In a wireless application with multiple communication links, the data rate of eachudlink is subject to degradation due to transmitting interference from other links. Audcompetitive wireless game then arises as each link acts as a player maximizing itsudown data rate. The game outcome can be evaluated using the solution concept ofudgame equilibria. However, when significant interference among the links arises,uduniqueness of equilibrium is not guaranteed. To select among multiple equilibria,udthe sum of network rate or social welfare is used as the selection criterion. Thisudthesis aims to offer the theoretical foundation and the computational tool for determiningudapproximate correlated equilibria with global maximum expected socialudwelfare in polynomial games. Using sum of utilities as the global objective, weudgive two theoretical and two wireless-specific contributions.ud1. We give a problem formulation for computing near-exact ε -correlated equilibriaudwith highest possible expected social welfare. We then give a sequentialudSemidefinite Programming (SDP) algorithm that computes the solution.udThe solution consists of bounds information on the social welfare.ud2. We give a novel reformulation to arrive at a leaner problem for computingudnear-exact ε -correlated equilibria using Kantorovich polynomials with sparsity.ud3. Forgoing near-exactness, we consider approximate correlated equilibria. Toudaccount for the loss in precision, we introduce the notion of regret. We giveudtheoretical bounds on the regrets at any iteration of the sequential SDP algorithm.udMoreover, we give a heuristic procedure for extracting a discreteudprobability distribution. Subject to players’ acceptance of the regrets, theudcomputed distributions can be used to implement central arbitrators to facilitateudreal-life implementation of the correlated equilibrium concept.ud4. We demonstrate how to compute Pareto-optimal solutions by dropping theudcorrelated equilibria constraints. For demonstration purpose, we focus onlyudon Pareto-optima with equal weights among the players.
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