Allen B. MacKenzie

Using game theory to analyze wireless ad hoc networks

The application of mathematical analysis to the study of wireless ad hoc networks has met with limited success due to the complexity of mobility and traffic models, the dynamic topology, and the unpredictability of link quality that characterize such networks. The ability to model individual, independent decision makers whose actions potentially affect all other decision makers renders game theory particularly attractive to analyze the performance of ad hoc networks. In this article we describe how various interactions in wireless ad hoc networks can be modeled as a game. This allows the analysis of existing protocols and resource management schemes, as well as the design of equilibrium-inducing mechanisms that provide incentives for individual users to behave in socially-constructive ways. We survey the recent literature on game theoretic analysis of ad hoc networks, highlighting its applicability to power control and waveform adaptation, medium access control, routing, and node participation, among others.

Cognitive networks: adaptation and learning to achieve end-to-end performance objectives

In this article we advance the idea of a cognitive network, capable of perceiving current network conditions and then planning, learning, and acting according to end-to-end goals. Cognitive networks are motivated by the complexity, heterogeneity, and reliability requirements of tomorrows networks, which are increasingly expected to self-organize to meet user and application objectives. We compare and contrast cognitive networks with related research on cognitive radios and cross-layer design. By defining cognitive networks, examining their relationship to other technologies, discussing critical design issues, and providing a framework for implementation, we aim to establish a foundation for further research and discussion

Game theory in communications: motivation, explanation, and application to power control

Game theory is a set of tools developed to model interactions between agents with conflicting interests, and is thus well-suited to address some problems in communications systems. We present some of the basic concepts of game theory and show why it is an appropriate tool for analyzing some communication problems and providing insights into how communication systems should be designed. We then provided a detailed example in which game theory is applied to the power control problem in a CDMA-like system.

Stability of multipacket slotted Aloha with selfish users and perfect information

Aloha is perhaps the simplest and most-studied medium access control protocol in existence. Only in the recent past, however, have researchers begun to study the performance of Aloha in the presence of selfish users. In this paper, we present a game-theoretic model of multipacket slotted Aloha with perfect information. We show that this model must have an equilibrium and we characterize this equilibrium. Using the tools of stochastic processes, we then establish the equilibrium stability region for some well-known channel models.

Selfish users in Aloha: a game-theoretic approach

Past studies of Aloha have emphasized system-wide goals such as achieving maximum throughput or minimum delay. We use game theory to analyze Aloha from the perspective of a selfish user. we construct an Aloha game and examine the optimal behavior of individual users. We show that the Aloha game has an equilibrium and that an Aloha system in which the users are selfish will be stable provided the attempt rate is sufficiently low. We then compare the performance of a selfish Aloha system with the performance of a centrally controlled slotted Aloha system. With some system parameters performance is near the optimum performance obtained by a centrally-controlled system. By utilizing a selfish-user assumption, it is possible to build systems which are robust and scalable.

Cooperative Game Theory for Distributed Spectrum Sharing

There is a need for new spectrum access protocols that are opportunistic, flexible and efficient, yet fair. Game theory provides a framework for analyzing spectrum access, a problem that involves complex distributed decisions by independent spectrum users. We develop a cooperative game theory model to analyze a scenario where nodes in a multi-hop wireless network need to agree on a fair allocation of spectrum. We show that in high interference environments, the utility space of the game is non-convex, which may make some optimal allocations unachievable with pure strategies. However, we show that as the number of channels available increases, the utility space becomes close to convex and thus optimal allocations become achievable with pure strategies. We propose the use of the Nash Bargaining Solution and show that it achieves a good compromise between fairness and efficiency, using a small number of channels. Finally, we propose a distributed algorithm for spectrum sharing and show that it achieves allocations reasonably close to the Nash Bargaining Solution.

