Article

# Repeated game theory as a framework for algorithm development in communication networks

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

## Abstract

This article presents a tutorial on how to use repeated game theory as a framework for algorithm development in communication networks. The article starts by introducing the basis of one-stage games and how the outcome of such games can be predicted, through iterative elimination and Nash equilibrium. In communication networks, however, not all problems can be modeled using one-stage games. Some problems can be better modeled through multi-stage games, as many problems in communication networks consist of several iterations or decisions that need to be made over time. Of all the multi-stage games, the infinite-horizon repeated games were chosen to be the focus in this tutorial, because optimal equilibrium settings can be achieved, contrarily to the suboptimal equilibria achieved in other types of game. With the theoretical concepts introduced, it is then shown how the developed game theoretical model, and devised equilibrium, can be used as a basis for the behavior of an algorithm, which is supposed to solve a particular problem and will be running at specific network devices. Copyright © 2015 John Wiley & Sons, Ltd.

## No full-text available

Article
Game theory has become a standard tool for depicting and demonstrating various game‐like phenomena by providing appropriate mathematical models and for analyzing and predicting agents' behaviors and their decisions by formalizing solution concepts. The conventional game model mainly concerns ideal systems that would always guarantee optimal responses, which appears unrealistic for practical game scenarios since decision‐making usually entails resource costs. Therefore, this study considers players' decision‐making in extensive games when the computational cost of searching the strategy space is limited. We start with a new mathematical model of extensive games that features a bound on computational resources during players' decision‐making process such that they can only foresee a part of the available alternatives in the future. This model is more appropriate in predicting players' strategies than the conventional model, under which we investigate the effects of computational costs on players' strategies as well as the computational complexity. Furthermore, a simulation experiment is performed to seek the connection between the amount of resources and the goodness of the outcomes. This study is expected to provide a foundation for players' rational decision‐making with computational costs.
Article
Full-text available
The growth of wireless communication toward fifth generation will lead to the existence of number of access technologies to provide seamless connectivity and form heterogeneous network environment. Earlier, there was single access technology to run applications, but 5G will have heterogeneous network environment and provide separate network for each application. As compared with 4G, 5G will provide increase in data rate, decrease in delay, increase in quality of service, and so on because of its various enabling technologies. Therefore, for each application, selection of best access network via its enabling technology is an important task. This selection is done either at user terminal side or at network operator side by combining preferences for network attributes and network parameters. In this paper, to enjoy 5G, selection is done in a heterogeneous networks environment for enabling technologies like device‐to‐device communication, spectrum sharing, enhancing quality of experience, energy efficiency, and so on. This selection is done via optimization techniques for a fixed duration video clip that is to be transmitted from a device running low in battery. The selection environment composed of UMTS, WLAN1, and WLAN2 as available networks. The simulation results show that the network selected for each enabling technology supports various features of 5G. Also, error analysis of selection results is done using confidence interval estimate at 90%, 92%, and 95% confidence level. From results obtained, it is seen that different optimization techniques used to access network for different enabling technologies (providing 5G features) prove to be useful for future 5G network.
Conference Paper
Full-text available
The currently growing demand for information and communication technologies (ICTs), and multimedia services, is generating a fast expansion of digital traffic. To fulfill such demands, new generation access architectures have been proposed that try to integrate and optimize available technologies. Besides allowing new services to emerge, such architectures also offer a great opportunity to develop new methods that try to increase energy efficiency by proper equipment management and sharing of resources. Here we focus on energy saving in Fibre-Wireless (FiWi) access networks, which provide high bandwidth and ubiquity to future multimedia services and applications. The goal is to exploit the path diversity of mesh FiWi networks to improve energy efficiency. A model based on network formation game theory is developed, creating ground for energy efficient routing algorithms. To obtain stable and efficient networks, the use of a new stability concept, which avoids unconnected nodes, is proposed and a dynamic network formation process is presented and applied to the model. Our results show that significant energy efficiency gains can be obtained. It is also shown that gateway placement can have a strong impact on energy efficiency.
