When designing these etiquettes, we need to balance the benefit of the individual radio against the needs of the network. This balancing act is complicated by the interactive decision processes that arise when a cognitive radio reacts to the adaptations of other cognitive radios in the system. The interactive behavior is problematic, since infinite adaptation loops can be spawned that, while seemingly beneficial to a single device, are detrimental to the network. It would be wise to understand these interactive decision processes before the deployment of cognitive radios becomes widespread.

Using game theory-a set of mathematical tools and models for analyzing interactive decision processes-researchers and designers can analyze an etiquette to predict its impact on the device and the system. Aided by this analysis, the cognitive-radio designer seeks to create etiquettes that are efficient, fair, stable and predictable for all radios in the locality.

An illustration of a game model of a cognitive-radio network is shown above. While a more realistic example would include more radios and more waveforms, this example can be used to explain the basic concepts associated with the application of game theory to the analysis of cognitive-radio networks.

In this example, two radios (players) can choose among three different waveforms (actions) and are guided in their choice of waveforms by decision rules, perhaps specified as part of a cognition cycle. The choice of waveforms by each radio, which in game theory parlance specifies a point in the action space, produces a network state (a point in the outcome space) from which the radios make some relevant observations. In this case, estimated SINR (g ,1,g 2 )is presumably measured at the receiving end of each radio's link.

Based on the values (utilities) assigned to these observations (u1, u2) and, perhaps, on past observations and expectations about the other radio's behavior, the radios then proceed with their decision-making process for the next iteration in the recursive process.

Of particular interest to a game theorist is identifying which waveform combinations result in a fixed point in the recursion-that is, a point at which no radio would choose to change its waveform. In game theory terminology, this fixed point is called a Nash equilibrium. Other issues that a game theorist would be interested in examining include determining the desirability of these fixed points, convergence criteria for reaching them and the stability of these fixed points.

More information on cognitive radio and its analysis using game theory can be found at www.mprg.org/gametheory.

James (Jody) Neel (janeel@vt.edu), a PhD student at Virginia Polytechnic Institute and State University

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