Network Connection Games with Disconnected Equilibria (original) (raw)

Network creation games: structure vs anarchy

2017

We study Nash equilibria and the price of anarchy in the classical model of Network Creation Games introduced by Fabrikant et al. In this model every agent (node) buys links at a prefixed price a > 0 in order to get connected to the network formed by all the n agents. In this setting, the reformulated tree conjecture states that for a > n, every Nash equilibrium network is a tree. Since it was shown that the price of anarchy for trees is constant, if the tree conjecture were true, then the price of anarchy would be constant for a > n. Moreover, Demaine et al. conjectured that the price of anarchy for this model is constant. Up to now the last conjecture has been proven in (i) the lower range, for a = O(n1-o?) with o? = 1 and (ii) in the upper range, for a > 65n. In ?log n contrast, the best upper bound known for the price of anarchy for the remaining range is 2O(vlog n). In this paper we give new insights into the structure of the Nash equilibria for different ranges of ...

On a network creation game

Proceedings of the twenty-second annual symposium on Principles of distributed computing - PODC '03, 2003

We introduce a novel game that models the creation of Internet-like networks by selfish node-agents without central design or coordination. Nodes pay for the links that they establish, and benefit from short paths to all destinations. We study the Nash equilibria of this game, and prove results suggesting that the "price of anarchy" [4] in this context (the relative cost of the lack of coordination) may be modest. Several interesting extensions are suggested.

New Insights into the Structure of Equilibria for the Network Creation Game

ArXiv, 2020

We study the sum classic network creation game introduced by Fabrikant et al. in which n players conform a network buying links at individual price α. When studying this model we are mostly interested in Nash equilibria (ne) and the Price of Anarchy (PoA). It is conjectured that the PoA is constant for any α. Up until now, it has been proved constant PoA for the range α = O(n1−δ1) with δ1 > 0 a positive constant, upper bounding by a constant the diameter of any ne graph jointly with the fact that the diameter of any ne graph plus one unit is an upper bound for the PoA of the same graph. Also, it has been proved constant PoA for the range α > n(1 + δ2) with δ2 > 0 a positive constant, studying extensively the average degree of any biconnected component from equilibria. Our contribution consists in proving that ne graphs satisfy very restrictive topological properties generalising some properties proved in the literature and providing new insights that might help settling the...

Selfish Network Creation with Non-uniform Edge Cost

ArXiv, 2017

Network creation games investigate complex networks from a game-theoretic point of view. Based on the original model by Fabrikant et al. [PODC'03] many variants have been introduced. However, almost all versions have the drawback that edges are treated uniformly, i.e. every edge has the same cost and that this common parameter heavily influences the outcomes and the analysis of these games. We propose and analyze simple and natural parameter-free network creation games with non-uniform edge cost. Our models are inspired by social networks where the cost of forming a link is proportional to the popularity of the targeted node. Besides results on the complexity of computing a best response and on various properties of the sequential versions, we show that the most general version of our model has constant Price of Anarchy. To the best of our knowledge, this is the first proof of a constant Price of Anarchy for any network creation game.

Calculating the Price of Anarchy for Network Formation Games

Arxiv preprint arXiv:1108.4115, 2011

We model the formation of networks as the result of a game where by players act selfishly to get the portfolio of links they desire most. The integration of player strategies into the network formation model is appropriate for organizational networks because in these smaller networks, dynamics are not random, but the result of intentional actions carried through by players maximizing their own objectives. This model is a better framework for the analysis of influences upon a network because it integrates the strategies of the players involved. We present an Integer Program that calculates the price of anarchy of this game by finding the worst stable graph and the best coordinated graph for this game. We simulate the formation of the network and calculated the simulated price of anarchy, which we find tends to be rather low.

The Calculation and Simulation of the Price of Anarchy for Network Formation Games

2011

We model the formation of networks as the result of a game where by players act selfishly to get the portfolio of links they desire most. The integration of player strategies into the network formation model is appropriate for organizational networks because in these smaller networks, dynamics are not random, but the result of intentional actions carried through by players maximizing their own objectives. This model is a better framework for the analysis of influences upon a network because it integrates the strategies of the players ...

On a Bounded Budget Network Creation Game

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).

Near-optimal network design with selfish agents

Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, 2003

We introduce a simple network design game that models how independent selfish agents can build or maintain a large network. In our game every agent has a specific connectivity requirement, i.e. each agent has a set of terminals and wants to build a network in which his terminals are connected. Possible edges in the network have costs and each agent's goal is to pay as little as possible. Determining whether or not a Nash equilibrium exists in this game is NP-complete. However, when the goal of each player is to connect a terminal to a common source, we prove that there is a Nash equilibrium as cheap as the optimal network, and give a polynomial time algorithm to find a (1 + ε)-approximate Nash equilibrium that does not cost much more. For the general connection game we prove that there is a 3-approximate Nash equilibrium that is as cheap as the optimal network, and give an algorithm to find a (4.65 + ε)-approximate Nash equilibrium that does not cost much more.

The Ineciency of Equilibria in a Network Creation Game with Packet Forwarding

sina.sharif.edu

We study a novel variation of network creation games in which the players (vertices) form a graph by building undirected edges to each other with the goal of reducing their costs of using the network. The model we introduce assumes that a minimal set of nodes with high reachability from others are handed the responsibility of routing the traffic alongside the network. For this purpose, we suggest that a minimum dominating set (MDS) of the graph would be a reasonable choice as the intermediate nodes, thus the players in one such set would incur an extra cost for forwarding. We study the Nash equilibrium in this model assuming an extra cost of β is evenly shared among all the nodes in a MDS. We prove upper bounds on the price of anarchy, the worst-case ratio of the social cost of Nash equilibria of the network to that of socially optimum solution, for different values of β. Specifically, we show this inefficiency is modest for β = n since the price of anarchy is O(n 1/3 ). We also prove a tight upper bound of Θ(n) for β = n 2 , and also give some upper bounds when β takes a value between n and n 2 . 1+ 3 , where d is the diameter of G S , and β = n 1+ .