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where gi (p) = h i k N h k pk h i2 pi . Further evaluation leads to the result that this price function has an EPF if h j p j = h i pi . Note that this is only satis ed when the received powers are identical, which will generally not be true. Thus the cost function does not have an EPF and the nonlinear group priced game is not an OPG. Also note that Equation (16.23) cannot be guaranteed to be a supermodular game either as properly chosen power vectors p and p* will yield different signs for the second partial derivative of the cost functions.
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Therefore neither the better response dynamic nor the best response dynamic will assuredly converge, and a more complex convergence dynamic is required. As the repeated game dynamic is guaranteed for convergence, it can still be used. Thus this modi cation of the pricing function signi cantly complicated the network. Additional examples of game theory applications in resource allocation modeling can be found in References [116 127] and routing in [79 115].
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16.7 BIOLOGICALLY INSPIRED NETWORKS Current Internet protocols were never planned for the emerging pervasive environments where the amount of information will be enormous. The communications requirements placed by these protocols on the low cost sensor and tag nodes are in direct contradiction to the fundamental goals of these nodes, being small, inexpensive and maintenance-free. Biological systems provide insights into principles which can be adopted to completely rede ne the basic concepts of control, structure, interaction and function of the emerging pervasive environments. The study of the rules of genetics and evolution combined with mobility leads to the de nition of service-oriented communication systems which are autonomous and autonomously self-adaptive. Based on References [128 131] in this section we discuss how this paradigm shift, which views a network only as a randomly selforganizing by-product of a collection of self-optimizing services, may become the enabler of the new world of omnipresent low cost pervasive environments of the future.
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16.7.1 Bio-analogies In Carreras et al. [131] the depicted scenario services are associated with living organisms. Service is de ned by chromosomes. In this way service evolves and adapts to the environment constantly and autonomously. By analogy with living organisms, chromosomes are collections of genes that are the smallest service (related) data unit and inborn intelligence/instincts and thus represent all the information needed for the organism to function and service to be executed. Like in nature, this concept de nes a complete life-cycle of the organisms and therefore of services. The life cycle starts from the birth of an organism, goes through the reproduction and ends with the death. Reproduction and evolution occur, applying evolution rules inherited from nature. Fitness is measuring the correspondence of the organism s genetic information with the environment and determines the exchange of information (genetic information). Therefore no-end-to-end communication concept exists in these systems. Information is only exchanged as needed, locally, between mating organisms. Environment is determining the natural selection based on the tness of the organisms, with the environment leading to the best services possible as a function of the environment. In this concept the service is the organism. A scenario is envisioned where users will be more and more interested in a service able to provide reliable localized information. The role of the service will be, for instance, to provide answers to questions like How is the weather around the train station or Where will I nd a free parking space around there Services will be hosted on users devices and will go around through the physical movement
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