Stackelberg Game Theoretic Framework in Cognitive Green Heterogeneous Networks

Introduction

Game theory is a branch of mathematics modeling, analyzing and designing the strategic interactions among autonomous decision makers. These players are usually assumed to be selfish and rational, which mean that they are always pursuing the utility maximization without considering the others’ strategy, utility the context. However, these actions have mutual, probably conflicting, consequences. Game theory has developed for decades to model problems in the field of economics, and it has recently been applied to wireless network problems, in most cases to solve the resource allocation problems in a competitive environment. Certainly, with its promising applications in particular for the decade, game theory including both strategic non-cooperative game and cooperative game is also used in access control, scheduling, network security, interference management and mitigation, even in the field of network information theory.

The reason that game theory is an appropriate choice for studying various problems in communications is multi-fold. First, nodes in the network are autonomous agents, making decisions only for their own interests. Game theory provides us sufficient theoretical tools to analyze the network users’ behaviors and actions. Second, game theory primarily deals with distributed optimization, which often requires local information only. Thus, it enables us to design distributed algorithms.

Games can be classified into two categories, strategic form game and extensive form game. The strategic form game is a one-shot game. In this game, the players make their decisions simultaneously without knowing what others will do. On the contrary, the extensive form game represents the structure of interactions between players and defines possible orders of moves. The repeat game is the most simple dynamic game as an example of the extensive form game, in which each stage is a repetition of the same strategic game. At the beginning of each stage, players observe the past history of strategies before making decisions. The number of stages may be finite or infinite. The utility of each player is the accumulated utility through all the stages. Therefore, players care not only the current utility but also the future utilities. The Stackelberg game is another extensive form game, which is used to model the competition between one player, called the leader, and a set of players, called the followers. In this game, the leader takes action first and then the followers take actions. The leader knows that the followers observe its action and take actions accordingly. The Nash equilibrium in the Stackelberg game is called Stackelberg equilibrium. Although non-cooperative game also has found extensive application in wireless networks, we concentrate on the survey of Stackelberg game theoretic applications in the recent promising wireless communication networks including cognitive radio networks, heterogeneous cellular networks, cooperative relay networks.