Index

Absent-Minded Driver’s problem, 143

absolute zero, 161

act, 2, 39

Aesop, 5

Aesop’s principle, 145, 161

affine function, 50

affine transformation, 16

Alchian, Armen, 13

all things considered, 139

Allais, Maurice, 22, 130

Allais’ paradox, 43

almost convergent, 108, 112

alpha-max-min, 156

ambiguity, 113

ambiguity aversion, 168

Anscombe, Elizabeth, 119

Archimedean axiom, 41

argument by design, 127

Arrow, Ken, 3, 61, 148

asymmetric relation, 10

Aumann, Robert, 34, 119, 152, 172

axiom of choice, 79

Ayer, A. J., 21

backward induction, 32

Banach, Stefan, 79, 108

Banach limit, 107, 108, 112

Banach–Tarski paradox, 79

base-rate fallacy, 83, 102

Bayes, Thomas, 83, 126

Bayes’ rule, 83, 126

Bayesian, 95

Bayesian decision theory, 2, 95, 116

Bayesian epistemology, 137

Bayesianism, ix, 1, 96, 126

Bentham, Jeremy, 8, 15, 38, 63

Bernoulli, Daniel, 37

Bernoulli, Jacob, 75, 128

Bernoulli, Nicholas, 37

Bernoulli trial, 105

Bertrand, Joseph, 86

best reply, 28

Billingsley, Patrick, 105

Bingham, Nicholas, 81

binomial distribution, 127

black box, 104

Blackburn, Simon, 21

Borel, Émile, 106, 169

Borel set, 78

Brams, Steve, 31

Broome, John, 64

Calude, Cristian, 99

cardinal utility, 16

Carnap, Rudolf, 95

causal utility fallacy, 19

Chaitin, Greg, 99

characteristic of a commodity, 47

charge, 82, 109

Choquet integral, 93, 165

Church, Alonzo, 101, 113

Church–Turing hypothesis, 146

Clark, Michael, 17

closed set, 17

cluster point, 109

collective, 100

common knowledge, 139

compact set, 17

compound lottery, 40

concave function, 50

conditional probability, 83

Condorcet’s paradox, 61

convex function, 50

countable additivity, 81

countable set, 16, 80

counterfactual, 33

counterfactual event, 87

credence, 95

Damasio, Antonio, 8

Dawid, Philip, 102

de Fermat, Pierre, 75

de Finetti, Bruno, 81, 94, 96, 104, 116, 124

de Moivre, Abraham, 75

decision problem, 2

decreasing marginal utility, 38, 50

dense set, 17

Descartes, René, 138

direct utility function, 6

dominant strategy, 28

Dow, James, 168, 169

Dutch book, 123

Eichberger, Jürgen, 169

Ellsberg, Daniel, 89

Ellsberg paradox, 89

Emerson, Ralph Waldo, 117

empathetic preferences, 71

empathy, 70

epistemology, 137

Epstein, Larry, 168

equilibrium selection problem, 170

event, 76

expected utility theory, 39

extended sympathy preferences, 70

extensive form, 31

Fagin, Ron, 89

feasible, 3

felicity, 19

Ferejohn, John, 31

Fine, Terence, 109

finite additivity, 81, 103

Fisher, Ronald, 95, 96

Gödel, Kurt, 125, 146

game against Nature, 25

game theory, 25

game tree, 31

Gibbard, Alan, 21

Gigerenzer, Gerd, 103

Gilboa, Itzhak, 1, 92

Gillies, Donald, 129

Giovannoni, Francesco, x, 88

Giron, F. J., 90, 125, 164

Goffman, Casper, 106, 180

Good, Irving, ix, 89, 96

Goodin, Robert, 62

Gorman, William, 47, 143

Greenberg, Joseph, 169

Hacking, Ian, 75

Hahn–Banach theorem, 107

Haldane, J. B. S., 150

Halpern, Joe, 89

Hammond, Peter, 2, 64

Hanany, Eran, 168

Hardin, Russell, 62

Harsanyi, John, 62, 64, 128, 172

Harsanyi doctrine, 73, 128

Hausdorff, Felix, 79

Hausdorff’s paradox of the sphere, 89

Hempel’s paradox, 84

Herman, Chernoff, 161

Hintikka, Jaako, 138

Hirshleifer, John, 52

Hobbes, Thomas, 3, 7, 61, 138

Horatio principle, 79

Houthakker’s axiom, 12, 156

Howson, Colin, 134

Hume, David, 1, 4, 63, 70, 98, 152

Hurwicz, Leonid, 155

Hurwicz coefficient, 166

Hurwicz criterion, 155

Huygens, Christian, 75

ideal observer, 62

ignorance, 154

impartial spectator, 62

imperfect recall, 143

independence, 86, 103, 166

independence axiom, 41

indifference, 12

indifference curve, 18

indirect utility function, 6

information set, 31, 139

inner measure, 88

instrumental preferences, 5

insurance, 53

intensity of preference, 66

interpersonal comparison of utility, 67

intrinsic preferences, 6

Jaynes, Edwin, 128

Jeffrey, Richard, 7, 31

Jevons, Stanley, 15

Kadane, Joseph, 2, 83

Kahneman, Daniel, 58, 83

Kant, Immanuel, 2, 4, 98

Kaplan, D., 146

Karni, Ed, 7

Kelsey, David, 2, 169

Keynes, John Maynard, 95, 129

Klibanoff, Peter, 162, 168

Knight, Frank, 35

knowledge, 137

knowledge operator, 137

Kolmogorov, Andrei Nikolaevich, 75

Kreps, David, 119

Kuhn, Harold, 143, 170

Laplace, Pierre-Simon, 75, 128

