Abstract
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, such as the existence of a value and optimal strategies for two-person zero-sum games, and the existence of a Nash equilibrium in mixed strategies for finite nonzero-sum games.
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Notes
- 1.
This is generally so in a Bayesian, incomplete information game: maximizing the expected payoff of a player over all his types is equivalent to maximizing the payoff per type.
- 2.
If prices are in smallest monetary units this somewhat artificial consequence is avoided. See Problem 6.7.
- 3.
In mathematical notation the strategy set of player 2 is the set [0, ∞)[0, ∞).
- 4.
Also here the assumption is that the players know the game. This means, in particular, that the players know each other’s valuations.
- 5.
The difference is that, for instance, single types may not play a best reply in a Nash equilibrium since they have probability zero and therefore do not influence the expected payoffs.
- 6.
For example, Walker and Wooders (2001).
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Peters, H. (2015). Noncooperative Games: Extensions. In: Game Theory. Springer Texts in Business and Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46950-7_6
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