Absolute value, 473 second-price sealed-bid, 397 Action, 13 silent-exit, 391 Action combination, 13 Vickrey, 397 Action set, 13 Auditing, 100 Advertising, 348, 350 Authority (medium), 205 Affiliation, 425 Axelrod tournament, 169 Affine transformation, 82 Agent, 182 All-pay , 399 , 129 Almost , 65 Bagehot Model, 260 Amazon auction, 391 Bandit Anonymity, 360 two-armed bandit, 60 Argentina, 1 Bankruptcy constraint, 212, 240 Ascending auction, 390 Bargaining, 409, 469 Assumptions, 2 Battle of the sexes, 28, 35, 103 Assurance game, 35 Bayesian equlibrium, 56 Asymmetric information, 51 Beer-Quiche game, 174 Auction, 127 Behavior , 98 Belief all-pay, 399 posterior, 56 Amazon, 391 Beliefs, 324 ascending auction, 390 , 49, 64 common-value, 387 complete robustness, 164 descending, 398 concordant, 49 dollar, 402 forward induction, 173 Dutch, 398 intuitive criterion, 163, 174 eBay, 391 mutual knowledge, 49 English auction, 390 out-of-equilibrium beliefs, 159 first-price, 392 passive conjectures, 160, 163 first-price sealed-bid, 392 posterior, 57 loser-pays, 402 prior, 55 open-cry auction, 390 prior beliefs, 57 open-exit auction, 390, 391 Bertrand, 90, 101, 437 private-value, 386 Best reply, 19 second-price, 397 , 19, 88

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Bilateral trading, 370 , 139, 194, 245 Bimatrix game, 23 individual rationality constraint, 195, 203 Biology, 123, 151 interim participation, 269 Blackboxing, 3, 118 nonpooling constraint, 323 Boiling-in-oil contract, 197 nonseparating constraint, 247 Bottle Imp, The,117 participation constraint, 194, 203, 245 Boundary, 32 self-selection, 245 Bourgeois strategy, 146 Continuous function, 476 Branch, 43 Continuous strategy space, 87 Bridge, 98 Continuum, 73, 99, 476 Brouwer fixed point theorem, 484 Continuum of Nash equilibria, 76 Budget-balancing constraint, 228, 295 Contract Burning money, 173 boiling-in-oil, 197 efficiency wage, 211, 235 first-best, 194 Capacity, 468 forcing, 187 Capacity constraints, 437 full-insurance, 225 Cardinal utility, 33 linear, 187 Cascade, 61 menu of contracts, 292 Certainty, 50 second-best, 194, 237 Chainstore paradox, 129 selling the store, 199 Chatterjee–Samuelson Mechanism, 375 shifting support scheme, 199 , 80, 286 threshold, 187 Chicken, 99, 358 Contractible, 192 Closed interval, 474 Contraction, 476 Closed loop, 122 Contribution games, 83 Cloud, 46 Convex function, 476 Co-opting, 236 Convex set, 476 Coalition, 380 Cooperate, 34 Coalition-proof , 120 Cooperative game, 21, 88 Coarsening, 47 Coordination games, 29, 83 Coarser, 47 Correlated strategy, 80 Coase conjecture, 469 Correspondence, 476 Coinsurance, 225 Countersignalling, 345 Colonel Blotto games, 101 Cournot, 87, 94, 102, 104, 175, 433, 467, 470 Common knowledge, 49, 64, 176 Cournot–Nash equilibrium, 89 Common-value auction, 387 Cream skimming, 257 Communication, 33 Cross-checking, 87 Compact, 475 Cumulative density function, 481 Comparative statics, 449 Competition constraint, 247 Competitive fringe, 101 Decision theory, 12 Complementary inputs, 453 Decision tree, 15 Complements, strategic, 102 Deductible, 225 , 51, 53 Defect, 34 Complete robustness, 164 Descending auction, 398 Completely mixed, 70 Deviations, 34 Concave function, 476 Differential games, 99 Concordant beliefs, 49 Differentiated Bertrand game, 449, 470 Conditional likelihood, 57 Differentiation Congestion, 468 vertical differentiation, 454 Constraint Dimensionality, 132 bankruptcy, 212, 240 Discontinuous reaction function, 97 budget-balancing, 228, 295 Discoordination games, 83 capacity, 437 Discount factor, 486 competition, 247 Discount rate, 486