large world, 2

law of large numbers, 105

Layard, Richard, 63

Lebesgue, Henri, 77

Ledyard, John, 21

Leibniz, Gottfried, 32, 146

Levi, Isaac, 88

Lewis, David, 30

lexicographic preferences, 17

limit point, 109

Lindley, Dennis, 1

linear combination, 106

linear function, 106

Lo, K. Chung, 169

logical probability, 95

loss function, 91

lottery, 40

lower probability, 88

Luce, Duncan, x, 66, 68, 130, 154, 161

Machina, Mark, 58

marginalist revolution, 15

Marinacci, Massimo, 162, 169

Marquis de Condorcet, 61

Marx, Karl, 61

Maschler, Michael, 172

Matching Pennies, 99, 135, 169

maximin criterion, 52, 155, 169

Maxwell, Nicholas, 150

measurable set, 75

middle frequency, 109

Mill, John Stuart, 62

Milnor, John, 52, 157, 162

Mini-Poker, 141

minimax criterion, 91

minimax regret criterion, 156

mixed strategy, 169

money pump, 13, 123

Montague, R., 146

Moore, G. E., 64

Morgenstern, Oskar, 16, 36, 39

muddling box, 115, 164

Mukerji, Sujoy, 162, 169

multiplicative Hurwicz criterion, 166

Nash, John, 157, 169

Nash equilibrium, 26, 29, 169

necessity, 151

neoclassical economics, 20

Newcomb’s problem, 30

Newton, Isaac, 76

nonadditive probability, 92, 165

normative theory, 22

Nozick, Robert, 30

O’Hagan, Anthony, 83

objective probability, 94

odds, 123

one-player game, 25

optimal, 3

ordinal utility, 15

original position, 69, 73

outer measure, 88

output set, 104

paradox of preference, 17

partition, 78, 140

Pascal, Blaise, 75

Pascal’s wager, 57

payoff, 25

Pedrick, George, 106, 180

perfect recall, 143

point of accumulation, 109

poker, 141

Popper, Karl, 95, 109, 113, 151

positive theory, 22

possibility operator, 137

possibility set, 140

posterior probability, 127

practical reason, 2

preference relation, 10

preference satisfaction, 21

prevision, 91

principle of indifference, 128

principle of insufficient reason, 128, 154

prior probability, 127

Prisoners’ Dilemma, 21, 26

probability space, 81

procedural rationality, 63

prospect theory, 58

proximate cause, 13

public event, 139

pure strategy, 169

Pythagoras, 1

quasi-Bayesian decision theory, 91, 164

quasi-probability, 165

Quine, Willard, 150

Quinn, Warren, 18

Rényi, Alfréd, 75, 97

Rachels, Stuart, 18

Raiffa, Howard, x, 66, 68, 130, 154, 161

Ramsey, Frank, 7, 94, 116, 124, 134

random, 101

randomizing box, 104

randomizing device, 96

rational choice theory, 21

rationalism, 1

Rawls, John, 39, 52, 62, 69

Riley, John, 52

Rios, S., 90, 125, 164

risk, 94

risk neutral, 53

Robbins, Lionel, 15, 67

Rubin, Herman, 161

Rumsfeld, Donald, 139

Ryan, Matthew, 168

sample space, 76

Samuelson, Larry, x

Samuelson, Paul, 7, 38

Savage, Leonard, ix, 2, 22, 95, 116, 154, 163

Schervish, Mark, 2

Schmeidler, David, 1, 89, 92, 93

Seidenfeld, Teddy, 2, 88

self-interest, 21

selfishness axiom, 20

Sen, Amartya, 9, 11, 63, 65

Shin, Hyun, 169

sigma-algebra, 81

small world, 2, 117

Smith, Adam, 70

social choice, 60

Solovay, Robert, 79

Stecher, Jack, x

strategic form, 31

strategic uncertainty, 25

St Petersburg paradox, 37

subadditive function, 92

subgame, 32

subjective equilibrium, 135

subjective probability, 94, 125

substantive rationality, 63

superadditive function, 92

supermodularity, 93

Suppes, Patrick, 70, 89

sure-thing principle, 121

Sutton, John, 89

sympathy, 70

Tarski, Alfred, 79, 149

teleological argument, 64

Temkin, Larry, 18

transferable utility, 68

transitive relation, 10

truism, 139, 149

truth, 149

Turing halting problem, 147

Turing machine, 146

Tversky, Amos, 23, 58, 83

ultimate cause, 13

umbrella principle, 28

uncertainty aversion, 168

upper probability, 88

util, 8

utilitarian welfare function, 65

utility, 8

utility function, 14

van Bentham, Johan, 146

vector space, 106

veil of ignorance, 68

venus throw, 97

Vienna circle, 98

Vitali, Giuseppe, 78

Voltaire, François-Marie, 5

von Mises, Ludwig, 100

von Mises, Richard, 96, 100

Von Neumann, John, 16, 36, 39, 53, 99, 140, 169

Voorhoeve, Alex, 18

Vovk, Vladimir, 102

Wagon, Stan, 79

Wakker, Peter, x

Wald, Abraham, 91, 101

Walley, Peter, 91, 109

weak preference, 12

welfare, 60

Werlang, Serge, 168, 169

Weymark, John, 64

Wittgenstein, Ludwig, 114

Xu, Zibo, x

Zeckhauser’s paradox, 44

zero–one utilitarianism, 69

zero-sum game, 53