Choices and strategies: knowing how to play the game
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
RBA
2012
|
| Schriftenreihe: | Everything is mathematical
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | 143 S. Ill., graph. Darst. |
Internformat
MARC
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025431057 | ||
Datensatz im Suchindex
| _version_ | 1804149694202380288 |
|---|---|
| adam_text | Contents
Preface
........................................................................................................................................................... 11
Chapter
1.
A Brief History of the Relationship Between
Mathematics and Games
....................................................................................................... 13
Serious mathematics and playful mathematics, pure and applied
.......................... 14
Mathematics and games up to the 17th century
.............................................................. 16
Games and mathematics in the ancient civilisations
.............................................. 16
Games and mathematics in the middle ages
................................................................ 20
Mathematics and games during the Renaissance
..................................................... 24
Mathematical games from the 17th century to the present day
............................. 27
The rise of mathematical puzzles: the 17th and 18th centuries
..................... 28
Mathematical games in the 19th and 20th centuries
............................................. 32
The appearance of game theory
................................................................................................. 38
Chapter
2.
Strategy Games and Problem Solving
................................................... 41
The concept of a winning strategy
........................................................................................... 42
Exploiting advantages, defining strategies.
Nim
games
.............................................. 45
Towards the definition of a strategy
.......................................................................................... 48
Game
1
(two players):
20
wins
............................................................................................. 48
Game
2
(two players):
100
loses
........................................................................................... 49
Game
3
(two players): Complete generalisation
....................................................... 50
A complex
strategy:The
game of
Nim
.................................................................................. 51
Game
4
(two players): First version of
Nim
................................................................ 51
Game
5
(two players):
Marienbad ...................................................................................... 53
Aim of the game: Equivalence and difference
................................................................... 56
Game
6
(two players): Hexagonal advance
................................................................... 56
Game
7
(two players):Add the last item
........................................................................ 57
Game
8
(two players):Tsyanshidzi
..................................................................................... 58
Game
9
(two players): Save the queen
............................................................................. 58
Game
10
(two players):The daisy
....................................................................................... 58
Games and pseudo-games
............................................................................................................... 60
Game
11
(two players): Only odd
...................................................................................... 61
Game
12
(two players): Circles and squares
................................................................. 61
CONTENTS
Chapter
3. Games
of
Chance ................................................................................................... 65
The man who didn t want to lose
-
games of chance
and the birth of probability
.................................................................................................... 65
Chance tamed. The mathematical study of probabilities
............................................. 68
A matter of counting. Does order matter?
........................................................................... 72
Situation
1 .......................................................................................................................................... 72
Situation
2 .......................................................................................................................................... 73
Situation
3 .......................................................................................................................................... 74
Situation
4.......................................................................................................................................... 75
Lottery numbers and other false intuitions
.......................................................................... 76
The whims of probability
................................................................................................................ 76
Playing bowls
................................................................................................................................... 77
A standard die
.................................................................................................................................. 77
What is the probability of winning?
................................................................................. 77
A disputed draw
............................................................................................................................. 79
An uninteresting bet
................................................................................................................... 79
Shared birthdays
............................................................................................................................. 80
Chance has no memory
................................................................................................................... 81
Tossing a coin
.................................................................................................................................. 81
Gameshow
......................................................................................................................................... 84
Mathematics and expectations
...................................................................................................... 85
A betting game with three dice
........................................................................................... 86
Early registration
............................................................................................................................ 87
Can the bank be beaten? Probability and repeated events
......................................... 88
Chapter
4.
Game Theory
............................................................................................................. 91
The principles of game theory
.................................................................................................... 91
When is equilibrium reached?
.................................................................................................... 96
An abstract game with pure strategies
..................................................................................... 98
Elections and restaurants: applications of games
with pure strategies
...................................................................................................................... 100
Manifestos
.......................................................................................................................................... 100
The location of a restaurant
................................................................................................... 102
When there is no equilibrium: mixed strategies
............................................................... 103
Determining an optimal mixed strategy
........................................................................ 103
Applications of mixed strategies
.................................................................................................. 106
CONTENTS
Growth of a company
................................................................................................................ 107
Taking a penalty
............................................................................................................................. 108
Advantages and drawbacks of the minimax method
.....................................................
Ill
Chapter
5.
The Game of Life: Theoretical Applications
in the Real World
.................................................................................................................... 115
The mathematics of cooperation: non-zero-sum-games
............................................ 116
A fair idea: Nash s equilibrium
..................................................................................................... 120
Prisoner s dilemma and other classic problems
.................................................................. 123
The prisoner s dilemma
............................................................................................................ 124
The game of chicken
.................................................................................................................. 128
Cooperate or die:The hawk-dove game
....................................................................... 130
Games with more than two players
.......................................................................................... 132
η
person games
....................................................................................................................................... 133
Cooperative games, partnerships and distributions
......................................................... 135
Example
1 .......................................................................................................................................... 135
Example
2 .......................................................................................................................................... 135
Example
3 .......................................................................................................................................... 136
Bibliography
............................................................................................................................................ 139
Index
............................................................................................................................................................. 141
Choices and Strategies
Knowing how to play the game
Game playing
—
an ever-popular pastime
-
has always
prompted intriguing mathematical explanations and
formulations. This process reached its climax in the second
half of the last century when, in the heat of the Cold War,
against a backdrop of ideological and military confrontation
between global superpowers, modern game theory was
developed to analyse winning strategies that can be used to
tackle all types of conflicts.
|
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| language | English |
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| physical | 143 S. Ill., graph. Darst. |
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| spelling | Deulofeu Piquet, Jordi Verfasser aut Choices and strategies knowing how to play the game Jordi Deulofeu London RBA 2012 143 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Everything is mathematical Spieltheorie (DE-588)4056243-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Spieltheorie (DE-588)4056243-8 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431057&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431057&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Deulofeu Piquet, Jordi Choices and strategies knowing how to play the game Spieltheorie (DE-588)4056243-8 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4151278-9 |
| title | Choices and strategies knowing how to play the game |
| title_auth | Choices and strategies knowing how to play the game |
| title_exact_search | Choices and strategies knowing how to play the game |
| title_full | Choices and strategies knowing how to play the game Jordi Deulofeu |
| title_fullStr | Choices and strategies knowing how to play the game Jordi Deulofeu |
| title_full_unstemmed | Choices and strategies knowing how to play the game Jordi Deulofeu |
| title_short | Choices and strategies |
| title_sort | choices and strategies knowing how to play the game |
| title_sub | knowing how to play the game |
| topic | Spieltheorie (DE-588)4056243-8 gnd |
| topic_facet | Spieltheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431057&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025431057&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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