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Title: Computation of approximate welfare-maximizing correlated equilibria and pareto-optima with applications to wireless communication
Author: Kong, Fook Wai
ISNI:       0000 0004 2732 040X
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2012
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In a wireless application with multiple communication links, the data rate of each link is subject to degradation due to transmitting interference from other links. A competitive wireless game then arises as each link acts as a player maximizing its own data rate. The game outcome can be evaluated using the solution concept of game equilibria. However, when significant interference among the links arises, uniqueness of equilibrium is not guaranteed. To select among multiple equilibria, the sum of network rate or social welfare is used as the selection criterion. This thesis aims to offer the theoretical foundation and the computational tool for determining approximate correlated equilibria with global maximum expected social welfare in polynomial games. Using sum of utilities as the global objective, we give two theoretical and two wireless-specific contributions. 1. We give a problem formulation for computing near-exact ε -correlated equilibria with highest possible expected social welfare. We then give a sequential Semidefinite Programming (SDP) algorithm that computes the solution. The solution consists of bounds information on the social welfare. 2. We give a novel reformulation to arrive at a leaner problem for computing near-exact ε -correlated equilibria using Kantorovich polynomials with sparsity. 3. Forgoing near-exactness, we consider approximate correlated equilibria. To account for the loss in precision, we introduce the notion of regret. We give theoretical bounds on the regrets at any iteration of the sequential SDP algorithm. Moreover, we give a heuristic procedure for extracting a discrete probability distribution. Subject to players’ acceptance of the regrets, the computed distributions can be used to implement central arbitrators to facilitate real-life implementation of the correlated equilibrium concept. 4. We demonstrate how to compute Pareto-optimal solutions by dropping the correlated equilibria constraints. For demonstration purpose, we focus only on Pareto-optima with equal weights among the players.
Supervisor: Rustem, Berc Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral