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).     

Extending the notion of rationality of selfish agents: Second Order Nash equilibria

Motivated by the increasing interest of the Computer Science community in the study and understanding of non-cooperative systems, we present a novel model for formalizing the rational behavior of agents with a more farsighted view of the consequences of their actions. This approach yields a framework creating new equilibria, which we call Second Order equilibria, starting from a ground set of traditional ones. By applying our approach to pure Nash equilibria, we define the set of Second Order pure Nash equilibria and present their applications to the Prisoner’s Dilemma game, to an instance of Braess’s Paradox in the Wardrop model and to the KP model with identical machines.     

A new model for selfish routing

In this work, we introduce and study a new, potentially rich model for selfish routing over non-cooperative networks, as an interesting hybridization of the two prevailing such models, namely the KPmodel [E. Koutsoupias, C.H. Papadimitriou, Worst-case equilibria, in: G. Meinel, S. Tison (Eds.), Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, in: Lecture Notes in Computer Science, vol. 1563, Springer-Verlag, 1999, pp. 404–413] and the Wmodel [J.G. Wardrop, Some theoretical aspects of road traffic research, Proceedings of the of the Institute of Civil Engineers 1 (Pt. II) (1952) 325–378].     

Existence and uniqueness of the Nash equilibrium in the non-cooperative QoS routing

Researchers dealing with game theoretic issues are well aware that the definition of a model capturing some physical behaviours such as the routing, the pricing, the flow and congestion control, the admission control just to mention some examples in the telecommunication field, is a difficult task, but it is only half of the overall effort. As a matter of fact, a key aspect is the analysis of the equilibrium (or equilibria) towards which the game will (hopefully) converge. The existence, the uniqueness, the efficiency and the structure of the equilibrium are some of the typical properties which are investigated. In this article, we propose a game theoretic model for quality of service (QoS) routing in networks implementing a Differentiated Service model for the QoS support. In particular, we focus on a parallel link network model and we consider a non-cooperative joint problem of QoS routing and dynamic capacity allocation. For this model, we demonstrate that the Nash equilibrium exists, so overcoming a typical problem in the existence proofs appeared in many papers in the area of routing game since 1990s, and we explicitly obtain a suitable set of relations characterising its structure. Moreover, we prove that Nash equilibrium uniqueness cannot be guaranteed in general.     

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.     

Pareto-optimal Nash equilibrium in capacity allocation game for self-managed networks

In this paper we introduce a capacity allocation game which models the problem of maximizing network utility from the perspective of distributed noncooperative agents. Motivated by the idea of self-managed networks, in the developed framework the decision-making entities are associated with individual transmission links, deciding on the way they split capacity among concurrent flows. An efficient decentralized algorithm is given for computing a strongly Pareto-optimal strategies, constituting a pure Nash equilibrium. Subsequently, we discuss the properties of the introduced game related to the Price of Anarchy and Price of Stability. The paper is concluded with an experimental study.     

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.     

A topology Nash game for tumoral antiangiogenesis

Tumoral angiogenesis plays a critical role in the process of growth of cancerous tumors. We consider activators and inhibitors of angiogenesis as players of a Nash game. From the activator’s point of view, the medium formed by existing blood vessels, surrounding tissue, and the tumor outer surface is seen as a porous medium. In contrast, the inhibitor sees the same medium as an elastic structural environment. We then define a competition between activator and inhibitor distributions. The aim of the activator is to minimize the pressure drop, while the inhibitor’s aim is to minimize the elastic compliance of the surrounding host tissue or, in a duel version, minimize the drainage of the tumoral neovascularization. Numerical results illustrate how (theoretical) tumors develop multiple channels as an optimal response to the optimal distribution of inhibitors.     

On the complexity of constrained Nash equilibria in graphical games

A widely accepted rational behavior for non-cooperative players is based on the notion of Nash equilibrium. Although the existence of a Nash equilibrium is guaranteed in the mixed framework (i.e., when players select their actions in a randomized manner) in many real-world applications the existence of “any” equilibrium is not enough. Rather, it is often desirable to single out equilibria satisfying some additional requirements (in order, for instance, to guarantee a minimum payoff to certain players), which we call constrained Nash equilibria.In this paper, a formal framework for specifying these kinds of requirement is introduced and investigated in the context of graphical games, where a player p may directly be interested in some of the other players only, called the neighbors of p. This setting is very useful for modeling large population games, where typically each player does not directly depend on all the players, and representing her utility function extensively is either inconvenient or infeasible.Based on this framework, the complexity of deciding the existence and of computing constrained equilibria is then investigated, in the light of evidencing how the intrinsic difficulty of these tasks is affected by the requirements prescribed at the equilibrium and by the structure of players’ interactions. The analysis is carried out for the setting of mixed strategies as well as for the setting of pure strategies, i.e., when players are forced to deterministically choose the action to perform. In particular, for this latter case, restrictions on players’ interactions and on constraints are identified, that make the computation of Nash equilibria an easy problem, for which polynomial and highly-parallelizable algorithms are presented.     