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Discounting, 131, 486 Equilibrium refinement, 28 Discrete strategy spaces, 87, 96 Equilibrium strategies, 18 Dollar Auction, 402 ESS, 143 Dominance, 20 Evolutionarily stable strategy, 143 stochastic, 203, 489 Evolutionary dynamics, 147 Dominance solvable, 24 Exemplary theory, 2 Dominant strategy, 20 Exemplifying theory, 2 Dominant-strategy equilibrium, 20 Existence, 95, 434, 467 Dominant-strategy mechanism, 295 Expected externality mechanism, 377 Dominated Exponential distribution, 481 weakly, 23 Extensive form, 43 Dominated strategy, 20 Extrinsic uncertainty, 80 dominates, 489 Double auction mechanism, 372 Double-sided moral hazard, 202 Feedback, 122 Duels, 77, 124 Finer, 47 Durable monopoly, 462 First-best contract, 194 Dutch auction, 398 First-mover advantage, 29, 94 Dynamic consistency, 122 First-order condition, 72 Dynamic programming, 473 First-order condition approach, 195 First-order stochastic dominance, 489 First-price auction, 392 eBay auction, 391 First-price sealed-bid auction, 392 Econometrics of estimating Fixed point theorems, 473, 484 models, 99 Brouwer fixed point theorem, 484 Edgeworth paradox, 437, 440 Kakutani fixed point theorem, 485 Efficiency wages, 211, 235, 241 Focal points, 32 Efficient rationing, 437, 468 Folk theorem, 131 End node, 43 Forcing contract, 187 End point, 43 Ford, Henry, 264 English auction, 390 Forgiving, 170 Entry deterrence, 111 Forward induction, 173 epsilon equilibrium, 148 Four P’s, 93 Equilibrium, 18 Full insurance, 225 Bayesian, 56 Fully insured, 223 Bertrand equilibrium, 90 Fully revealing, 248 coalitionproof equilibrium, 120 Cournot–Nash equilibrium, 89 epsilon, 148 Game theory, 11 iterated-dominance equilibrium, 23 history, 6, 34 maximin equilibrium, 134 Game tree, 16, 43 Nash equilibrium, 26 Games perfect Bayesian equilibrium, 158, 159, 173 bimatrix games, 23 perfect Markov equilibrium, 142 Colonel Blotto games, 101 pooling equilibrium, 163, 247 contribution games, 83 , 161, 163, 246, 247 cooperative games, 88 , 158 coordination games, 29, 83 Stackelberg equilibrium, 101, 123 differential games, 99 strong equilibrium, 117 discoordination games, 83 perfect equilibrium, 109 matrix games, 23 weak equilibrium, 117 nonzero-sum games, 25 Weak-dominance equilibrium, 23 one-shot games, 129 Equilibrium concept, 18 timing games, 77 Equilibrium , 18 two-by-two games, 81 Equilibrium path, 108, 171 variable-sum games, 25 Equilibrium point, 35 zero-sum games, 25

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Gang of Four models, 167, 172 Interbuyer price discrimination, 296, 299 Generically, 476, 485 Interim participation constraints, 269 Genovese, Kitty, 83 Interquantity price discrimination, 296 Good news, 489 Interval Gratitude, 150 closed interval, 474 Greatest lower bound, 475 open interval, 474 Gresham’s law, 269 Intuitive criterion, 163, 174 Grim strategy, 130 Invade, 143 Groves Mechanism, 293, 318 Invariance, 359 Inverse-intensity rationing, 438 Invertible, 194 Harsanyi doctrine, 54 Irrationality, 123 Hawk–Dove game, 144 Iterated-dominance equilibrium, 23 Hazard rates, 490 High-to-low rationing, 437 History of game theory, 6 Kakutani fixed point theorem, 485 Hold-up potential, 218 Kyle model, 261 Hotelling location game, 446 Hotelling pricing game, 442 Lattice, 477 Least upper bound, 475 Least-cost avoider principle, 217 Imperfect information, 49 Likelihood, 57 Implicit function theorem, 186, 450 conditional, 57 Incentive compatibility constraint, 139, 194, marginal, 56, 57 245 Limit pricing, 175, 341, 342 Incomplete information, 51, 53 Linear contract, 187 Incomplete information folk theorem, 169 Linear equilibrium, 373 Increasing differences in parameters, 453, 483 Linkage principle, 427 Increasing differences in strategies, 453, 483 Location models, 441 Independence, 387 Lognormal distribution, 482 Independence of irrelevant alternatives, 360 Loser-pays auction, 402 Indifference curves, 186, 303 Low-to-high rationing, 439 Individual rationality constraint, 195, 203 Induction backward, 129 Madman theory, 123 forward, 173 Marginal likelihood, 56, 57 Infimum, 475 Marginal revenue approach, 409 Infinite horizon model, 137 , 98, 142 Information Marshall, Alfred, 6 almost perfect information, 65 Maskin Matching Scheme, 279, 370 asymmetric information, 51 Matrix game, 23 certainty, 50 Maximand, 478 complete information, 51, 53 Maximin equilibrium, 134 imperfect information, 49 Maximin strategy, 133 incomplete information, 51, 53 Mean-preserving spread, 478, 489 perfect information, 49 Measure zero, 478 private information, 51 Mechanism, 370 symmetric information, 51 Chatterjee–Samuelson, 375 uncertainty, 50 dominant–strategy, 295 Information partition, 47 double auction, 372 Information set, 14, 45 expected externality, 377 Informational rents, 296, 311 Mediation, 33 Informed player, 182 Menu of contracts, 292 Insurance, 203, 222, 264, 274 Metric, 478 Integration by parts, 477 payoff, 132 Intensity rationing, 437, 438 Minimax strategies, 132

