Games in Extensive and Strategic Forms

Sergiu Hart

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This chapter serves as an introduction to some of the basic concepts that are used (mainly) in Part I ("Non-Cooperative") of this Handbook. It contains, first, formal definitions as well as a few illustrative examples, for the following notions: games in extensive form (Section 1), games in strategic form (Section 3), pure and mixed strategies (Sections 2 and 4, respectively), and equilibrium points (Section 5). Second, two classes of games that are of interest are presented: games of perfect information, which always possess equilibria in pure strategies (Section 6), and games with perfect recall, where mixed strategies may be replaced by behavior strategies (Section 7).

There is no attempt to cover the topics comprehensively. On the contrary, the purpose of this chapter is only to introduce the above basic concepts and results in as simple a form as possible. In particular, we deal throughout only with finite games. The reader is referred to the other chapters in this Handbook for applications, extensions, variations, and so on.