Conference Paper
Full-text available
Book
Full-text available
Game theory is the mathematical study of interaction among independent, self-interested agents. The audience for game theory has grown dramatically in recent years, and now spans disciplines as diverse as political science, biology, psychology, economics, linguistics, sociology, and computer science, among others. What has been missing is a relatively short introduction to the field covering the common basis that anyone with a professional interest in game theory is likely to require. Such a text would minimize notation, ruthlessly focus on essentials, and yet not sacrifice rigor. This Synthesis Lecture aims to fill this gap by providing a concise and accessible introduction to the field. It covers the main classes of games, their representations, and the main concepts used to analyze them. Table of Contents: Games in Normal Form / Analyzing Games: From Optimality to Equilibrium / Further Solution Concepts for Normal-Form Games / Games with Sequential Actions: The Perfect-information Extensive Form / Generalizing the Extensive Form: Imperfect-Information Games / Repeated and Stochastic Games / Uncertainty about Payoffs: Bayesian Games / Coalitional Game Theory / History and References / Index
Article
Full-text available
This paper proposes a characterization of optimal strategies for playing certain repeated coordination games whose players have identical preferences. Players' optimal coordination strategies reflect their uncertainty about how their partners will respond to multiple-equilibrium problems; this uncertainty constrains the statistical relationships between their strategy choices players can bring about. The authors show that optimality is nevertheless consistent with subgame-perfect equilibrium. Examples are analyzed in which players use precedents as focal points to achieve and maintain coordination, and in which they play dominated strategies with positive probability in early stages in the hope of generating a useful precedent. Copyright 1990 by The Econometric Society.
Chapter
Work at the intersection of computer science and game theory is briefly surveyed, with a focus on the work in computer science. In particular, the following topics are considered: various roles of computational complexity in game theory, including modelling bounded rationality, its role in mechanism design, and the problem of computing Nash equilibria; the price of anarchy, that is, the cost of using decentralizing solution to a problem; and interactions between distributed computing and game theory.
Book
Article
Cooperative game theory can be applied to orthogonal frequency division multiple access (OFDMA) networks for fair resource allocation. In this work, we consider a comprehensive cross-layer framework including physical and medium access control layer requirements. We apply two cooperative games, nontransferable utility (NTU) game and transferable utility (TU) game, to provide fairness in OFDMA networks. In NTU game, fairness is achieved by defining appropriate objective function, whereas in TU game, fairness is provided by forming the appropriate network structure. For NTU game, we analyze the Nash bargaining solution as a solution of NTU game taking into account channel state information and queue state information. In a TU game, we show that coalition among subcarriers to jointly provide rate requirements leads to better performance in terms of power consumption. The subcarrier's payoff is determined according to the amount of payoff which that subcarrier brings to the coalition by its participation. We show that although NTU and TU games are modeled as rate adaptive and margin adaptive problems, respectively, both solutions provide a fair distribution of resources with minimum fairness index of 0.8. Copyright © 2012 John Wiley & Sons, Ltd.
Article
During the last decade, a plentiful number of active queue management schemes have been proposed, but their main objectives are simply allocating the buffer resource to all flows evenly, or protecting responsive flows from being degraded by unresponsive flows. However, the sending rates of the responsive flows can be determined diversely, and not all unresponsive flows have aggressively high sending rates. Furthermore, it is rational to reserve a portion of the buffer resource for certain privileged traffic. Grounded by these evidences, in this paper, we present a resilient active queue management algorithm, named Prior-Core-based Buffer Allocation considering diverse congestion control algorithms, fair-unresponsive flows, and some privileged traffic. Our approach is based on stochastic cooperative game theory, where the payoffs yielded by cooperation are described by random variables, and the core is defined only over the distribution of these random payoffs; the core in this situation is called the prior-core. As a result, it is shown that our buffer allocation, yielded by the prior-core, achieves completely fair allocation for those flows whose requirement does not exceed the fair-share regardless of the responsiveness, whereas aggressive flows are restricted according to availability of the buffer; all these are verified through ns-2 simulation experiments. Copyright © 2014 John Wiley & Sons, Ltd.