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Minimax theorem, 135 Open-set problem, 24, 117 Minimax value, 132 Opportunism, 218 Mixed extension, 70 Order of play, 14, 43 Mixed strategy, 69 Ordinal utility, 33 Mixing density, 395 Out-of-equilibrium behavior, 63, 173 Modelling by example, 172 Out-of-equilibrium beliefs, 159 Monitoring, 100, 232, 238 complete robustness, 164 Monotone likehood ratio property, 203 forward induction, 173 Monty Hall, 66 intuitive criterion, 163, 174 Moral hazard, 192 passive conjectures, 163 double-sided, 202 Outcome, 15 Moral hazard with hidden knowledge, 277 Outcome matrix, 41, 64 Move, 13 Overlapping generations model, 141, 151 Multiple equilibria, 19, 335 Overtaking criterion, 148 Mutual knowledge, 49 Myerson–Satterthwaite model, 369, 383 Pareto strongly Pareto-dominates, 21 Nash bargaining solution, 359, 382 weakly Pareto dominates, 21 Nash equilibrium, 26 Pareto perfection, 120 Nature, 13 Pareto-efficient, 22 New York, 32 Partial adverse selection, 252 Niceness, 169 Partial insurance, 225 No-fat modelling, 2 Participation constraint, 194, 203, 245 Node, 43, 64 Partition end node, 43 information, 47 end point, 43 Passive conjectures, 160, 163 predecessor, 43 Path, 43 starting node, 43 equilibrium, 108, 171 successor, 43 Payoff, 13, 97 Noisy duel, 77 minimax payoff, 132 Nonconcave payoff function, 97 Payoff-equating method, 74 Noncontractible, 224 Peacock’s tail, 348 Nonconvex strategy space, 96 Perfect Bayesian equilibrium, 158, 159, 173 Noncooperative game, 21 Perfect information, 49 Nonlinear pricing, 296, 300 Perfect Markov equilibrium, 142 Nonpooling constraint, 247, 323 Perfect price discrimination, 296, 298 Nonresponders, 468 Perfect recall, 98 Nonseparating constraint, 247 Perfection, 122 Nonverifiable, 224, 280 Perfectness Nonzero-sum game, 25 perfect Bayesian equilibrium, 158, 159, 173 Normal distribution, 482 subgame perfectness, 18, 108 Normal form, 41 trembling-hand perfectness, 158 Perpetuity, 478 Philosophy, 34 Oligopoly, 471, 472 Players, 13 One-price equilibrium, 373 Nature, 13 One-shot game, 129 pseudo-players, 13 One-sided asymmetry, 381 Pliny, 124 One-sided prisoner’s dilemma, 34, 136 Poker, 52 One-to-one, 478 Police game, 100 Open interval, 474 Pooling equilibrium, 163, 247 Open loop, 122 Postcontractual adverse selection, 277 Open strategy space, 96 Posterior belief, 56, 57 Open-cry auction, 390 Predecessor, 43 Open-exit auction, 390 Price cap, 304

