CHAPTER 15 - Game theory and optimality of iterative methods

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This chapter discusses game theory and optimality of iterative methods. To estimate the effectiveness of iterative methods the criterion of optimum strategy from game theory is used. This chapter defines a game as a triple (Σ, Ω, K), where Σ, Ω are compact convex sets, and K = Κ(σ, ω) is a continuous function, defined on Σ × Ω (σ ∈ Σ, ω ∈ Ω), convex with respect to σ for fixed ω ∈ Ω, and concave with respect to ω for fixed σ ∈ Σ. It is assumed that Σ, Ω are strategy spaces for player I and player II, respectively. The chapter then states the main theorem of game theory. It also generalizes some results on the case of weighted distributed masses.