A Beautiful Math
Page 29
Maynard Smith, John, 77–78, 85, 241
Mazlish, Bruce, 13–14
McFee, Bruce, 155
McGill University, 123
Meyer, David, 185–188, 189, 190
Mice, tail-test reaction, 122–124
Microsoft, 158, 185, 187, 189
Milgram, Stanley, 146
Minimax theorem, 33, 34, 43–49, 58, 237, 239
Minority game, 175, 176–177
Mogil, Jeffrey, 123, 124
Montague, Read, 4, 94–95, 97–99, 100–101, 104, 105, 106
Moore, Demi, 144
Moral philosophy, 15
Morgenstern, Oskar, 26, 27, 34–36, 37–40, 42, 49–50, 51, 52–53, 55, 60, 95, 217, 220
Motions, laws of, 135
Multiple-person games, 53–54, 208
Myerson, Roger, 51, 52
N
NASA Ames Research Center, 4, 199, 209
Nasar, Sylvia, vi, 2, 29, 54, 246
Nash, John Forbes, vi, 1, 2, 3, 7, 8, 29, 50, 51–52, 54–56, 59–61, 66, 70, 140, 164, 220, 221
Nash equilibrium, 111, 142
acceptance of, 59, 125
assumptions and calculations, 125, 209, 225–229
bargaining problem, 55–56, 66
and Code of Nature, 52
and conflict strategy, 70, 104
dissertation, 59–61
economic game theory and, 32, 60, 220, 240
evolutionary game theory and, 74–75, 80, 83, 89, 124, 223, 241
fixed-point theorems and, 58–59
gas laws and, 140, 201
hawk-dove game, 228–229
Hobbes's social preferences as, 129
limitations, 209
network, 163, 166
payoff matrix, 62
principle, 57–58
Prisoner's Dilemma, 61–64
probability theory and, 199, 200, 208–209, 212
public goods game, 61, 64–66
quantum mechanics and, 187
in social interactions, 175
zero-sum game, 225–227
National Science Foundation, 115, 165
Natural law, 19, 128.
See also Code of Nature
Natural selection, 24–25, 78.
See also Evolutionary game theory
Nature vs. nurture controversy, 121–124
Networks.
See also Social networks actors, 144–145, 153, 154–155–156, 157, 245
airline, 155
applications, 147–148, 149, 151, 160–161, 166
biochemical, 151, 160–161
clusters/clustering coefficient, 149, 152, 153–154, 157
and Code of Nature, 145, 163
commonalities, 151
competitive interactions, 160, 161, 166
degree coefficient, 154
degrees of separation, 145–146, 149, 154, 155–156
evolution, 151, 157–158, 159–163
game theory and, 145, 159–163, 222, 235
growth, 151, 157, 163, 167–168
hubs, 154, 155, 157, 161
Internet, 146, 149, 158, 160
Kevin Bacon game, 144–146, 149
links, 148–149, 150, 152, 155, 156, 158–159
mathematical models, 153–154, 159
Nash equilibrium, 163
in nature, 151, 153, 158, 160–161
neural, 151, 153, 157
nodes, 148, 150, 151, 152, 154, 155–156
origins, 148, 149–151
path length, 153, 154
power grids, 157
and power laws, 156–157
preferential attachment, 157, 158, 160, 163
and quantum physics, 235
random connections, 148, 149, 152, 154, 155–156
regular lattice, 151–152, 154, 155
scale-free, 156–157, 159, 163, 246
self-organization, 157
small-world (intermediate) model, 149–153, 154, 156, 157, 158
statistical mechanics and, 5, 143, 145, 163, 166, 180
strategy, 161–162
strongly connected components, 159
ubiquitousness, 146–147, 153, 159
World Wide Web, 147, 149–150, 157, 158–159, 160
Neurobiology.
