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In ad-hoc networks, the nodes are primarily decentralized in nature. The absence of a central controller because of the decentralization characteristic of these impromptu networks results in autonomous operations for each of the individual users. In such networks, the decisions taken by the users are based on perceived measures or statistics which are collected dynamically. Decision taken by one node affects and influences the other nodes. The scenario of such a network can be optimized using the principles of game theory. The final model of the scenario can be formulated as a non-cooperative game. Algorithms based on this model are devised for ad hoc networks. Applications of such algorithms include pricing schemes for distributed beamforming, bandwidth allocation as well as power control games. Asynchronous Distributed Pricing is a virtual pricing scheme for transmitting power optimization in ad hoc networks. In this algorithm, the difference between the value of a given performance metric and the price paid to attain it determines a user’s payoff and the network objective is to maximize the sum of all users’ payoff. However, the determination of the utility function essentially determines the global convergence of the sum of all users’ payoff. Supermodularity conditions are fundamental constraints for global convergence of utilities in a pricing game which have been previously defined. This paper obtains suitable utility functions satisfying the aforementioned constraints. This paper also demonstrates that performance characteristics of different utilities vary considerably under similar network parameters. This paper also assesses the optimality of utility functions under Signal-to-Interference-plus-Noise ratio as well as Signal-to-Interference ratio based calculations and also explores the difference in performance characteristics obtained by the addition of a significant value of noise variance in the Asynchronous Distributed Pricing algorithm.

Convergence Performance Of Sinr And Sir Utilities For A Distributed Resource Allocation Game