In Chaps. 2–5 we have studied noncooperative games in which the players have finitely many (pure) strategies. The reason for the finiteness restriction is that in such games special results hold, like the existence of a value and optimal strategies for two-person zerosum games, and the existence of a Nash equilibrium in mixed strategies for finite nonzerosum games.
The basic game-theoretical concepts discussed in these chapters can be applied to much more general games. Once, in a game-theoretic situation, the players, their possible strategies, and the associated payoffs are identified, the concepts of best reply and of Nash equilibrium can be applied. Also the concepts of backward induction, subgame perfection, and perfect Bayesian equilibrium carry over to quite general extensive form games. In games of incomplete information, the concept of player types and the associated Nash equilibrium (Bayesian Nash equilibrium) can be applied also if the game has infinitely many strategies.
The bulk of this chapter consists of various, diverse examples verifying these claims. The main objective of the chapter is, indeed, to show how the basic game-theoretic apparatus can be applied to various different conflict situations; and, of course, to show these applications themselves.
In Sect. 6.1 we generalize some of the concepts of Chaps. 2–3. This section serves only as background and general framework for the examples in the following sections. Concepts specific to extensive form games and to incomplete information games are adapted later, when they are applied. In Sects. 6.2–6.7 we discuss, respectively, Cournot competition with complete and incomplete information, Bertrand competition, Stackelberg equilibrium, auctions with complete and incomplete information, mixed strategies with objective probabilities, and sequential bargaining. Variations on these topics and various other topics are treated in the problem section.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Noncooperative Games: Extensions. In: Game Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69291-1_6
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DOI: https://doi.org/10.1007/978-3-540-69291-1_6
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