广义Nash平衡点和切换控制在对策论中的应用

通过把平衡点和决策者的动机耦合的方法,提出了广义纳什平衡点这一新概念.决策者的动机通常有两类：一是最大化自己的利益,另一则是最大化对手的利益.如果每一个决策者的动机都是第一类,一个理性的群体就会形成,整个系统最终会达到第一类平衡点（也就是经典的纳什平衡点）.如果每一个决策者的动机都是第二类,一个有智慧的群体就会形成,整个系统最终会达到第二类平衡点.同时,切换控制被用来帮助决策者确定他们的动机.     

基于排斥技术的QPSO算法在纳什均衡中的应用

基于量子行为的粒子群优化算法(QPSO)是一种随机的全局优化搜索新方法。文章系统地介绍了PSO算法、QPSO算法和“repulsion”技术。在对QPSO算法和基于“repulsion”技术的PSO算法分析的基础上,提出了基于“repulsion”技术的QPSO算法。将该算法用于求解混合纳什均衡。实验表明,新算法在解的收敛性和稳定性等方面优于QPSO算法。     

Energy-efficient power allocation for selfish cooperative communication networks using bargaining game

In commercial networks,user nodes operating on batteries are assumed to be selfish to consume their energy solely to maximize their own benefits,e.g.,data rates.In this paper,we propose a bargaining game to perform the power allocation for the selfish cooperative communication networks.In our system,two partner nodes can act as a source as well as a relay for each other,and each node is with an energy constraint to transmit one frame.Consider a selfish node is willing to seek cooperative transmission only if the data rate achieved through cooperation will not lower than that achieved through noncooperation by using the same amount of energy.The energy-efficient power allocation problem can be modeled as a cooperative game.We proved that there exists a unique Nash bargaining solution (NBS) for the game by verifying that the game is indeed a bargaining problem.Thus,the two objectives,i.e.,system efficiency and user fairness specified in the selfish networks can be achieved.Simulation results show that the NBS scheme is efficient in that the performance loss of the NBS scheme to that of the maximal overall rate scheme is small while the maximal-rate scheme is unfair.The simulation results also show that the NBS result is fair in that both nodes could experience better performance than they work independently and the degree of cooperation of a node only depends on how much contribution its partner can make to improve its own performance.     

AODV路由协议的安全性改进

针对Ad Hoc网络易遭受黑洞攻击而造成大量丢包现象的安全问题,提出了一种基于非合作博弈理论的安全路由方法。以Ad Hoc网络节点和恶意节点为对象建立双人博弈模型,理论分析证明该模型存在纳什均衡点,即对博弈的双方均存在优势策略。Ad Hoc网络根据自己的优势策略选择路由进行防御和网络传输,恶意节点根据自己的优势策略采取网络攻击行为。分析和仿真结果表明,新方法能有效地选择比较安全的路由,从而减少了恶意节点对Ad Hoc网络进行黑洞攻击造成的影响,降低了路由开销和网络丢包率。     

Bargaining game theoretic power control in selfish cooperative relay networks

Wireless cooperative communications require appropriate power allocation (PA) between the source and relay nodes. In selfish cooperative communication networks, two partner user nodes could help relaying information for each other, but each user node has the incentive to consume his power solely to decrease its own symbol error rate (SER) at the receiver. In this paper, we propose a fair and efficient PA scheme for the decode-and-forward cooperation protocol in selfish cooperative relay networks. We formulate this PA problem as a two-user cooperative bargaining game, and use Nash bargaining solution (NBS) to achieve a win-win strategy for both partner users. Simulation results indicate that the NBS is fair in that the degree of cooperation of a user only depends on how much contribution its partner can make to decrease its SER at the receiver, and efficient in the sense that the SER performance of both users could be improved through the game.     

Analysis of a simple capacity game

We study a two‐player two‐fare‐class static single‐period capacity allocation game with complete information. Nonnested (partitioned) booking limit policies are investigated in both noncooperative and cooperative situations. We show the existence of unique Nash equilibrium in the noncooperative situation. In the cooperative game, we analyze the cost saving of the two players and investigate the concavity of the objective function. For both noncooperative and cooperative settings, we assume the demands to be a truncated normal distribution and provide a comprehensive sensitivity analysis to discover the effects of unit revenue, rejection cost, and transfer rate on the equilibrium solution. Our numerical experiments show that the nonnested model can be a good approximation to the nested booking limit model. For the cooperative setting, we identify conditions that give rise to improvements in the total system revenue. Finally, under each game‐theoretic setting, we present the managerial implications of our solutions along with numerical examples.     

On the structure and complexity of worst-case equilibria

In the resource allocation game introduced by Koutsoupias and Papadimitriou, n$n$ jobs of different weights are assigned to m$m$ identical machines by selfish agents. For this game, it has been conjectured by several authors that the fully mixed Nash equilibrium (FMNE) is the worst possible w.r.t. the expected maximum load over all machines. Assuming the validity of this conjecture, computing a worst-case Nash equilibrium for a given instance was trivial, and approximating the Price of Anarchy for this instance would be possible by approximating the expected social cost of the FMNE by applying a known FPRAS.