reached within $\Theta(n^2)$ rounds. Convergence to a pure Nash equilibrium, however, is not guaranteed. We present simulation results that suggest that loop-free best-response walks always exist, but may not be polynomially bounded. We also study a special family of \emph{regular} wirings, the class of Abelian Cayley graphs, in which all nodes imitate the same wiring pattern, and show that if $n$ is sufficiently large no such regular wiring can be a pure Nash equilibrium.

2019

Game theory is a powerful approach to analyze settings which result from selfish behavior. This research aims to investigate models from different game theory areas: Network Creation Games, Schellings Segregation and Strategic Facility Location. I propose extensions of the classical simple models with more realistic assumptions and to analyze these models with respect to the existence of stable states, the Price of Anarchy and convergence dynamics.

There has been recent interest in showing that real networks, designed via optimization, may possess topological properties similar to those investigated by the Network Science community. This suggests that the Network Science community's view that topological properties such as scale-freeness are not the result of some immutable physical laws, but in fact intentional optimization. Recently, it was shown that stable graphs with an arbitrary degree sequence may result from a stability point of a collaborative game. In this paper, we present an integer program (IP) whose solutions yield graphs with a degree sequence, that is closest to a given degree sequence in the Manhattan metric. Stable graphs to the graph formation game and solutions to the IP in this paper, may be non-unique. We relate graphical solutions of the given IP to stable collaboration networks via the price of anarchy which we can calculate exactly as the result of another integer program.

Proceedings of the 2016 ACM Conference on Economics and Computation - EC '16, 2016

We study mechanisms for candidate selection that seek to minimize the social cost, where voters and candidates are associated with points in some underlying metric space. The social cost of a candidate is the sum of its distances to each voter. Some of our work assumes that these points can be modeled on a real line, but other results of ours are more general. A question closely related to candidate selection is that of minimizing the sum of distances for facility location. The difference is that in our setting there is a fixed set of candidates, whereas the large body of work on facility location seems to consider every point in the metric space to be a possible candidate. This gives rise to three types of mechanisms which differ in the granularity of their input space (voting, ranking and location mechanisms). We study the relationships between these three classes of mechanisms. While it may seem that Black's 1948 median algorithm is optimal for candidate selection on the line, this is not the case. We give matching upper and lower bounds for a variety of settings. In particular, when candidates and voters are on the line, our universally truthful spike mechanism gives a [tight] approximation of two. When assessing candidate selection mechanisms, we seek several desirable properties: (a) efficiency (minimizing the social cost) (b) truthfulness (dominant strategy incentive compatibility) and (c) simplicity (a smaller input space). We quantify the effect that truthfulness and simplicity impose on the efficiency.

2011

We consider a network creation game in which each player (vertex) has a fixed budget to establish links to other players. In our model, each link has unit price and each agent tries to minimize its cost, which is either its local diameter or its total distance to other players in the (undirected) underlying graph of the created network. Two versions of the game are studied: in the MAX * A preliminary version of this paper appeared in version, the cost incurred to a vertex is the maximum distance between the vertex and other vertices, and in the SUM version, the cost incurred to a vertex is the sum of distances between the vertex and other vertices. We prove that in both versions pure Nash equilibria exist, but the problem of finding the best response of a vertex is NP-hard. We take the social cost of the created network to be its diameter, and next we study the maximum possible diameter of an equilibrium graph with n vertices in various cases. When the sum of players' budgets is n − 1, the equilibrium graphs are always trees, and we prove that their maximum diameter is Θ(n) and Θ(log n) in MAX and SUM versions, respectively. When each vertex has unit budget (i.e. can establish link to just one vertex), the diameter of any equilibrium graph in either version is Θ(1).

Proceedings of the 26th ACM symposium on Parallelism in algorithms and architectures - SPAA '14, 2014

Network creation games have been extensively studied, both from economists and computer scientists, due to their versatility in modeling individual-based community formation processes, which in turn are the theoretical counterpart of several economics, social, and computational applications on the Internet. In their several variants, these games model the tension of a player between her two antagonistic goals: to be as close as possible to the other players, and to activate a cheapest possible set of links. However, the generally adopted assumption is that players have a common and complete information about the ongoing network, which is quite unrealistic in practice. In this paper, we consider a more compelling scenario in which players have only limited information about the network they are embedded in. More precisely, we explore the game-theoretic and computational implications of assuming that players have a complete knowledge of the network structure only up to a given radius k, which is one of the most qualified local-knowledge models used in distributed computing. To this respect, we define a suitable equilibrium concept, and we provide a comprehensive set of upper and lower bounds to the price of anarchy for the entire range of values of k, and for the two classic variants of the game, namely those in which a player's cost-besides the activation cost of the owned links-depends on the maximum/sum of all the distances to the other nodes in the network, respectively. These bounds are finally assessed through an extensive set of experiments.

2004

We study mechanisms that can be modelled as coalitional games with transferable utilities, and apply ideas from mechanism design and game theory to problems arising in a network design setting. We establish an equivalence between the game-theoretic notion of agents being substitutes and the notion of frugality of a mechanism. We characterize the core of the network design game and relate it to outcomes in a sealed bid auction with VCG payments. We show that in a game, agents are substitutes if and only if the core of the forms a complete lattice. We look at two representative games-Minimum Spanning Tree and Shortest Path-in this light.

Handbook of Applied Algorithms, 2008

Most of the existing and foreseen complex networks, such as the Internet, are operated and built by thousands of large and small entities (autonomous agents), which collaborate to process and deliver end-to-end flows originating from and terminating at any of them. The distributed nature of the Internet implies a lack of coordination among its users. Instead, each user attempts to obtain maximum performance according to his own parameters and objectives.

2005

We discuss some new algorithmic and complexity issues in coalitional and dynamic/evolutionary games, related to the understanding of modern selfish and Complex networks. In particular: (a) We examine the achievement of equilibria via natural distributed and greedy approaches in networks. (b) We present a model of a coalitional game in order to capture the anarchy cost and complexity of constructing equilibria in such situations. (c) We propose a stochastic approach to some kinds of local interactions in networks, that can be viewed also as extensions of the classical evolutionary game theoretic setting.

arXiv (Cornell University), 2022

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.