Article
Network selection mechanisms have a significant role in guaranteeing the QoS for users in a heterogeneous wireless networks environment. These mechanisms allow the selection of an optimal wireless network to satisfy the needs of users. Users are provided with the opportunity to select from multiple connectivity opportunities available all over various wireless networks. Furthermore, the network operators themselves can execute active selection strategies that facilitate proper decision making, in which user preferences are considered. This study proposes a new noncooperative competing game-theoretic model and strategy space based on user preference. This model can solve network selection problems and capture the inter-linkages of decisions taken by various networks. A generalized simple additive weighting method is incorporated into the framework of noncooperative game theory. In addition, the utility function is employed to assess the usefulness of the system. Simulation results and analysis illustrate the efficacy of the suggested model in attaining optimum network utility for heterogeneous wireless networks while optimizing user satisfaction.
Article
SUMMARY Femtocell technology has been drawing considerable attention as a cost-effective means of improving cellular coverage and capacity. However, under co-channel deployment, femtocell system in dense environment may incur high uplink interference to existing macrocells and experiences strong inter-cell interference at the same time. To manage the uplink interference to macrocell, as well as the inter-cell interference, this paper proposes a price-based uplink interference management scheme for dense femtocell systems. Specifically, on the one hand, to guarantee the macrocell users' quality of service, the macrocell base station prices the interference from femtocell users (FUEs) subject to a maximum tolerable interference power constraint. On the other hand, the inter-cell interference is also taken into consideration. Moreover, a Stackelberg game model is adopted to jointly study the utility maximization of the macrocell base station and FUEs. Then, in order to reduce the amount of information exchange, we design a distributed power allocation algorithm for FUEs. In addition, admission control is adopted to protect the active FUEs' performance. Numerical results show that the price-based interference management scheme is effective. Meanwhile, it is shown that the distributed power allocation combined with admission control is capable of robustly protecting the performance of all the active FUEs. Copyright © 2013 John Wiley & Sons, Ltd.
Article
Conflicts between animals of the same species usually are of limited war'' type, not causing serious injury. This is often explained as due to group or species selection for behaviour benefiting the species rather than individuals. Game theory and computer simulation analyses show, however, that a limited war'' strategy benefits individual animals as well as the species.
Article
Fibre-Wireless (FiWi) access networks have been proposed as flexible and cost-effective solutions for future access networks. At the wireless mesh section, wireless routers have to forward both local traffic from directly connected users and foreign traffic from neighbour wireless routers. How to allocate resources to local and foreign traffic at each router in a balanced way, while avoiding starvation of routers requiring less resources, is a fundamental issue that must be solved so that new services emerge. Here, we develop a repeated game framework for bandwidth allocation and propose an algorithm that allocates bandwidth in a fair manner. The algorithm is able to detect over claiming routers and avoid possible denial of service that these may cause to others. Moreover, unfruitful use of resource is prevented, avoiding the forwarding of packets that would be dropped at some point later in the path, and queueing delay conditions are kept similar among local and foreign traffic. These fair network conditions open way for QoS support since it is easier to ensure the operationality of services.
Book
"This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. This sixtieth anniversary edition includes not only the original text but also an introduction by Harold Kuhn, an afterword by Ariel Rubinstein, and reviews and articles on the book that appeared at the time of its original publication in the New York Times, tthe American Economic Review, and a variety of other publications. Together, these writings provide readers a matchless opportunity to more fully appreciate a work whose influence will yet resound for generations to come.