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Price discrimination, 181, 296, 315, 318, Rent dissipation, 402 382, 471 Rents interbuyer, 296, 299 informational, 296, 311 interquantity, 296 Repeated prisoner’s dilemma, 129, 177 nonlinear pricing, 296, 300 Reports, 370 perfect, 296, 298 Reputation, 136 Price dispersion, 263 Reservation utility, 185, 195 Principal, 182, 201 Reserve price, 409 Principal–agent models, 182 Residual claimant, 199 Prior beliefs, 55, 57 Responders, 468 Prisoner’s dilemma, 20 , 282, 314 one-sided prisoner’s dilemma, 136 Revenue equivalence theorem, 403 Private information, 51 Risk, 487 Private-value auction, 386 Risk aversion, 115, 194, 241, 255, 487 Procurement, 316 Risk neutral, 487 Producers, The, 195 Profile, strategy, 17 Proof, 4 proportional rationing, 439 Schelling, Thomas, 32 Provocability, 169 Scissors-Paper-Stone, 98 Pseudo-players, 13 Screening, 330, 348 Pure strategy, 69 Second-best contract, 194, 237 Second-mover advantage, 94 Second-order stochastic dominance, 489 Quadratic formula, 479 Second-price auction, 397 Quadratic utility function, 102 Second-price sealed-bid, 397 Quality, 138 Security value, 132 Quantity discount, 315 Self-selection constraint, 245 Quasi-concave, 478 Selling the store, 199 Quasilinear utility, 478 Sender-receiver game, 284 Separability, 148, 203, 462 Separating equilibrium, 161, 163, 246, 247 Rao-Blackwell Theorem, 203 Sequential equilibrium, 158 Ratchet effect, 315, 319 Serially undominated, 24 Rate-of-return regulation, 304 Service flow, 462 Rational expections, 35 Settlement range, 116 Rationalizable strategy, 35 , 380 Rationing, 437 Share auctions, 428 efficient rationing, 437, 468 Shaw, George Bernard, 4 high-to-low rationing, 437 Shifting support scheme, 199 intensity rationing, 437, 438 Signal jamming, 341, 342, 351 inverse-intensity rationing, 438 Signalling, 320, 348 low-to-high rationing, 439 Silent duel, 77 proportional rationing, 439 Silent-exit auction, 391 Reaction functions, 88, 434 Single-crossing property, 301, 302, 324 discontinuous reaction functions, 97 Singleton, 47 Realizations, 13 Slack, 237 Rebel Without a Cause,99 Smooth supermodular game, 453 Recoordination, 120 Smooth supermodularity, 482 Refinement, 47 Soccer, 98 Refinements, equilibrium, 28, 324 , 18 Regression to the mean, 60 Splitting a pie, 357 Renegotiation, 218 Stability, 89 Renegotiationproofness, 120 Stackelberg equilibrium, 89, 101, 123

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Stackelberg follower, 89 Switching costs , 141 Stackelberg game, 94 Symmetric information, 51 Stackelberg leader, 89 Synergism, 468 Stackelberg warfare, 101 Starting node, 43 State of the world, 53 Take-it-or-leave-it offer, 185 State-space diagram, 222, 274 Team, 227, 240 Stationary, 172 Team theory, 238 Stochastic dominance, 203, 489 Tender Trap, 35 Strategic complements, 94, 102, 453 Testing, 266, 272, 273 Strategic form, 41 Three-step procedure, 195 Strategic substitutes, 94, 102 Threshold contract, 187 Time consistency, 122 Strategically equivalent, 398 Time line, 44 Strategy, 17 Timing games, 77 behavior, 98 Tit-for-Tat, 130, 147, 167, 169 bourgeois, 146 Tournaments, 101, 214, 236 completely mixed, 70 Tremble, 99, 110 correlated strategy, 80 Trembling-hand perfectness, 158, 398 evolutionarily stable strategy, 143 Trigger strategies, 149 grim, 130 Triopoly, 104 Markov strategy, 98, 142 Truth-telling, 283 maximin , 133 Tucker, Albert, 33 minimax, 132 Two-Armed Bandit, 60 mixed, 69 Two-by-two games, 20, 33, 81 pure , 69 Two-part tariff, 318 rationalizable, 35 Two-sided asymmetry, 381 tit-for-tat, 130, 147, 167, 169 Type, 53 trigger, 149 weakly dominant, 23 Strategy combination, 17 , 358 Strategy profile, 17 Unbounded strategy space, 96 Strategy set, 17, 111 Uncertainty, 50 Strategy space, 17 Uniform distribution, 481 discrete, 87, 96 Uninformed player, 182 nonconvex, 96 Uniqueness, 19, 103, 467 open, 96 Unobservable, 224 unbounded, 96 Unravelling, 281, 316 Strict, 479 Utility Strong equilibrium, 117 cardinal, 33 ordinal, 33 Strongly Pareto-dominates, 21 quadratic, 102 Subgame, 109, 157 quasilinear utility, 478 Subgame perfect Nash equilibrium, 109 reservation, 185, 195 Subgame perfectness, 18, 108 von Neumann-Morgenstern utility, 51, 65 Substitutes, strategic, 94, 102 Successor, 43 Sufficient statistic condition, 197, 202 Value Summation, 473 minimax value, 132 Sunspot models, 80 Variable-sum game, 25 Supergame, 149 Vengeance, 150 Supermodular games, 449, 482 Verifiable, 192 Supermodularity, 95, 452, 482 Vertical differentiation, 454 Support, 479 Vickrey auction, 397 Supremum, 475 von Neumann–Morgenstern utility, 51, 65 Swiss Cheese Game, 82 Voting, 125

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The Wallet Game, 424 Wicksteed, 4 War of Attrition, 76, 99, 107, 402 Winner’s Curse, 408, 414, 429 Weak, 479 Weak equilibrium, 117 weak-dominance equilibrium, 23 Yardstick competition, 214 Weakly dominant strategy, 23 Weakly dominated, 23 Weakly Pareto-dominates, 21 Zero-sum game, 25

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