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
