A First Course on Zero-Sum Repeated GamesSpringer Science & Business Media, 7 mrt 2002 - 204 pagina's The purpose of the book is to present the basic results in the theory of two-person zero-sum repeated games including stochastic games and repeated games with incomplete information. It underlines their relation through the operator approach and covers both asymptotic and uniform properties. The monograph is self-contained including presentation of incomplete information games, minmax theorems and approachability results. It is adressed to graduate students with no previous knowledge of the field. |
Inhoudsopgave
Introduction and examples | 1 |
12 On the use of information | 3 |
13 On the notion of value in long games | 6 |
14 Miscellaneous | 9 |
15 Notes | 13 |
Games with incomplete information | 15 |
22 Concavity | 16 |
23 Approachable vectors | 19 |
53 Big Match | 93 |
algebraic approach | 98 |
asymptotic approach | 99 |
the value | 101 |
57 Markov decision processes | 104 |
58 Comments and extensions | 113 |
59 Exercices | 114 |
510 Notes | 117 |
24 Dual game | 21 |
25 Notes | 23 |
Repeated games with lack of information on one side | 25 |
32 Basic properties | 28 |
33 Preliminary results | 32 |
34 Asymptotic approach | 34 |
35 Recursive structure and operator approach | 38 |
36 Infinite game | 45 |
37 Comments and extensions | 48 |
38 Exercises | 53 |
39 Notes | 54 |
Repeated games with lack of information on both sides | 55 |
43 Infinite game | 57 |
44 Asymptotic approach | 60 |
45 The functional equation | 64 |
46 Recursive structure and operator approach | 68 |
47 Comments and extensions | 78 |
48 Exercises | 82 |
49 Notes | 87 |
Stochastic games | 89 |
existence | 90 |
Advances | 119 |
63 Incomplete information games with no signals | 126 |
64 Stochastic games with signals | 132 |
65 Stochastic games with incomplete information | 135 |
66 Notes | 148 |
Minmax theorems and duality | 151 |
A3 Sions theorem and applications | 156 |
A4 Convexity and separation | 158 |
A5 Mixed extension | 159 |
A7 The value operator and the derived game | 160 |
A8 Fenchels duality | 162 |
A9 Comments | 164 |
Approachability theory | 165 |
Operators and repeated games | 173 |
C2 Bounded variation | 177 |
C3 Approximate fixed points | 178 |
Recursive structure and operators | 180 |
Kuhns Theorem for repeated games | 191 |
References | 195 |
| 203 | |
Veelvoorkomende woorden en zinsdelen
absorbing games absorbing payoff approach Assume asymptotic Aumann behavior Big Match bounded Chapter compact concave consider converges convex convex combination convex set Corollary corresponding defined denotes distribution dual game exists ɛ-optimal finite Game Theory games with incomplete games with lack given guarantee hence implies induction inequality infinite game International Journal Jensen's inequality Journal of Game Kohlberg lack of information Lemma lim sup lim vn Markov Markov decision processes martingale matrix max{u maxmin Mertens J.-F minmax theorem mixed strategies move of Player Note obtains optimal strategy play optimally Player 1 plays Player 1 resp posterior posterior probability probability Proof properties Proposition pure strategies recursive recursive formula repeated games result follows satisfies Section sequence sequential games signals similarly Sorin space stochastic games strategy of Player vector payoffs vx(p Wn+1 Zamir