Atomic routing games on maximum congestion

We study atomic routing games on networks in which players choose a path with the objective of minimizing the maximum congestion along the edges of their path. The social cost is the global maximum congestion over all edges in the network. We show that the price of stability is 1. The price of anarchy  , PoA$PoA$, is determined by topological properties of the network. In particular, PoA=O(?+logn)$PoA=O(?+logn)$, where ?$?$ is the length of the longest path in the player strategy sets, and n$n$ is the size of the network. Further, κ−1≤PoA≤c(κ²+log²n)$\kappa -1\le PoA\le c({\kappa }^2+{log}^{2}n)$, where κ$\kappa$ is the length of the longest cycle in the network, and c$c$ is a constant.     

When ignorance helps: Graphical multicast cost sharing games

In non-cooperative games played on highly decentralized networks the assumption that each player knows the strategy adopted by any other player may be too optimistic or even infeasible. In such situations, the set of players of which each player knows the chosen strategy can be modeled by means of a social knowledge graph in which nodes represent players and there is an edge from i to j if i knows j. Following the framework introduced in [7], we study the impact of social knowledge graphs on the fundamental multicast cost sharing game in which all the players want to receive the same communication from a given source in an undirected network. In the classical complete information case, such a game is known to be highly inefficient, since its price of anarchy can be as high as the total number of players ρ. We first show that, under our incomplete information setting, pure Nash equilibria always exist only if the social knowledge graph is directed acyclic (DAG). We then prove that the price of stability of any DAG is at least and provide a DAG lowering the classical price of anarchy to a value between and log²ρ. If specific instances of the game are concerned, that is if the social knowledge graph can be selected as a function of the instance, we show that the price of stability is at least , and that the same bound holds also for the price of anarchy of any social knowledge graph (not only DAGs). Moreover, we provide a nearly matching upper bound by proving that, for any fixed instance, there always exists a DAG yielding a price of anarchy less than 4. Our results open a new window on how the performances of non-cooperative systems may benefit from the lack of total knowledge among players.     

Bounded Budget Connection (BBC) games or how to make friends and influence people,on a budget

Motivated by applications in social and peer-to-peer networks, we introduce the Bounded Budget Connection (BBC) game and study its pure Nash equilibria. We have a collection of n   players, each with a budget for purchasing links. Each link has a cost and a length. Each node has a preference weight for each node, and its objective is to purchase outgoing links within its budget to minimize its sum of preference-weighted distances to the nodes. We show that determining if a BBC game has pure Nash equilibria is NP-hard. We study (n,k)$(n,k)$-uniform BBC games, where all link costs, lengths, and preferences are equal and every budget equals k  . We show that pure Nash equilibria exist for all (n,k)$(n,k)$-uniform BBC games and all equilibria are essentially fair. We construct a family of equilibria spanning the spectrum from minimum to maximum social cost. We also analyze best-response walks and alternative node objectives.     

基于非合作动态博弈的网络安全主动防御技术研究

目前基于博弈的网络安全主动防御技术大多采用静态博弈方式.针对这种静态方式无法应对攻击者攻击意图和攻击策略动态变化的不足,基于非合作、非零和动态博弈理论提出了完全信息动态博弈主动防御模型.通过"虚拟节点"将网络攻防图转化为攻防博弈树,并给出了分别适应于完全信息和非完全信息两种场景的攻防博弈算法.理论分析和实验表明相关算法...     

Selfish bin covering

In this paper, we address the selfish bin covering problem, which is greatly related both to the bin covering problem, and to the weighted majority game. What we are mainly concerned with is how much the lack of central coordination harms social welfare. Besides the standard PoA and PoS, which are based on Nash equilibrium, we also take into account the strong Nash equilibrium, and several new equilibrium concepts. For each equilibrium concept, the corresponding PoA and PoS are given, and the problems of computing an arbitrary equilibrium, as well as approximating the best one, are also considered.     

Exact and approximate equilibria for optimal group network formation

We consider a process called the Group Network Formation Game, which represents the scenario when strategic agents are building a network together. In our game, agents can have extremely varied connectivity requirements, and attempt to satisfy those requirements by purchasing links in the network. We show a variety of results about equilibrium properties in such games, including the fact that the price of stability is 1 when all nodes in the network are owned by players, and that doubling the number of players creates an equilibrium as good as the optimum centralized solution. For the general case, we show the existence of a 2-approximate Nash equilibrium that is as good as the centralized optimum solution, as well as how to compute good approximate equilibria in polynomial time. Our results essentially imply that for a variety of connectivity requirements, giving agents more freedom can paradoxically result in more efficient outcomes.     

