Author(s): Wayne F.Bialas
Year: 2001
Language: English
Pages: 115
Classification of game theory problems......Page 1
Games in extensive form......Page 3
Cooperative games......Page 6
Dynamic games......Page 7
Basic ideas......Page 8
Stability......Page 10
Developing Mixed Strategies......Page 11
A more formal statement of the problem......Page 16
Proof of the minimax theorem......Page 17
The minimax theorem and duality......Page 20
Basic ideas......Page 23
Properties of Nash strategies......Page 24
Finding Nash mixed strategies......Page 26
The Lemke-Howson algorithm......Page 29
Basic ideas......Page 33
Nash solutions with mixed strategies......Page 34
An introductory example......Page 39
Basic ideas......Page 44
The structure of extensive games......Page 46
Structure in extensive form games......Page 48
An example by Kuhn......Page 52
Basic ideas......Page 57
The formalities......Page 60
The basic theory......Page 62
What results from the axioms......Page 63
Certainty equivalents......Page 66
Some introductory examples......Page 68
Cooperative games with transferable utility......Page 69
Superadditivity......Page 78
Strategic equivalence......Page 80
Normalization......Page 81
Pollution game......Page 83
Balanced sets and the core......Page 84
The Shapley value......Page 87
The Shapley axioms......Page 88
A generalization of the Shapley value......Page 89
Some introductory examples......Page 95
Multilevel mathematical programming......Page 99
A more general definition......Page 101
The two-level linear resource control problem......Page 102
Properties of $S^2$......Page 103
An Illustration......Page 105
Coalition Formation......Page 106
Results......Page 107
Examples and Computations......Page 108
Homework......Page 113
