A Course In Game Theory by Martin J. Osborne and Ariel Rubinstein -- MIT Press, 1997 (fourth printing)
This book is writtein for a graudate level theory course. It covers (mostly in terms of set theory) the economics of games. It begins with classical problems (BoS, Prisoner's Dillema) where multiple players are attempting to decide what actions to take.
It isn't really an AI theory, although it covers many topics that could be related to it (punishing players for not cooperating, and punishing punishers in retaliation). The actual functions involved could be implemented as probabalistic state machines over sets -- something that makes effective real-time multiple-player logic that has a believeable degree of randomness.
This would be a useful book for designing better players, and helping balance different types of characters so that you don't have to later 'nerf' an over-powerful type or boost a weak one. The book feels like a graudate level text, and needs a good bit of experience with set theory. The basic form of the theories are sets of the form < actions, players, preference relations 1, preference relations 2 > where actions is a set of all legal actions, players is the set of players, preferences are (fairly large) sets of "what would be desirable if I did x when player n does y. If you can't figure out how to turn that into a probabalistic state machine, then this book isn't for you.
Chapters:
1. Introduction
Section 1 Strategic Games
2. Nash Equilibrium
3. Mixed,
correlated, and Evolutionary Equilibrium
4. Rationalizability
and Iterated Elimination of Dominated Actions
5. Knowledge and
Equilibrium
Section 2 Extensive Games with Perfect
Information
6. Extensive games with Perfect Information
7. Bargaining Games
8. Repeated Games
9. Complexity
Considerations in Repeated Games
10. Implementation Theory
Section 3 Extensive Games with Imperfect Information
11. Extensive Games with Imperfect Information
12. Sequential
Equilibrium
Coalitional Games
13. The Core
14. Stable
Sets, the Bargaining Set, and the Shapley Value
15. The Nash
Solution