Book
Personalized and continuing relationships play a central role in any society. Economists have built upon the theories of repeated games and reputations to make important advances in understanding such relationships. Repeated Games and Reputations begins with a careful development of the fundamental concepts in these theories, including the notions of a repeated game, strategy, and equilibrium. Mailath and Samuelson then present the classic folk theorem and reputation results for games of perfect and imperfect public monitoring, with the benefit of the modern analytical tools of decomposability and self-generation. They also present more recent developments, including results beyond folk theorems and recent work in games of private monitoring and alternative approaches to reputations. Repeated Games and Reputations synthesizes and unifies the vast body of work in this area, bringing the reader to the research frontier. Detailed arguments and proofs are given throughout, interwoven with examples, discussions of how the theory is to be used in the study of relationships, and economic applications. The book will be useful to those doing basic research in the theory of repeated games and reputations as well as those using these tools in more applied research. Available in OSO: http://www.oxfordscholarship.com/oso/public/content/economicsfinance/0195300793/toc.html
Article
This paper reports the results of six experiments and analyses performed to explore the applicability of the non-constant-sum case of the theories of von Neumann-Morgenstern, and others, to the actual behavior of people playing games or involved in bargaining situations. The paper suggests directions in which the theory of games might be modified and extended to improve its applicability and usefulness. A "split-the-difference principle" is suggested to augment the usual theory, so as to specify the exact amount of payments to be made in an ordinary two-person bargaining situation such as the sale of a used car. The application of this principle seems satisfactory in the experiments. One experiment suggests that, in a sequence of trials in the same game situation, people tend to start near an equilibrium point and then try to find a better equilibrium, if there is one. The experiments show examples of non-optimal behavior of the bargainers when the judgment necessary to estimate the relevant payoff is obscure. A fair division of five parcels of objects among five players when each player attaches different values to the parcels is outlined and computed, and the effect of coalitions is discussed.
Conference Paper
We consider algorithmic problems in a distributed setting where the participants annot be assumed to follow the algorithm but rather their own self-interest. As such pxticipants, termed agents, are capable of manipulating the algorithm, the algorithm designer should ensure in advance that the agents’ interests are best served by behaving correctly. Following notions from the field of mechanism design, we suggest a framework for studying such algorithms. In this model the algorithmic solution is adorned with payments to the participants and is termed a mechanism. The payments should be carefully chosen a6 to motivate all participants to act as the algorithm designer wishes. We apply the standard tools of mechanism design to algorithmic problems and in particular to the shortest path problem. Our main technical contribution concerns the study of a representative problem, task scheduling, for which the standard tools do not suffice. We present several theorems regarding this problem including an approximation me&anism, lower bounds and a randomized mechanism. We also suggest and motivate extensions to the basic model and prove improved upper bounds in the extended model. Many open problems are suggested as well.
Article
The behavior of a given wireless station may affect the communication capabilities of a neighboring one, notably because the radio communication channel is usually shared in wireless networks. In this tutorial, we carefully explain how situations of this kind can be modelled by making use of game theory. By leveraging on four simple running examples, we introduce the most fundamental concepts of non-cooperative game theory. This approach should help students and scholars to quickly master this fascinating analytical tool without having to read the existing lengthy, economics-oriented books; it should also assist them in modelling the problems of their own.
Article
In self-organizing ad hoc networks, all the networking functions rely on the contribution of the participants. As a basic example, nodes have to forward packets for each other in order to enable multi-hop communication. In recent years, incentive mechanisms have been proposed to give nodes incentive to cooperate, especially in packet forwarding. However, the need for these mechanisms was not formally justified. In this paper, we address the problem of whether cooperation can exist without incentive mechanisms. We propose a model based on game theory and graph theory to investigate equilibrium conditions of packet forwarding strategies. We prove theorems about the equilibrium conditions for both cooperative and non-cooperative strategies. We perform simulations to estimate the probability that the conditions for a cooperative equilibrium hold in randomly generated network scenarios. As the problem is involved, we deliberately restrict ourselves to a static configuration. We conclude that in static ad hoc networks - where the relationships between the nodes are likely to be stable - cooperation needs to be encouraged. forwarding. However, the need for these mechanisms was not formally justified. In this paper, we address the problem of whether cooperation can exist \emph{without} incentive mechanisms. We propose a model based on game theory and graph theory to investigate equilibrium conditions of packet forwarding strategies. We prove theorems about the equilibrium conditions for both cooperative and non-cooperative strategies. We perform simulations to estimate the probability that the conditions for a cooperative equilibrium hold in randomly generated network scenarios. As the problem is involved, we deliberately restrict ourselves to a static configuration. We conclude that in static ad hoc networks -- where the relationships between the nodes are likely to be stable -- cooperation needs to be encouraged.
Article
Two long-lived players play a repeated coordination game. I show the restrictions on players' beliefs which imply that cooperation is optimal play. Journal of Economic Literature Classification Number: D83.
