Mathematical Foundations for Signal Processing, Communications, and Networking

Chapter 19  Game Theory

Erik G. Larsson^‡ and Eduard Jorswieck^♯

^‡Linköping University, Sweden

^♯Technical University of Dresden, Germany

19.1    Introduction

Game theory is about optimization with multiple, conflicting objective functions. In conventional optimization, there is a single objective function that usually has a well-defined maximum or minimum. Finding this optimum point is then a matter of applying an appropriate numerical method. In game theory, the notion of optimality is not defined in terms of the maximum or minimum of a single cost function. Rather, the typical objective is to maximize two (or more) functions jointly, where the functions are coupled in such a way that increasing one of them necessarily means that the other must ...