Game theory:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English Hebrew |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2013
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| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Cover Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXVI, 979 S. graph. Darst. |
| ISBN: | 1107005485 9781107005488 |
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| 100 | 1 | |a Mashler, Mikhaʾel |d 1927-2008 |e Verfasser |0 (DE-588)119158108 |4 aut | |
| 240 | 1 | 0 | |a Torat ha-mishakim |
| 245 | 1 | 0 | |a Game theory |c Michael Maschler ; Eilon Solan ; Shmuel Zamir |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2013 | |
| 300 | |a XXVI, 979 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804150131922042880 |
|---|---|
| adam_text | Contents
Acknowledgments page
xiv
Notations
xv
Introduction
xxiii
1
The game of chess
1
1.1
Schematic description of the game
1
1.2
Analysis and results
2
1.3
Remarks
7
1.4
Exercises
7
2
Utility theory
9
2.1
Preference relations and their representation
9
2.2
Preference relations over uncertain outcomes: the model
12
2.3
The axioms of utility theory
14
2.4
The characterization theorem for utility functions
19
2.5
Utility functions and
affine
transformations
22
2.6
Infinite outcome set
23
2.7
Attitude towards risk
23
2.8
Subjective probability
26
2.9
Discussion
27
2.10
Remaries
31
2.11
Exercises
31
3
Extensive-form games
39
3.1
An example
40
3.2
Graphs and trees
41
3.3
Game trees
42
3.4
Chomp: David Gale s game
47
3.5
Games with chance moves
49
3.6
Games with imperfect information
52
3.7
Exercises
57
vii
viii
} Contents
4
Strategic-form games
75
4.1
Examples and definition of strategic-form games
76
4.2
The relationship between the extensive form and the
strategic form
82
4.3
Strategic-form games: solution concepts
84
4.4
Notation
85
4.5
Domination
85
4.6
Second-price auctions
91
4.7
The order of elimination of dominated strategies
95
4.8
Stability: Nash equilibrium
95
4.9
Properties of the Nash equilibrium
100
4.10
Security: the maxmin concept
102
4.11
The effect of elimination of dominated strategies
106
4.12
Two-player zero-sum games
110
4.13
Games with perfect information
118
4.14
Games on the unit square
121
4.15
Remarks
128
4.16
Exercises
128
5
Mixed strategies
144
5.1
The mixed extension of a strategic-form game
145
5.2
Computing equilibria in mixed strategies
152
5.3
The proof of Nash s Theorem
166
5.4
Generalizing Nash s Theorem
170
5.5
Utility theory and mixed strategies
172
5.6
The maxmin and the minmax in
w
-player games
176
5.7
Imperfect information: the value of information
180
5.8
Evolutionarily stable strategies
186
5.9
Remarks
194
5.10
Exercises
194
6
Behavior strategies and Kuhn s Theorem
219
6.1
Behavior strategies
221
6.2
Kuhn s Theorem
226
6.3
Equilibria in behavior strategies
235
6.4
Kuhn s Theorem for infinite games
238
6.5
Remarks
243
6.6
Exercises
244
IX
;
Contents
7
Equilibrium refinements
251
7.1
Subgame
perfect equilibrium
252
7.2
Rationality, backward induction, and forward induction
260
7.3
Perfect equilibrium
262
7.4
Sequential equilibrium
271
7.5
Remarks
284
7.6
Exercises
284
8
Correlated equilibria
300
8.1
Examples
301
8.2
Definition and properties of correlated equilibrium
305
8.3
Remarks
313
8.4
Exercises
313
9
Games with incomplete information and common priors
319
9.1
The Aumann model of incomplete information and the concept
of knowledge
322
9.2
The Aumann model of incomplete information with beliefs
334
9.3
An infinite set of states of the world
344
9.4
The Harsanyi model of games with incomplete
information
345
9.5
Incomplete information as a possible interpretation of
mixed strategies
361
9.6
The common prior assumption: inconsistent beliefs
365
9.7
Remarks
367
9.8
Exercises
368
10
Games with incomplete information: the general model
386
10.1
Belief spaces
386
10.2
Belief and knowledge
391
10.3
Examples of belief spaces
394
10.4
Belief subspaces
400
10.5
Games with incomplete information
407
10.6
The concept of consistency
415
10.7
Remarks
423
10.8
Exercises
423
11
The universal belief space
440
11.1
Belief hierarchies
442
11.2
Types
450
Ί
Contents
11.3 Definition
of the universal belief space
453
11.4
Remarks
456
11.5
Exercises
456
12
Auctions
461
12.1
Notation
464
12.2
Common auction methods
464
12.3
Definition of a sealed-bid auction with private values
465
12.4
Equilibrium
468
12.5
The symmetric model with independent private values
471
12.6
The Envelope Theorem
484
12.7
Risk aversion
488
12.8
Mechanism design
492
12.9
Individually rational mechanisms
500
12.10
Finding the optimal mechanism
501
12.11
Remarks
508
12.12
Exercises
509
13
Repeated games
519
13.1
The model
520
13.2
Examples
521
13.3
The 7-stage repeated game
524
13.4
Characterization of the set of equilibrium payoffs of the 7-stage repeated
game
530
13.5
Infinitely repeated games
537
13.6
The discounted game
542
13.7
Uniform equilibrium
546
13.8
Discussion
554
13.9
Remarks
555
13.10
Exercises
555
14
Repeated games with vector payoffs
569
14.1
Notation
570
14.2