Article
Economists have lately been called upon not only to analyze markets, but to design them. Market design involves a responsibility for detail, a need to deal with all of a market's complications, not just its principle features. Designers therefore cannot work only with the simple conceptual models used for theoretical insights into the general working of markets. Instead, market design calls for an engineering approach. Drawing primarily on the design of the entry level labor market for American doctors (the National Resident Matching Program), and of the auctions of radio spectrum conducted by the Federal Communications Commission, this paper makes the case that experimental and computational economics are natural complements to game theory in the work of design. The paper also argues that some of the challenges facing both markets involve dealing with related kinds of complementarities, and that this suggests an agenda for future theoretical research. Copyright The Econometric Society 2002.
Article
Economists have lately been called upon not only to analyze markets, but to design them. Market design involves a responsibility for detail, a need to deal with all a market's complications, not just its principle features. Designers therefore cannot work only with the simple conceptual models used for theoretical insights into the general working of markets. Instead, market design calls for an engineering approach. Drawing primarily on the design of the entry level labor market for American doctors (the National Resident Matching Program), and on the design of the auctions of radio spectrum conducted by the Federal Communications Commission, this paper makes the case that experimental and computational economics are natural complements to game theory in the work of design. The paper also argues that some of the challenges facing both markets involve dealing with related kinds of complementarities, and that this suggests an agenda for future theoretical research. 1 This paper has a checkered history. Versions of it were delivered as the Leatherbee Lecture at the Harvard Business School on April 21, 1999, as the Fisher-Schultz Lecture at the European meeting of the Econometric Society in Santiago de Compostela, on August 31, 1999, and as the Pazner Lecture at the University of Tel Aviv, on February 29, 2000. I have also struggled with some of these issues in my Clarendon Lectures at Oxford in April 1998, in Roth and Sotomayor (1990), Roth (1991), Roth and Peranson (1999), Roth (2000), and in the market design sections of my webpage at http://www.economics.harvard.edu/~aroth/alroth.html, and in the class on market design I co-taught with Paul Milgrom at Harvard in the Spring of 2001. This paper has benefited from the many helpful comments I received on those earlier oc...
Article
We consider algorithmic problems in a distributed setting where the participants cannot be assumed to follow the algorithm but rather their own self-interest. As such participants, termed agents, are capable of manipulating the algorithm, the algorithm designer should ensure in advance that the agents' interests are best served by behaving correctly. Following notions from the field of mechanism design, we suggest a framework for studying such algorithms. In this model the algorithmic solution is adorned with payments to the participants and is termed a mechanism. The payments should be carefully chosen as to motivate all participants to act as the algorithm designer wishes. We apply the standard tools of mechanism design to algorithmic problems and in particular to the shortest path problem. Our main technical contribution concerns the study of a representative problem, task scheduling, for which the standard tools do not suffice. We present several theorems regarding this problem including an approximation mechanism, lower bounds and a randomized mechanism. We also suggest and motivate extensions to the basic model and prove improved upper bounds in the extended model. Many open problems are suggested as well. 1
Repeated Games,Center for Operations Research & Econometrics
• Mertens J
• Sorin S
• Zamir S
The New Palgrave Dictionary of Economics
• Halpern JY
Game Theory 101: The Complete Textbook
• William Spaniel
William Spaniel, Game Theory 101: The Complete Textbook, Sep. 2011.
• Oskar John Von Neumann
• Morgenstern
John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior, Princeton, NJ, Princeton University Press, 1944.
Nash equilibria of packet forwarding strategies in wireless ad hoc networks Essentials of Game Theory: A Concise, Multidisciplinary Introduction
• Márk Félegyházi
• Jean-Pierre Hubaux
• Levente Buttyán
Márk Félegyházi, Jean-Pierre Hubaux, Levente Buttyán, " Nash equilibria of packet forwarding strategies in wireless ad hoc networks, " IEEE Transactions on Mobile Computing, vol. 5, no. 5, pp. 463–476, Mar. 2006. [18] Kevin Leyton-Brown and Yoav Shoham, Essentials of Game Theory: A Concise, Multidisciplinary Introduction, 1st ed. Morgan and Claypool Publishers, Jun. 2008.
• John Von
• Oskar Morgenstern
John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior, Princeton, NJ, Princeton University Press, 1944.