Abstract 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.
Many interesting results in algorithmic game theory applied to computer networks have been obtained in the last ten years. In @cite_30 two TCP clients are interpreted as players in the prisoner dilemma game. Another game-theoretical analysis of TCP is given in @cite_57 , focusing on the Vegas version of this protocol. In @cite_66 it is shown that the noncooperative games for flow control problems have Pareto-inefficient Nash equilibria.
@cite_30 @cite_57 @cite_66
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We use the tools from game theory to understand the impacts of the inherent congestion pricing schemes in TCP Vegas as well as the problems of parameter setting of TCP Vegas on its performance. It is shown how these inherent pricing schemes result in a rate control equilibrium state that is a Nash equilibrium which is also a global optimum of the all-Vegas networks. On the other hand, if the TCP Vegas’ users are assumed to be selfish in terms of setting their desired number of backlogged packets in the buffers along their paths, then the network as a whole, in certain circumstances, would operate very inefficiently. This poses a serious threat to the possible deployment of Vegas-based TCP (such as FAST TCP) in the future Internet. In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of this problem in which competitors, who may control a nonnegligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which the competing freight companies have market power. Other applications include intelligent transportation systems, competition among telecommunication network service providers, and scheduling with flexible machines. Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully efficient solution from the system's point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency that depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino, we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, Nash equilibria of atomic network games may be less efficient than the corresponding Wardrop equilibria. When competitors are completely symmetric, we provide a characterization of the Nash equilibrium using a potential function, and prove that this counterintuitive phenomenon does not arise. Finally, we study a pricing mechanism that elicits more coordination from the players by reducing the worst-case inefficiency of Nash equilibria. Bottleneck congestion games properly model the properties of many real-world network routing applications. They are known to possess strong equilibria—a strengthening of Nash equilibrium to resilience against coalitional deviations. In this paper, we study the computational complexity of pure Nash and strong equilibria in these games. We provide a generic centralized algorithm to compute strong equilibria, which has polynomial running time for many interesting classes of games such as, e.g., matroid or single-commodity bottleneck congestion games. In addition, we examine the more demanding goal to reach equilibria in polynomial time using natural improvement dynamics. Using unilateral improvement dynamics in matroid games pure Nash equilibria can be reached efficiently. In contrast, computing even a single coalitional improvement move in matroid and single-commodity games is strongly NP-hard. In addition, we establish a variety of hardness results and lower bounds regarding the duration of unilateral and coalitional improvement dynamics. They continue to hold even for convergence to approximate equilibria. Game theoretic models have found widespread use in the analysis and design of radio resource management algorithms for a wide variety of systems such as cellular, ad hoc and sensor networks. The fundamental principle behind such models and much of game theory has been the reliance on expected utility theory (EUT). In this paper, we consider a simple wireless random access game where instead of following the precepts of EUT, the players follow the precepts of Prospect Theory (PT), a theory developed by Kahneman and Tversky to explain real-life decision making that often deviates from the behavior expected under EUT. Specifically, we consider a game where selfish players adjust their transmission probabilities over a collision channel according to rewards received for successful transmission while incurring energy and delay costs. We compare and contrast the Nash equilibria achieved under both EUT and PT and highlight the differences in them.