Bounded budget betweenness centrality game for strategic network formations

In computer networks and social networks, the betweenness centrality of a node measures the amount of information passing through the node when all pairs are conducting shortest path exchanges. In this paper, we introduce a strategic network formation game in which nodes build connections subject to a budget constraint in order to maximize their betweenness in the network. To reflect real world scenarios where short paths are more important in information exchange in the network, we generalize the betweenness definition to only count shortest paths with a length limit ? in betweenness calculation. We refer to this game as the bounded budget betweenness centrality game and denote it as ?- B³C game, where ? is the path length constraint parameter.We present both complexity and constructive existence results about Nash equilibria of the game. For the nonuniform version of the game where node budgets, link costs, and pairwise communication weights may vary, we show that Nash equilibria may not exist and it is NP-hard to decide whether Nash equilibria exist in a game instance. For the uniform version of the game where link costs and pairwise communication weights are one and each node can build k links, we construct two families of Nash equilibria based on shift graphs, and study the properties of Nash equilibria. Moreover, we study the complexity of computing best responses and show that the task is polynomial for uniform 2- B³C games and NP-hard for other games (i.e. uniform ?- B³C games with ?≥3 and nonuniform ?- B³C games with ?≥2).     

A network pricing game for selfish traffic

The success of the Internet is remarkable in light of the decentralized manner in which it is designed and operated. Unlike small scale networks, the Internet is built and controlled by a large number of disparate service providers who are not interested in any global optimization. Instead, providers simply seek to maximize their own profit by charging users for access to their service. Users themselves also behave selfishly, optimizing over price and quality of service. Game theory provides a natural framework for the study of such a situation. However, recent work in this area tends to focus on either the service providers or the network users, but not both. This paper introduces a new model for exploring the interaction of these two elements, in which network managers compete for users via prices and the quality of service provided. We study the extent to which competition between service providers hurts the overall social utility of the system. A preliminary version of this paper appeared in the proceedings of 24th annual ACM SIGACT-SIGOPS symposium on principles of distributed computing, July 17–20, 2005, Las Vegas, Nevada, USA. The work of Ara Hayrapetyan was supported in part by NSF ITR grant CCR-0325453. The work of éva Tardos was supported in part by NSF grant CCR-0311333, ITR grant CCR-0325453, and ONR grant N00014-98-1-0589. The work of Tom Wexler was supported in part by NSF ITR grant CCR-0325453.     

Edge Pricing of Multicommodity Networks for Selfish Users with Elastic Demands

We examine how to induce selfish heterogeneous users in a multicommodity network to reach an equilibrium that minimizes the social cost. In the absence of centralized coordination, we use the classical method of imposing appropriate taxes (tolls) on the edges of the network. We significantly generalize previous work (Yang and Huang in Transp. Res. Part B 38:1–15, [2004]; Karakostas and Kolliopoulos in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 268–276, [2004]; Fleischer et al. in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 277–285, [2004]) by allowing user demands to be elastic. In this setting the demand of a user is not fixed a priori but it is a function of the routing cost experienced, a most natural assumption in traffic and data networks. Research supported by MITACS and a NSERC Discovery grant.     

Network Design with Weighted Players

We consider a model of game-theoretic network design initially studied by Anshelevich et al. (Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS), pp. 295–304, 2004), where selfish players select paths in a network to minimize their cost, which is prescribed by Shapley cost shares. If all players are identical, the cost share incurred by a player for an edge in its path is the fixed cost of the edge divided by the number of players using it. In this special case, Anshelevich et al. (Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS), pp. 295–304, 2004) proved that pure-strategy Nash equilibria always exist and that the price of stability—the ratio between the cost of the best Nash equilibrium and that of an optimal solution—is Θ(log k), where k is the number of players. Little was known about the existence of equilibria or the price of stability in the general weighted version of the game. Here, each player i has a weight w _i ≥1, and its cost share of an edge in its path equals w _i times the edge cost, divided by the total weight of the players using the edge. This paper presents the first general results on weighted Shapley network design games. First, we give a simple example with no pure-strategy Nash equilibrium. This motivates considering the price of stability with respect to α-approximate Nash equilibria—outcomes from which no player can decrease its cost by more than an α multiplicative factor. Our first positive result is that O(log w _max)-approximate Nash equilibria exist in all weighted Shapley network design games, where w _max is the maximum player weight. More generally, we establish the following trade-off between the two objectives of good stability and low cost: for every α=Ω(log w _max), the price of stability with respect to O(α)-approximate Nash equilibria is O((log W)/α), where W is the sum of the players’ weights. In particular, there is always an O(log W)-approximate Nash equilibrium with cost within a constant factor of optimal. Finally, we show that this trade-off curve is nearly optimal: we construct a family of networks without o(log w _max/ log log w _max)-approximate Nash equilibria, and show that for all α=Ω(log w _max/log log w _max), achieving a price of stability of O(log W/α) requires relaxing equilibrium constraints by an Ω(α) factor. Research of H.-L. Chen supported in part by NSF Award 0323766. Research of T. Roughgarden supported in part by ONR grant N00014-04-1-0725, DARPA grant W911NF-04-9-0001, and an NSF CAREER Award.     

