Index

f-nucleon, 156

BANZHAF value, 169

BERNOULLI’s inequality, 87

BOLTZMANN

distribution, 212

value, 175

BOLTZMANN distribution, 122

BRAESS’s paradox, 119

BROUWER’s theorem, 209

CHOQUET integral, 162

DE BRUIJN’s game, 39

DE MÉRÉ’s game, 83

DIRAC function, 138

EULER’s number, 20

FARKAS lemma, 208

FECHNER’s law, 19

GIBBS distribution, 122

GRUNDY number, 47

HADAMARD

product, 11, 192

HARSANYI dividend, 139

HEISENBERG picture, 195

HILBERT space, 14

JACOBI matrix, 65

KELLY formula, 81

KELLY strategy, 82

LAGRANGE

function, 62

game, 62, 66

LOVÁSZ extension, 162

MÖBIUS transform, 138

MARKOV

chain, 197, 215

operator, 197

METROPOLIS process, 125

mex of numbers, 46

MONGE

algorithm, 160, 211

extension, 161

function, 161

vector, 160

NASH

equilibrium, 117

flow, 119

PYTHAGORAS’ theorem, 12

SCHRÖDINGER picture, 194

SHANNON, 92

SHANNON’s information, 20

SHAPLEY value, 169

SPRAGUE-GRUNDY, 46

VON NEUMANN’s theorem, 60

WARDROP, 118

adjoint, 184

algorithm

MONGE, 160, 211

greedy, 145

balanced

positively, 148

strongly, 150

balanced game, 148

bet, 82

binary algebra, 17, 48

bounded, 203

canonical linear program, 72

channel

capacity, 91

communication, 89

characteristic function, 135

checkmate, 34

chess, 21

circuit, 105

closed, 203

coalition, 112, 133

formation, 175

fuzzy, 113, 148

generalized, 148

grand, 137

rational, 152

common knowledge, 96

compact, 203

complementary slackness, 63

complex number, 16

concave

cooperative game, 163

convex, 108

combination, 205

set, 205

cooperation, 112

fuzzy, 199

cooperative game

generalized, 193

core, 152

least, 153

open, 153

cover, 149

covering value, 149

covex

function, 206

density matrix, 196

divergence, 214

dual linear program, 70, 73

duality operator, 137

economy, 22

efficiency, 170

efficient, 146, 152, 170

eigenvalue, 185

entropy, 21, 213

equilibrium, 55, 106

NASH, 117

zero-sum game, 55

equivalence

strategic, 44

evident, 96

evolution, 23, 196

excess, 158

exchange economy, 22

fixed-point, 209

fortune formula, 81

frogs, 36

function, 6

LAGRANGE, 62

characteristic, 135

objective, 62

partition, 122

pseudo-boolean, 135

wave, 196

fuzzy, 113

G-strategy, 82

game, 24

n-person, 28

DE BRUIJN, 39

LAGRANGE, 62

abstract, 24

additive, 141

algebra, 41

alternating, 34

balanced, 148

combinatorial, 33

congruent, 42

convex, 57, 164

cooperative, 133

fuzzy, 113

impartial, 45

linear programming, 73

matrix, 54, 116

network, 145

neutral, 45

nim, 36

potential, 114

production, 142

randomized, 59

recursive, 35

submodular, 167

supermodular, 164

threshold, 147

unanimity, 138

voting, 147

zero-sum, 54

grand coalition, 137

graph

combinatorial, 9

greedy

algorithm, 167

greedy algorithm, 145

growth

arithmetic, 77

geometric, 78

hermitian

matrix, 188

representation, 188

imaginary unit, 16

incidence vector, 8

inequality

primal-dual, 56

information, 19, 20

information function, 95

inner product, 184

intensity, 19

interaction

binary, 190

graph, 189

instance, 189

KKT-conditions, 65

knowledge function, 95

linear program, 72, 73

dual, 70

logarithm, 20

natural, 20

matrix

density, 196

hermitian, 188

matrix game, 54, 116

misère, 38

modular, 165

move, 24

negation, 41

neighborhood, 106

net return, 78

nim game, 36

node, 9

norm

complex, 184

euclidian, 11, 182

normal winning rule, 38

normalization, 136

nucleolus, 158

nucleon, 156

objective, 25

observable, 194

odds, 82

fair, 83, 88

open, 203

option, 34

orthogonal, 12, 182

packing, 148

partition function, 212

path independence, 105

payoff

feasible, 150

polyhedron, 71, 207

potential

marginal, 104

primal-dual, 56

principal component, 198

Prisoner’s dilemma, 28

probability

conditional, 98

distribution, 18

probability distribution, 205

product

matrix, 12

hermitian, 184

inner, 11

pseudo-boolean, 135

quantum game, 200

quantum system, 194

randomized game, 59

real world, 3

recursive, 35

red hats, 93

roulette, 84

rule, 25

selfadjoint, 185

shadow price, 66

simulated annealing, 126

slackness

complementary, 63

social justice, 130

solution

VON NEUMANN and MORGENSTERN, 151

concept, 151

zero-sum game, 55

spectral decomposition, 185

spectral theorem, 185

St. Petersburg

game, 76

paradox, 76

stable set, 151

stage of a game, 24

standard linear program, 69

strategy, 28

υ-greedy, 40

doubling, 84

submodular, 167

sum of games, 42

sum theorem, 49

super-exponential growth, 37

supermodular, 164

symmetric difference, 141

symmetry decomposition, 182

system, 21

decision, 22

quantum, 194, 200

state, 21

traffic, 23

temperature, 124

time, 23

trace, 13

traffic flow, 118

transferable utility, 134

transpose, 9

trust matrix, 90

TU-game, 135

unitary, 185

utility, 25

aggregated, 115

concave, 27, 108

convex, 108

function, 25, 111

logarithmic, 77

matrix, 29

measure, 104

potential, 106

tranferable, 134

utility function

local, 104

value, 168

BANZHAF, 169

BOLTZMANN, 174

SHAPLEY, 169

covering, 149

expected, 18

linear, 168

marginal, 141

random, 170

vector

marginal, 172

vector space, 14

vertex, 9

voting game, 147

welfare, 176

winning rule, 38

zero-sum game, 54