See also Brain game theory applications, 3, 6, 8
Neuroeconomics, 174
animal studies, 99–100
brain chemistry and processes, 94–95, 99–102, 105
and Code of Nature, 92, 102, 106–109
hormone changes, 105–106
landmark research, 99, 106
principles, 3–4
risk takers (matchers) vs. conservatives (optimizers), 101–102
trust-related brain activity, 103–106
utility, 99–100
New York University, 99
Newton, Isaac, 2, 21, 26, 35, 69, 135
Newtonian determinism, 130
Newtonian physics, 12, 21, 128, 129, 130
Noncooperative games
math for, 200
Nash's theory, 51, 52, 59–61
and statistical physics, 201
Northern Illinois University, 120
Northwestern University, 11
Notre Dame University, 156
Nowak, Martin, 75–76, 85, 86, 87, 88, 89, 90
O
Opinion formation and transmission, 167–168, 169, 171–173, 174
Origin of Species (Darwin), 24, 26
Orma (Kenya), 116, 117–118, 220
Osama bin Laden, vi
Oxytocin, 105–106
P
Pacheco, Jorge, 163
Pack behavior, 169, 171
Page, Scott, 178–179, 180
Paley, William, 24, 25–26
Paradoxes
perfect future knowledge, 34–35
Pascal, Blaise, 130, 197–198, 248
Pelorat, Janov, 5
Penny flipping game, 61, 141, 182–183, 186–189, 208
Perfect future knowledge, 34–35
Perfect information, 33
Petty, William, 129
Pfeiffer, Thomas, 160, 161
Phase transitions, 169, 170, 171
Physics.
See also Newtonian physics;
Sociophysics;
Statistical mechanics
and economic game thoery, 165, 167, 180–181
game theory applications, 4, 7, 8, 36
Physiocrats, 15, 16
Pinker, Steven, 112–113
Platt, Michael, 99
Pocket calculators, 1
Poe, Edgar Allan, 61
Poisson, Siméon-Denis, 132
Poker, 30, 68, 75, 239
bluffing, 43, 48
Political economy, 12, 17, 20–21, 25
Political science, 3
Power laws, 156–157
Prediction of human behavior, 111
Preference. See Social preferences;
Utility
Preferential attachment, 157, 158, 160, 163
Price, George, 77–78, 241
Princeton University, 2, 18, 35, 51, 55, 100, 106, 224
Principia (Newton), 35, 69, 129, 219
Prisoner's Dilemma, 61–64, 71, 87, 88, 107, 161–162, 163, 189, 192, 193, 240
Probability distributions
adjustment, 214–215
in game theory, 140–142, 209–210
of gas molecules, 140–142
measuring uncertainty in, 205–207
of mixed strategies, 140, 200, 208, 210–211, 215, 238
quantum mechanics and, 196
Probability theory, 130–131, 132.
See also Statistics
applications, 208
early pioneers, 204, 248
and game theory, 140–142, 198, 199–202, 208–214
ignorance and, 205–208, 211
and information theory, 202–208
inventor, 197–198
and Nash equilibrium, 199, 200, 208–209
objective view, 203–204
Pascal's wager, 198, 211, 248
and psychohistory, 199, 214–215, 221
role in science, 197, 198–199, 202–203
and statistical physics, 142, 199, 220–221, 247
subjective view, 202–204
voting games, 214
Profit maximization. See Utility
Psychohistory, vi.
See also Sociophysics
Code of Nature model, vii, 8–9, 109, 113–114, 164, 181, 199, 219
hybrid research disciplines, 164–165
and manipulation of society, 174
probability theory and, 199, 214–215, 215, 221
and statistical mechanics, 4–5, 42, 125, 126–128, 178, 219
Psychology, 3, 69, 215.
