Naive Decision Making

T. W. Körner9780521516167, 0521516161

How should one choose the best restaurant to eat in? Can one really make money at gambling? Or predict the future? Naive Decision Making presents the mathematical basis for making everyday decisions, which my often be based on very little or uncertain data. Professor Körner takes the reader on an enjoyable journey through many aspects of mathematical decision making, with relatable observations, anecdotes and quotations. Topics include probability, statistics, Arrow’s theorem, Game Theory and Nash equilibrium. Readers will also gain a great deal of insight into mathematics in general and the role it can play within society. Suitable for those with elementary calculus, this book is ideal as a supplementary text for undergraduate courses in probability, game theory and decision making. Engaging and intriguing, it will also appeal to all those of a mathematical mind. To aid understanding, many exercises are included, with solutions available online.

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Table of contents :
Contents……Page 5
Introduction……Page 8
1.1 Money for nothing……Page 13
1.2 The ideal bookmaker……Page 17
1.3 Negative money……Page 21
1.4 Probability and expectation……Page 22
1.5 Back to the races……Page 27
1.6 Betting last at the tote……Page 31
1.7 Betting first……Page 37
1.8 Real race-tracks……Page 43
2.1 The laws of probability……Page 46
2.2 Cards, dice and coin tossing……Page 50
2.3 Random variables……Page 55
2.4 Independence……Page 61
2.5 A law of large numbers……Page 72
2.6 A long day at the races……Page 83
2.7 The two-horse race……Page 90
3.1 Bernard Shaw……Page 95
3.2 Annuities……Page 98
3.3 Smallpox……Page 105
3.4 Should we inoculate?……Page 111
3.5 Utility and Jensen’s inequality……Page 115
4.1 The three towers……Page 123
4.2 Euclid’s algorithm……Page 125
4.3 Arithmetic modulo n……Page 132
4.4 Arithmetic modulo p……Page 140
4.5 Arithmetic modulo pq……Page 145
4.6 Mr Jonas entertains……Page 152
5.1 Find the largest……Page 160
5.2 Records……Page 162
5.3 How to choose a restaurant……Page 165
5.4 Back to sorting……Page 171
5.5 Shortest paths……Page 178
6.1 Marrying……Page 188
6.2 Voting……Page 195
6.3 Preferring……Page 201
7.1 Scissors, Paper, Stone……Page 207
7.2 Scissors, Paper……Page 211
7.3 Can we generalise?……Page 216
7.4 Morra……Page 221
7.5 Can we generalise further?……Page 225
7.6 A noisy duel……Page 228
8.1 An evening out……Page 233
8.2 Technical points……Page 239
8.3 What about reality?……Page 242
8.4 Fixed points……Page 245
8.5 Nash equilibrium……Page 248
8.6 and othersHawks,doves……Page 252
9.1 A, B and C……Page 261
9.2 The three-sided duel……Page 264
9.3 One-person duels……Page 269
9.4 HHH……Page 279
9.5 Tit for tat……Page 283
9.6 Foundational matters……Page 289
10.1 How to gamble if you must……Page 294
10.2 Boldness be my friend……Page 298
10.3 Difference and differential equations……Page 304
10.4 The casino’s view……Page 310
10.5 A flutter on the lottery……Page 320
10.6 Life is a lottery……Page 328
11.1 Coin tossing……Page 333
11.2 A needle in a haystack……Page 336
11.3 Tchebychev improved……Page 338
11.4 A better needle?……Page 343
12.1 First the music, then the words……Page 347
12.2 Mathematics and decision making……Page 353
Appendix A: The logarithm……Page 357
Appendix B: Cardano……Page 363
Appendix C: Huygens’s problems……Page 370
Appendix D: Hints on pronunciation……Page 376
Bibliography……Page 378
Index……Page 382