An introduction to decision theory
This up-to-date introduction to decision theory offers comprehensive and accessible discussions of decision-making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice th...
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge introductions to philosophy
|
| Schlagworte: | |
| Online-Zugang: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
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| 100 | 1 | |a Peterson, Martin |d 1975- |e Verfasser |0 (DE-588)143564277 |4 aut | |
| 245 | 1 | 0 | |a An introduction to decision theory |c Martin Peterson |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a X, 317 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Cambridge introductions to philosophy | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 500 | |a Includes bibliographical references | ||
| 520 | 3 | |a This up-to-date introduction to decision theory offers comprehensive and accessible discussions of decision-making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice theory. No mathematical skills are assumed, and all concepts and results are explained in non-technical and intuitive as well as more formal ways. There are over 100 exercises with solutions, and a glossary of key terms and concepts. An emphasis on foundational aspects of normative decision theory (rather than descriptive decision theory) makes the book particularly useful for philosophy students, but it will appeal to readers in a range of disciplines including economics, psychology, political science and computer science. | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface
page
ix
1
Introduction
1
1.1
Normative and descriptive decision theory
3
1.2
Rational and right decisions
4
1.3
Risk, ignorance and uncertainty
5
1.4
Social choice theory and game theory
8
1.5
A very brief history of decision theory
10
2
The decision matrix
17
2.1
States
19
2.2
Outcomes
22
2.3
Acts
27
2.4
Rival
formalisations
30
3
Decisions under ignorance
40
3.1
Dominance
41
3.2 Maximin
and leximin
43
3.3
Maximax and the optimism-pessimism rule
46
3.4
Minimax regret
49
3.5
The principle of insufficient reason
53
3.6
Randomised acts
56
4
Decisions under risk
64
4.1
Maximising what?
65
4.2
Why is it rational to maximise expected utility?
71
4.3
The axiomatic approach
73
4.4
Allais
paradox
78
4.5
Ellsberg s paradox
81
4.6
The St Petersburg paradox
83
4.7
The two-envelope paradox
86
vi
Contents
5
Utility
91
5.1
How to construct an ordinal scale
91
5.2 von
Neumann and Morgenstern s interval scale
94
5.3
Can utility be measured on a ratio scale?
106
5.4
Can we define utility without being able
to measure it?
110
6
The mathematics of probability
117
6.1
The probability calculus
118
6.2
Conditional probability
123
6.3
Bayes
theorem
125
6.4
The problem of unknown priors
127
7
The philosophy of probability
133
7.1
The classical interpretation
134
7.2
The frequency interpretation
136
7.3
The propensity interpretation
139
7.4
Logical and
epistemic
interpretations
141
7.5
Subjective probability
143
8
Why should we accept the preference axioms?
164
8.1
Must a rational preference be transitive?
165
8.2
Must a rational preference be complete?
169
8.3
The multi-attribute approach
172
8.4
Must a rational preference satisfy
the independence axiom?
176
8.5
Riskaversion
179
9
Causal vs. evidential decision theory
187
9.1
Newcomb s problem
187
9.2
Causal decision theory
190
9.3
Evidential decision theory
192
10
Bayesian vs. non-Bayesian decision theory
200
10.1
What is Bayesianism?
200
10.2
Arguments for and against Bayesianism
204
10.3
Non-Bayesian approaches
208
11
Game theory I: Basic concepts and zero-sum games
212
11.1
The prisoner s dilemma
214
11.2
A taxonomy of games
220
11.3
Common knowledge and dominance reasoning
224
Contents
vii
11.4
Two-person zero-sum games
229
11.5
Mixed strategies and the minimax theorem
232
12
Game theory II: Nonzero-sum and cooperative games
240
12.1
The Nash equilibrium
240
12.2
The battle of the sexes and chicken
244
12.3
The bargaining problem
247
12.4
Iterated games
251
12.5
Game theory and evolution
255
12.6
Game theory and ethics
257
13
Social choice theory
263
13.1
The social choice problem
265
13.2
Arrow s impossibility theorem
268
13.3
Sen on liberalism and the Pareto principle
273
13.4
Harsanyi s utilitarian theorems
276
14
Overview of descriptive decision theory
285
14.1
Observed violations of the expected utility
principle
285
14.2
Prospect theory
288
14.3
Violations of transitivity and completeness
290
14.4
The relevance of descriptive decision theory
292
Appendix A: Glossary
296
Appendix B: Proof of the
von Neumann-Morgenstern
theorem
302
Further reading
308
Index
314
|
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| discipline | Soziologie Mathematik Philosophie Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV035586198 |
| illustrated | Illustrated |
| index_date | 2024-09-19T15:27:00Z |
| indexdate | 2024-09-27T16:20:28Z |
| institution | BVB |
| isbn | 9780521888370 9780521716543 |
| language | English |
| lccn | 2008054042 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017641502 |
| oclc_num | 297147090 |
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| physical | X, 317 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Cambridge introductions to philosophy |
| spellingShingle | Peterson, Martin 1975- An introduction to decision theory Besliskunde gtt Jeux, Théorie des ram Prise de décision - Modèles mathématiques ram Mathematisches Modell Decision making Decision making Mathematical models Bayesian statistical decision theory Game theory Mathematisches Modell (DE-588)4114528-8 gnd Spieltheorie (DE-588)4056243-8 gnd Entscheidungsfindung (DE-588)4113446-1 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4056243-8 (DE-588)4113446-1 (DE-588)4204326-8 |
| title | An introduction to decision theory |
| title_auth | An introduction to decision theory |
| title_exact_search | An introduction to decision theory |
| title_full | An introduction to decision theory Martin Peterson |
| title_fullStr | An introduction to decision theory Martin Peterson |
| title_full_unstemmed | An introduction to decision theory Martin Peterson |
| title_short | An introduction to decision theory |
| title_sort | an introduction to decision theory |
| topic | Besliskunde gtt Jeux, Théorie des ram Prise de décision - Modèles mathématiques ram Mathematisches Modell Decision making Decision making Mathematical models Bayesian statistical decision theory Game theory Mathematisches Modell (DE-588)4114528-8 gnd Spieltheorie (DE-588)4056243-8 gnd Entscheidungsfindung (DE-588)4113446-1 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
| topic_facet | Besliskunde Jeux, Théorie des Prise de décision - Modèles mathématiques Mathematisches Modell Decision making Decision making Mathematical models Bayesian statistical decision theory Game theory Spieltheorie Entscheidungsfindung Bayes-Verfahren |
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