See also Evolutionary psychology
Public goods game, 61, 64–66, 90–92, 117–118, 194
Punishment, 90–92, 103, 107, 116, 242
Purdue University, 214
Q
Quantum communications, 189–192
Quantum game theory, vii, 7, 181
applications, 185, 189–190, 193–194
and Code of Nature, 195
communication systems, 189–192, 247
and evolutionary game theory, 195
Nash equilibrium, 187
origins, 185–189
penny flipping game, 182–183, 186–189, 247
Prisoner's Dilemma, 189, 192, 193
public goods game, 194
quantum computing and, 183, 185–186, 187
strategies, 185, 187, 188–189, 193, 195
voting application, 185, 190, 194–196
Quantum information physics, 187–188
Quantum mechanics
entanglement, 192–194, 195, 247
mathematical formulation, 29
multiple realities, 183, 184–185, 196
observation effects (decoherence), 184–185, 193
probability distributions, 196
pure and mixed states, 186
qubits, 187, 190–192
von Neumann and, 29, 185–186
Quartz, Steven, 122
Queen of Blood (film), 155
Quesnay, François, 15–16, 17, 125
Quetelet, Adolphe, 131, 132–134, 136–137, 138, 139, 199, 219
R
Rand Corporation, 2, 29, 246
Random
factors, 32, 34, 48
network connections, 148, 149, 152, 154, 155–156
number generator, 48
Rapoport, Anatol, 88, 245
Rathbone, Basil, 155
Rationality, 12
animals, 241
culture and, 115
defined, 67
emotions and, 95–96, 97, 115
game theory and, 21, 67, 69, 209
limited or bounded, 201, 209
natural selection as, 78
Reciprocal altruism, 86
Rényi, Alfréd, 148, 149
Repeated-games approach, 71, 163
Reputation, 87, 89
Reward, brain processes, 99–100, 107
Ricardo, David, 31
Risk taking, 101–102
Robert Wood Johnson Medical School, 122
Roth, Alvin, 63
Royal Swedish Academy of Sciences, 70
Rubenstein, Ariel, 68
Russell, Bertrand, 197
Rustichini, Aldo, 106
S
Samuelson, Paul, 52–53
Sanfey, Alan, 103–104
Santa Fe Institute, 165, 176, 180, 200
Santos, Francisco, 163
Savage, Leonard, 211–212, 249
Schelling, Thomas, 70–71
Schuster, Stefan, 160, 161
Schweber, Silvan, 24
"Science of man," 14
Sejnowski, Terrence, 122
Seldon, Hari, v–vi, 1, 4–5, 30, 34, 42, 113–114, 125, 137, 163, 174, 219
Self-interest/selfishness, 12, 21–23, 25, 31, 63, 69, 76, 104, 106–107, 110, 111–112, 116, 161, 162, 178
Self-organization, 157
Selten, Reinhard, 2
Set theory, 30, 33
Shannon, Claude, 204–205
Shor, Peter, 191
Shubik, Martin, 180–181
Sigmund, Karl, 87, 88
Simon, Herbert, 53
Skinner, B. F., 98
Small-world model, 149–153, 154, 156, 157, 158
Smith, Adam, 9, 12–26, 31, 35, 78, 106–107, 128, 219
Smith, Eric, 180–181
Smith, Roger, 11, 20–21
Snowdrift game, 162–163
"So long sucker" game, 61
Social cognitive neuroscience, 165
Social interactions.
See also Social networks
behavioral game theory and, 96–97, 108, 142, 174–175
magnetism analogy, 169–173
minority game, 175, 176–177
modeling, 68–69
molecular collision analogy, 153, 166, 168, 173, 201, 210
Nash equilibrium, 175
opinion formation and transmission, 167–168, 169, 171–173, 174
pack/crowd behavior, 170, 171
Social networks
acceptance of research on, 167
clustering property, 154, 157
contagion model, 173–175
degrees of separation, 145–146
evolutionary game theory and, 159–160, 162–163
growth of, 167–168, 224
links between nodes, 148–149
mathematical modeling, 159
Nash equilibrium and, 166
power laws and, 157
small-world property, 151
and statistical mechanics, 166
terrorist, 167
Social physics, 244.
See also Sociophysics
Social preferences, 111–112, 129
Social sciences, 3
Buckle's philosophy, 137–138
crime rates, 133–134
and game theory, 30, 38, 50, 53, 70, 119, 180
Hobbes theory, 129
long-term cooperative behavior, 71
metaphysical vs. scientific approach, 137–138
physics and, 132–135, 142–143
and statistics, 5, 129–132, 133–134, 138–139
Social validation model, 171–173
Sociobiology, 120, 223.
