LP-based Covering Games with Low Price of Anarchy

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3]

Dominating Set Games

In this paper we study cooperative cost games arising from domination problems on graphs.We introduce three games to model the cost allocation problem and we derive a necessary and su cient condition for the balancedness of all three games.Furthermore we study concavity of these games.game theory;cost allocation;cooperative games

Stability and Fairness in Models with a Multiple Membership

This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are indivisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness in metric environments with indivisible projects, where we also explore the performance of well-known solutions, such as the Shapley value and the nucleolus.Stability, Fairness, Membership, Coalition Formation

Stability and fairness in models with a multiple membership

This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are in- divisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness on metric environments with indivisible projects. To do so, we explore, among other things, the performance of several well-known solutions (such as the Shapley value, the nucleolus, or the Dutta-Ray value) in these environments.stability, fairness, membership, coalition formation

Stability and Fairness in Models with a Multiple Membership

This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are indivisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness in metric environments with indivisible projects, where we also explore the performance of well-known solutions, such as the Shapley value and the nucleolus.Stability, Fairness, Membership, Coalition Formation

Algorithm Instance Games

This paper introduces algorithm instance games (AIGs) as a conceptual classification applying to games in which outcomes are resolved from joint strategies algorithmically. For such games, a fundamental question asks: How do the details of the algorithm's description influence agents' strategic behavior? We analyze two versions of an AIG based on the set-cover optimization problem. In these games, joint strategies correspond to instances of the set-cover problem, with each subset (of a given universe of elements) representing the strategy of a single agent. Outcomes are covers computed from the joint strategies by a set-cover algorithm. In one variant of this game, outcomes are computed by a deterministic greedy algorithm, and the other variant utilizes a non-deterministic form of the greedy algorithm. We characterize Nash equilibrium strategies for both versions of the game, finding that agents' strategies can vary considerably between the two settings. In particular, we find that the version of the game based on the deterministic algorithm only admits Nash equilibrium in which agents choose strategies (i.e., subsets) containing at most one element, with no two agents picking the same element. On the other hand, in the version of the game based on the non-deterministic algorithm, Nash equilibrium strategies can include agents with zero, one, or every element, and the same element can appear in the strategies of multiple agents.Comment: 14 page

On some cost allocation problems in communication networks

New technologies prompted an explosion in the development of communication networks. Modern network optimization techniques usually lead to a design of the most profitable, or the least cost network that will provide some service to customers. There are various costs and gains associated with building and using a communication network. Moreover, the involved multiple network users and/or owners possibly have conflicting objectives. However, they might cooperate in order to decrease their joint cost or increase their joint profit. Clearly, these individuals or organizations will support a globally \u27attractive\u27 solution(s) only if their expectations for a \u27fair share\u27 of the cost or profit are met. Consequently, providing network developers, users and owners with efficiently computable \u27fair\u27 cost allocation solution procedures is of great importance for strategic management. This work is an overview of some recent results (some already published as well as some new) in the development of cooperative game theory based mechanisms to efficiently compute \u27attractive\u27 cost allocation solutions for several important classes of communication networks

A Low-Complexity Approach to Distributed Cooperative Caching with Geographic Constraints

We consider caching in cellular networks in which each base station is equipped with a cache that can store a limited number of files. The popularity of the files is known and the goal is to place files in the caches such that the probability that a user at an arbitrary location in the plane will find the file that she requires in one of the covering caches is maximized. We develop distributed asynchronous algorithms for deciding which contents to store in which cache. Such cooperative algorithms require communication only between caches with overlapping coverage areas and can operate in asynchronous manner. The development of the algorithms is principally based on an observation that the problem can be viewed as a potential game. Our basic algorithm is derived from the best response dynamics. We demonstrate that the complexity of each best response step is independent of the number of files, linear in the cache capacity and linear in the maximum number of base stations that cover a certain area. Then, we show that the overall algorithm complexity for a discrete cache placement is polynomial in both network size and catalog size. In practical examples, the algorithm converges in just a few iterations. Also, in most cases of interest, the basic algorithm finds the best Nash equilibrium corresponding to the global optimum. We provide two extensions of our basic algorithm based on stochastic and deterministic simulated annealing which find the global optimum. Finally, we demonstrate the hit probability evolution on real and synthetic networks numerically and show that our distributed caching algorithm performs significantly better than storing the most popular content, probabilistic content placement policy and Multi-LRU caching policies.Comment: 24 pages, 9 figures, presented at SIGMETRICS'1