In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a very simple network leads to some interesting mathematics, results, and open problems.

We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times—the total latency—is minimized. In many settings, it may be expensive or impossible to regulate network traffic so as to implement an optimal assignment of routes. In the absence of regulation by some central authority, we assume that each network user routes its traffic on the minimum-latency path available to it, given the network congestion caused by the other users. In general such a “selfishly motivated ” assignment of traffic to paths will not minimize the total latency; hence, this lack of regulation carries the cost of decreased network performance. In this article, we quantify the degradation in network performance due to unregulated traffic. We prove that if the latency of each edge is a linear function of its congestion, then the total latency of the routes chosen by selfish network users is at most 4/3 times the minimum possible total latency (subject to the condition that all traffic must be routed). We also consider the more general setting in which edge latency functions are assumed only to be continuous and nondecreasing in the edge congestion. Here, the total

This paper deals with the weighted majority game, which is a familiar example of voting systems. In 1960s, U.S. Supreme Court handed down a series of "one person one vote" decisions. After that, calculations of power indices using real data were carried out and presented as evidence in the courtroom. For example, the courts in New York State have accepted the Banzhaf index (also called the Coleman value or Chow parameters) as an appropriate measure for weighted voting systems. The calculation normally requires the aid of a computer and so many counties in U.S. hire specialized consultants, mathematicians or computer scientists (see [13]). 1 In this paper, we discuss some algorithms for calculating power indices. In Section 2, we define weighted majority games and related concepts. Section 3 defines three power indices, the Shapley-Shubik power index, the Banzhaf index and the Deegan-Packel index. Section 4 shows complexity classes of the problems for calculating power indices

Communication networks shared by selfish users are considered and modeled as noncooperative repeated games. Each user is interested only in optimizing its own performance by controlling the routing of its load. We investigate the existence of a NEP that achieves the system-wide optimal cost. The existence of a NEP that not only achieves the system-wide optimal cost but also yields a cost for each user no greater than its stage game NEP cost is shown for two-node multiple link networks. It is shown that more general networks where all users have the same source-destination pair have a NEP that achieves the minimum total system cost under a mild technical condition. It is shown general networks with users having multiple source-destination pairs don't necessarily have such an NEP.

Communication networks shared by selfish users are considered and modeled as nonco- operative repeated games. Each user is interested only in optimizing its own performance by controlling the routing of its load. We investigate the existence of a Nash equilibrium point (NEP) that achieves the system-wide optimum cost. The existence of a subgame- perfect NEP that not only achieves the system-wide optimum cost but also yields a cost for each user no greater than its stage game NEP cost is shown for two-node multiple link networks. It is shown that more general networks where all users have the same source-destination pair have a subgame-perfect NEP that achieves the minimum total system cost, under a mild technical condition. It is shown that general networks with users having multiple source-destination pairs do not necessarily have such an NEP.

Abstract—In the deregulated power industry, a generation company (GenCo) sells energy and ancillary services primarily through auctions in a daily market. Developing effective strategies to optimize hourly offer curves for a hydrothermal power system to maximize profits has been one of the most challenging and important tasks for a GenCo. This paper presents an integrated bidding and scheduling algorithm with risk management under a deregulated market. A stochastic mixed-integer optimization formulation having a separable structure with respect to individual units is first established. A method combining Lagrangian relaxation and stochastic dynamic programming is then presented to select hourly offer curves for both energy and reserve markets. In view that pumped-storage units provide significant energy and reserve at generating and pumping, the offering strategies are specially highlighted in this paper. Numerical testing based on an 11-unit system with a major pumped-storage unit in the New England market shows that the algorithm is computationally efficient, and effective energy and reserve offer curves are obtained in 4–5 min on a 600-MHz Pentium III PC. The risk management method significantly reduces profit variances and, thus, bidding risks. Index Terms—Deregulation, offering/bidding strategies, pumped-storage unit, reserve market, risk management.

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Abstract — This paper presents a new approach to integrated security and dependability evaluation, which is based on stochastic modeling techniques. Our proposal aims to provide operational measures of the trustworthiness of a system, regardless if the underlying failure cause is intentional or not. By viewing system states as elements in a stochastic game, we can compute the probabilities of expected attacker behavior, and thereby be able to model attacks as transitions between system states. The proposed game model is based on a reward- and cost concept. A section of the paper is devoted to the demonstration of how the expected attacker behavior is affected by the parameters of the game. Our model opens up for use of traditional Markov analysis to make new types of probabilistic predictions for a system, such as its expected time to security failure. Index Terms — stochastic models, integrating security and dependability, security measures, game theory I.

In this paper we formulate the prevention of Denial of Service (DoS) attacks in wireless sensor networks as a repeated game between an intrusion detector and nodes of a sensor network, where some of these nodes act maliciously. We propose a protocol based on game theory which achieves the design objectives of truthfulness by recognizing the presence of nodes that agree to forward packets but fail to do so. This approach categorizes different nodes based upon their dynamically measured behavior. Through simulation we evaluate proposed protocol using packet throughput and the accuracy of misbehaving node detection.

Abstract—Relay cooperation has been recognized as an important mechanism to enhance connectivity and throughput in multi-hop wireless networks, especially under varying channel conditions. One major problem of relay cooperation is that relaying always incurs energy and possibly delay costs. To a rational and selfish node these costs are worth incurring only if it receives at least comparable returns in the long term. In light of this, we propose a new incentive mechanism called bandwidth exchange (BE) where a node can delegate a portion of its bandwidth to another node in exchange for relay cooperation. In this paper we specifically study BE in the simple form of exchanging orthogonal frequency bands to provide incentives for relaying in a wireless network. Other forms of exchanging bandwidth such as delegation of time-slots or using spreading codes of different lengths are also possible. Using a Nash Bargaining framework, we explore the advantage of BE in both static and fading channels. I.