The model
572
14.3
Examples
573
14.4
Connections between approachable and excludable sets
574
14.5
A geometric condition for the approachability of a set
576
14.6
Characterizations of convex approachable sets
585
14.7
Application
1 :
Repeated games with incomplete information
590
14.8
Application
2:
Challenge the expert
600
14.9
Discussion
606
14.10
Remarks
607
14.11
Exercises
608
xi ) Contents
15
Bargaining games
622
15.1
Notation
625
15.2
The model
625
15.3
Properties of the Nash solution
626
15.4
Existence and uniqueness of the Nash solution
630
15.5
Another characterization of the Nash solution
635
15.6
The minimality of the properties of the Nash solution
639
15.7
Critiques of the properties of the Nash solution
641
15.8
Monotonicity
properties
643
15.9
Bargaining games with more than two players
650
15.10
Remarks
653
15.11
Exercises
653
16
Coalitional games with transferable utility
659
16.1
Examples
661
16.2
Strategic equivalence
668
16.3
A game as a vector in a Euclidean space
670
16.4
Special families of games
671
16.5
Solution concepts
672
16.6
Geometric representation of the set of imputations
676
16.7
Remarks
678
16.8
Exercises
678
17
The core
686
17.1
Definition of the core
687
17.2
Balanced collections of coalitions
691
17.3
The Bondareva-Shapley Theorem
695
17.4
Market games
702
17.5
Additive games
712
17.6
The consistency property of the core
715
17.7
Convex games
717
17.8
Spanning tree games
721
17.9
Flow games
724
17.10
The core for general coalitional structures
732
17.11
Remarks
735
17.12
Exercises
735
18
The Shapley value
748
18.1
The Shapley properties
749
18.2
Solutions satisfying some of the Shapley properties
751
18.3
The definition and characterization of the Shapley value
754
18.4
Examples
758
xii Contents
18.5 An alternative characterization
of the
Shapley
value
760
18.6 Application:
the
Shapley-Shubik
power index
763
18.7
Convex games
767
18.8
The consistency of the Shapley value
768
18.9
Remarks
774
18.10
Exercises
774
19
The bargaining set
782
19.1
Definition of the bargaining set
784
19.2
The bargaining set in two-player games
788
19.3
The bargaining set in three-player games
788
19.4
The bargaining set in convex games
794
19.5
Discussion
797
19.6
Remarks
798
19.7
Exercises
798
20
The nucleolus
801
20.1
Definition of the nucleolus
802
20.2
Nonemptiness and uniqueness of the nucleolus
805
20.3
Properties of the nucleolus
809
20.4
Computing the nucleolus
815
20.5
Characterizing the prenucleolus
816
20.6
The consistency of the nucleolus
823
20.7
Weighted majority games
825
20.8
The bankruptcy problem
831
20.9
Discussion
842
20.10
Remarks
843
20.11
Exercises
844
21
Social choice
853
21.1
Social welfare functions
856
21.2
Social choice functions
864
21.3
Non-manipulability
871
21.4
Discussion
873
21.5
Remarks
874
21.6
Exercises
874
22
Stable matching
884
22.1
The model
886
22.2
Existence of stable matching: the men s courtship algorithm
888
22.3
The women s courtship algorithm
890
xiii ) Contents
22.4
Comparing
matchings 892
22.5
Extensions
898
22.6
Remarks
905
22.7
Exercises
905
23
Appendices
916
23.1
Fixed point theorems
916
23.2
The Separating
Нурефіапе
Theorem
943
23.3
Linear programming
945
23.4
Remarks
950
23.5
Exercises
950
References
958
Index
968
|
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| spelling | Mashler, Mikhaʾel 1927-2008 Verfasser (DE-588)119158108 aut Torat ha-mishakim Game theory Michael Maschler ; Eilon Solan ; Shmuel Zamir 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2013 XXVI, 979 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Aus dem Hebr. übers. Game theory Spieltheorie (DE-588)4056243-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Spieltheorie (DE-588)4056243-8 s DE-604 Solan, Eilon 1968- Verfasser (DE-588)171780345 aut Zāmîr, Šemûʾēl Verfasser aut http://assets.cambridge.org/97811070/05488/cover/9781107005488.jpg Cover Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025776483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mashler, Mikhaʾel 1927-2008 Solan, Eilon 1968- Zāmîr, Šemûʾēl Game theory Game theory Spieltheorie (DE-588)4056243-8 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4123623-3 |
| title | Game theory |
| title_alt | Torat ha-mishakim |
| title_auth | Game theory |
| title_exact_search | Game theory |
| title_full | Game theory Michael Maschler ; Eilon Solan ; Shmuel Zamir |
| title_fullStr | Game theory Michael Maschler ; Eilon Solan ; Shmuel Zamir |
| title_full_unstemmed | Game theory Michael Maschler ; Eilon Solan ; Shmuel Zamir |
| title_short | Game theory |
| title_sort | game theory |
| topic | Game theory Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | Game theory Spieltheorie Lehrbuch |
| url | http://assets.cambridge.org/97811070/05488/cover/9781107005488.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025776483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mashlermikhaʾel torathamishakim AT solaneilon torathamishakim AT zamirsemuʾel torathamishakim AT mashlermikhaʾel gametheory AT solaneilon gametheory AT zamirsemuʾel gametheory |