Cognitive Radio and Networking Research at Virginia Tech

More than a dozen Wireless @ Virginia Tech faculty are working to address the broad research agenda of cognitive radio and cognitive networks. Our core research team spans the protocol stack from radio and reconfigurable hardware to communications theory to the networking layer. Our work includes new analysis methods and the development of new software architectures and applications, in addition to work on the core concepts and architectures underlying cognitive radios and cognitive networks. This paper describes these contributions and points towards critical future work that remains to fulfill the promise of cognitive radio. We briefly describe the history of work on cognitive radios and networks at Virginia Tech and then discuss our contributions to the core cognitive processing underlying these systems, focusing on our cognitive engine. We also describe developments that support the cognitive engine and advances in radio technology that provide the flexibility desired in a cognitive radio node. We consider securing and verifying cognitive systems and examine the challenges of expanding the cognitive paradigm up the protocol stack to optimize end-to-end network performance. Lastly, we consider the analysis of cognitive systems using game theory and the application of cognitive techniques to problems in dynamic spectrum sharing and control of multiple-input multiple-output radios.

Effect of Selfish Node Behavior on Efficient Topology Design

The problem of topology control is to assign per-node transmission power such that the resulting topology is energy efficient and satisfies certain global properties such as connectivity. The conventional approach to achieve these objectives is based on the fundamental assumption that nodes are socially responsible. We examine the following question: if nodes behave in a selfish manner, how does it impact the overall connectivity and energy consumption in the resulting topologies? We pose the above problem as a noncooperative game and use game-theoretic analysis to address it. We study Nash equilibrium properties of the topology control game and evaluate the efficiency of the induced topology when nodes employ a greedy best response algorithm. We show that even when the nodes have complete information about the network, the steady-state topologies are suboptimal. We propose a modified algorithm based on a better response dynamic and show that this algorithm is guaranteed to converge to energy-efficient and connected topologies. Moreover, the node transmit power levels are more evenly distributed, and the network performance is comparable to that obtained from centralized algorithms.

Asymptotic optimality for distributed spectrum sharing using bargaining solutions

Recent studies on spectrum usage reveal poor utilization, both spatially and temporally. Opportunistic use of licensed spectrum while limiting interference to primary users can enhance spectrum reuse and provide orders of magnitude improvement in available channel capacity. This calls for spectrum sharing protocols that are dynamic, flexible, and efficient, in addition to being fair to end users. We employ cooperative game theory to address the opportunistic spectrum access problem. Specifically, we develop a game-theoretic model to analyze a scenario in which nodes in a wireless network seek to agree on a fair and efficient allocation of spectrum. First, we show that in high interference environments, the utility space of the game is non-convex, making certain optimal allocations unachievable with pure strategies. To mitigate this, we show that as the number of channels available increases, the utility space approaches convexity, thereby making optimal allocations achievable with pure strategies. Second, by comparing and analyzing three bargaining solutions, we show that the Nash bargaining solution achieves the best tradeoff between fairness and efficiency, using a small number of channels. Finally, we develop a distributed algorithm for spectrum sharing that is general enough to accomodate non-zero disagreement points, and show that it achieves allocations reasonably close to the Nash bargaining solution.

A game theory perspective on interference avoidance

We show that the fixed power, synchronous interference avoidance (IA) scheme of (C. Rose et al, IEEE Trans. on Wireless Comm., vol.1, no.3, p. 415-427, 2002) employing the (greedy) eigen-iteration can be modeled as the recently developed potential game of (D. Monderer et al, Journal of Games and Economic Behavior, vol.14, no.0044, p.124-143, 1996). Motivated by the fact that receivers can make small mistakes, we consider the convergence of the eigen-iteration when noise is added in a manner similar to (P. Anigstein, IEEE Trans. On Inf. Theory vol.49, no.4, 2003). Further, we restrict ourselves to a class of signal environments that we call levelable environments. Applying game-theory, we obtain a convergence result similar to that of the Anigstein method, for levelable environments: arbitrarily small noise assures that the eigen-iteration almost surely converges to a neighborhood of the optimum signature set.