Abstract
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.
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