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This chapter provides an introduction to the concepts and results in noncooperative game theory that will be used in the subsequent evolutionary analysis. The material in this chapter is organized as follows: In section 1.1 the structure of finite normal-form games is outlined. In particular, the geometry of strategy spaces and multilinearity of payoff functions is emphasized. Section 1.2 discusses dominance orderings of a player's strategy space and formalizes the notion of "best replies." Section 1.3 considers Nash equilibria as fixed points of the best-reply correspondence, and studies some properties of the set of Nash equilibria. Section 1.4 gives a brief account of some point- and setwise refinements of the Nash equilibrium concept. Section 1.5 introduces some special notation for, and properties of, symmetric two-player games; the basic setting in chapters 2 through 4. Many of the examples introduced in the chapter will be used later to illustrate evolutionary concepts. |
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