Potential games and competitive scheduling in wireless networks

[摘要] (cont.) We use the theory of potential games to establish convergence of such mechanisms to an equilibrium. To this end, we study conditions under which the scheduling game is a potential game. This necessitates extending the known necessary conditions for the existence of ordinal potential in games. In this thesis, we show that the scheduling game has a twice continuously differentiable ordinal potential if and only if a rate alignment condition holds. In our third contribution, we investigate the related question of characterizing the ;;distance;; of an arbitrary game to an exact potential game. We provide a new framework based on combinatorial Hodge theory for projecting an arbitrary game to the set of exact potential games. We prove that the equilibria of a game are equilibria of its projection, where E is bounded by the projection error. Moreover, we show that the projection of a game to the set of exact potential games can be calculated using distributed consensus algorithms.

[发布机构] Massachusetts Institute of Technology