

algorithms which converge to stable allocations which minimize network interference.
Game theory provides the analysis tools needed to ensure your cognitive radio network behaves in a predictable, optimal manner instead of producing networked chaos. While game theory is a topic not encountered in traditional engineering curricula, we believe it is critical to successfully implementing cognitive radio as reflected in our long history developing the application of game theory to the design of cognitive radio networks. Researchers at CRT wrote the first paper which proposed the use of game theory to analyze cognitive radio networks, wrote the first paper which showed how game models can be used to predict convergence and stability properties of networks.
Our long academic involvement with game theory led to the creation of several short game theory tutorials which we can leverage to build a short course tailored to the needs of your organization. Topics covered by CRT in past game theory tutorials at DySPAN07 and the Wireless@VT Summer School include:
 Introduction to Game theory (basic game models, review of fundamental
mathematical concepts, relationship between game theory and cognitive radio networks)
 Equilibrium concepts (Nash, mixedstrategy equilibria, bargaining games,
Shapley values, Nash bargaining solutions)
 Equilibrium evaluation (Pareto efficiency, notions of fairness)
 The Notion of Time and Imperfections in Games and Networks (extensive
form games, repeated games, asynchronous repeated games, trembling hand models, noisy observations)
 Designing Cognitive Radio Networks to Yield Desired Behavior
(Punishment and Reward in Networks, Potential Games and Implicit Cooperation, supermodular games)
 Directions for future research and regulation
Recognizing that different companies have different backgrounds, we tailor each tutorial to the specific needs of each customer. For example, we adjusted the preceding topics to produce for L3CSW an expanded 2day tutorial with the following outline.
More information about the tutorials and engineering services offered by CRT is available on our Services page.







Unlike traditional radios, when cognitive radios are deployed in a network, the radios' conflicting goals lead to contention for networking resources. If not properly accounted for, this contention can lead to network instability, convergence to catastrophic resource allocations, or unpredictable behavior. However, as CRT has shown with its patents pending "zerooverhead" algorithms, this same distributed behavior can be managed to yield lowcomplexity