See also Evolutionary psychology
Socionomics, 165
Sociophysics.
See also Psychohistory computer simulations, 180
cultural diversity and, 177–181
and game theory, 175–177
magnetism analogy, 169–173
Nash equilibrium and, 60, 200
networks and, 145, 163, 166
and physics, 60
probability theory and, 132–135
Quetelet's average man, 133, 139
resistance to, 166–169
statistical mechanics, 142–143, 165, 166, 168–169, 174, 175, 199, 200, 210
temperature of society/players, 39–43, 165, 169, 173, 213, 214, 249
Specialization, 25, 78, 108
Spite, 63, 111
Stability. See Nash equilibrium
Stag hunt game, 61
Stalemate, 172
Stanford University, 61
Star Trek:
The Next Generation (TV), 182–183, 188
Statistical mechanics (physics)
applications, 128, 132–143, 166, 219, 221
and Asimov's psychohistory, 4–5, 42, 125, 126–128, 178, 219
canonical ensemble, 207–208
and Code of Nature, 128, 163
game theory and, vi, 4–5, 6, 7, 39–43, 128, 199–202
and kinetic theory of gases, 127–128, 135–140, 168–169, 175, 200, 210, 221
and maximum entropy principle, 201–202, 205–206, 213–214
mean-field theory, 175
network math and, 5, 143, 145, 163, 166, 180
noncooperative games and, 201
of phase transitions, 169, 170, 171
predictive powers, 127, 211–212
and probability theory, 142, 199, 220–221, 247
and social interactions, 142–143, 165–166, 174, 175, 199
Statistics.
See also Probability theory
Bayesian, 203
free will and, 134–135, 138
Gaussian distribution, 131, 139
interpreting, 134
measurement error, 130–131, 133, 139, 203
probability distributions, 140–142
and probability theory, 130–131, 132
Quetelet's average man, 133
social, 128–132
uncertainties, 131
Stauffer, Dietrich, 164, 173
Steiger, Rod, 154, 245
Stewart, Dugald, 20, 24
Stock market crashes, 171
Strategies.
See also Cooperation;
Noncooperative games
advantageous arrangement, 32–33, 49
altruism, 3, 77, 85–86, 87–88, 90, 92, 107, 111, 117, 161, 162
betrayal, 61–64
coalitions, 54, 58, 66
communication of, 193–194
conflict, 70, 83
cost of computing, 212–213
cultural diversity and, 114–119, 178–180
cultural evolution and, 111–112, 116–117, 124
defection, 64–66, 87, 88, 89, 90, 107, 193
defined, 42
eavesdropping, 81–83
in economic theory, 37, 42–43, 104–105
evolutionary, 78, 79, 81–82, 86–90, 107, 124–125
free-riding, 64–66, 90, 194
generous tit-for-tat, 89
mathematical principles, 32–33
minimax approach, 32, 43–49, 239
military example, 45–46
mixed, 42–44, 46–49, 54, 58, 64, 65–66, 80, 81, 91, 108, 118, 124, 140, 199, 220, 238, 239
network, 161–162
non-zero-sum games, 44
payoff matrix, 44–46, 49, 62, 80
population proportion and, 80
probability distributions, 140, 200, 208, 210–211, 215, 238
pure, 42–44, 220
quantum game theory, 185, 187, 188–189, 193, 195
random selection of, 48, 49, 141-142
reciprocation, 64, 65–65, 86–87, 90–92, 117
rules for behavior, 42–43, 179–180
self-interest/selfishness, 12, 21–23, 25, 31, 63, 69, 76, 104, 106–107, 110, 111–112, 116, 161, 162, 180, 194
social norms and expectations and, 194
social preferences and, 111–112
spectating, 81–83
strong reciprocity, 90
terrorist, 72
tit-for-tat, 87–90
zero-sum games, 33, 43–44, 54
Strategy of Conflict (Schelling), 70
Strogatz, Steven, 149–151, 152, 153, 154, 156, 157, 174
Sutherland, Donald, 155
Sympathy, 23, 107
Sznajd-Weron, Katarzyna, 169, 171–173