Coordination mechanisms for selfish scheduling

In machine scheduling, a set of jobs must be scheduled on a set of machines so as to minimize some global objective function, such as the makespan, which we consider in this paper. In practice, jobs are often controlled by independent, selfishly acting agents, which each select a machine for processing that minimizes the (expected) completion time. This scenario can be formalized as a game in which the players are job owners, the strategies are machines, and a player’s disutility is the completion time of its jobs in the corresponding schedule. The equilibria of these games may result in larger-than-optimal overall makespan. The price of anarchy is the ratio of the worst-case equilibrium makespan to the optimal makespan. In this paper, we design and analyze scheduling policies, or coordination mechanisms, for machines which aim to minimize the price of anarchy of the corresponding game. We study coordination mechanisms for four classes of multiprocessor machine scheduling problems and derive upper and lower bounds on the price of anarchy of these mechanisms. For several of the proposed mechanisms, we also prove that the system converges to a pure-strategy Nash equilibrium in a linear number of rounds. Finally, we note that our results are applicable to several practical problems arising in communication networks.     

Efficiency of Atomic Splittable Selfish Routing with Polynomial Cost Functions

Previous works on the inefficiency of selfish routing have focused on the Wardropian traffic equilibria with an infinite number of infinitesimal players, each controlling a negligible fraction of the overall traffic, but only very limited pseudo-approximation results have been obtained for the atomic selfish routing game with a finite number of players. In this note we examine the price of anarchy of selfish routing with atomic Cournot–Nash players, each controlling a strictly positive splittable amount of flow. We obtain an upper bound of the inefficiency of equilibria with polynomial cost functions, and show that the bound is 1 or there is no efficiency loss when there is only one player, and the bound reduces to the result established in the literature when there are an infinite number of infinitesimal players.     

Approximations for a Bottleneck Steiner Tree Problem

Abstract. In the design of wireless communication networks, due to a budget limit, suppose we could put totally n+k stations in the plane. However, n of them must be located at given points. Of course, one would like to have the distance between stations as small as possible. The problem is how to choose locations for other k stations to minimize the longest distance between stations. This problem is NP-hard. We show that if NP neq P , no polynomial-time approximation for the problem in the rectilinear plane has a performance ratio less than 2 and no polynomial-time approximation for the problem in the Euclidean plane has a performance ratio less than sqrt 2 and that there exists a polynomial-time approximation with performance ratio 2 for the problem in both the rectilinear plane and the Euclidean plane.     

G-Tree:基于引力指向技术减少拐弯的Steiner树算法

提出一种基于引力指向技术、以减少拐弯数为目标的最小直角Steiner树构造算法G-Tree.利用一个节点受到其他节点的引力来决定它的移动方向,并采用引力加权以考虑减少拐弯数,生成Steiner树后对拐弯数进行了进一步优化.减少拐弯数有助于在布线阶段减少可能的通孔,从而增强电路的可靠性和可制造性.实验结果表明,G-Tree算法在减少布线树的拐弯数方面有明显的效果.     

Cost Sharing Mechanisms for Fair Pricing of Resource Usage

We propose a simple and intuitive cost mechanism which assigns costs for the competitive usage of m resources by n selfish agents. Each agent has an individual demand; demands are drawn according to some probability distribution. The cost paid by an agent for a resource it chooses is the total demand put on the resource divided by the number of agents who chose that same resource. So, resources charge costs in an equitable, fair way, while each resource makes no profit out of the agents. We call our model the Fair Pricing model. Its fair cost mechanism induces a non-cooperative game among the agents. To evaluate the Nash equilibria of this game, we introduce the Diffuse Price of Anarchy, as an extension of the Price of Anarchy that takes into account the probability distribution on the demands. We prove:

基于Q学习的DDoS攻防博弈模型研究

新形势下的DDoS攻防博弈过程和以往不同,因此利用现有的方法无法有效地评估量化攻防双方的收益以及动态调整博弈策略以实现收益最大化。针对这一问题,设计了一种基于Q学习的DDoS攻防博弈模型,并在此基础上提出了模型算法。首先,通过网络熵评估量化方法计算攻防双方收益;其次,利用矩阵博弈研究单个DDoS攻击阶段的攻防博弈过程;最后,将Q学习引入博弈过程,提出了模型算法,用以根据学习效果动态调整攻防策略从而实现收益最大化。实验结果表明,采用模型算法的防御方能够获得更高的收益,从而证明了算法的可用性和有效性。     

Individually-optimal equilibria of noncooperative games in preference relations

For a game specified on a set of situations by preference relations of players, the individual optimum principle is considered that is a generalization of Nash, Berge, and Pareto optimum principles. On this basis, different types of equilibria and stability of game problems are characterized and investigated. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 171–179, January–February 2009.     

安全协议的博弈论机制

在博弈论框架下,基于纳什均衡设计安全协议的计算和通信规则.首先,提出安全协议的扩展式博弈模型,结合通用可组合安全的思想给出安全通信协议博弈参与者集合、信息集、可行策略、行动序列、参与者函数、效用函数等定义;在该模型下的安全协议能安全并发执行.其次,根据博弈的纳什均衡给出安全通信协议的形式化定义.最后,基于该机制给出一个安全协议实例,并分析该安全协议博弈机制的有效性.