## index

*Page numbers in boldface indicate pages on which objects are defined*.

A B C D E F G H I J K L M N O P Q R S T U V W Z

- Action
- extensive game with imperfect information,
**Definition 200.1** - extensive game with perfect information,
**Definition 89.1** - strategic game, 11

- extensive game with imperfect information,
- Action-determined beliefs,
**Definition 232.1** - ADD (Shapley value axiom), 292
- Addition of a superfluous move
- equivalence of extensive games, 206

- Additive coalitional game,
**Exercise 261.2** - Additivity axiom of Shapley value, 292
- Agent strategic form,
**250** - Agree to disagree, 75
- Agreements, set of
- bargaining game, 118
- Nash solution, Definition 300.1

- Air strike, Exercise 36.2
- Allocation
- competitive,
**269** - market with transferable payoff, 264

- competitive,
- Alternating offers bargaining,
*see*bargaining game of alternating offers - Approachable mixed strategy equilibrium, 42
- Armies, Exercise 101.3
- Assessment, 221,
**Definition 222.1**- consistent,
**Definition 224.2**

- consistent,
- Asymmetric abilities/perceptions, 6
- Asymmetric Nash solution,
**309** - Auction, Example 18.1
- first price, Exercise 18.2
- second price, Exercise 18.3
- imperfect information, Example 27.1

- Automaton,
*see*machine - Axiomatizations of the core, 275
- Axioms
- for knowledge function, 69-70
- for Nash solution, 305-307
- for Shapley value, 292

- Bach or Stravinsky?, Example 15.3
- Bayesian game, Exercise 27.2
- correlated equilibrium, 44, Example 46.1
- interpretation of mixed equilibrium, 40
- mixed extension, Example 34.1
- Nash equilibrium, Example 15.3
- with outside option, Example 110.1

- Backwards induction, 99
- Balanced contributions property for coalitional games,
**Definition 291.1** - Balanced game/collection of weights,
**262** - Balancing counterobjection,
*see*counterobjection - Bargaining game of alternating offers,
**120**- constant cost of delay, Exercise 125.2
- equilibria with delay, Exercise 125.2
- importance of procedure, 127
- more than two players, 130
- multiple equilibrium outcomes, Exercise 125.2, Exercise 128.1
- Nash equilibria, 121
- and Nash solution, 310-311
- opting out, 128
- pie with discrete elements, Exercise 128.1
- properties of subgame perfect equilibria, 125
- risk of breakdown, 129
- relation with Nash solution, Proposition 310.3

- subgame perfect equilibria, 121-127
- characterization, Proposition 122.1

- variant for coalitional game, Exercise 296.1
- variant with one party proposing, Exercise 127.1
- variant with simultaneous proposals, 127

- Bargaining problem (Nash),
**Definition 300.1** - Bargaining set of coalitional game,
**Definition 282.1**- and kernel, Lemma 285.1

- Bargaining solution,
**Definition 301.1**, 308- Nash,
**Definition 301.2**

- Nash,
- Battle of the sexes,
*see*Bach or Stravinsky? - Bayesian extensive game,
**Definition 231.1**- perfect Bayesian equilibrium,
**Definition 232.1**

- perfect Bayesian equilibrium,
- Bayesian game,
**Definition 25.1**- common prior belief, 75
- extensive with observable actions,
**Definition 231.1** - Nash equilibrium,
**Definition 26.1** - signaling game,
**237**

- Beer or Quiche, Example 244.2
- Behavioral strategy,
**Definition 212.1**- completely mixed, 224
- Nash equilibrium,
**216** - outcome-equivalence with mixed strategy, 214

- Belief system, 223
- Beliefs
- constraints in extensive game
- common beliefs, 222
- consistency with strategies, 221
- structural consistency, 222,
**Definition 228.1**

- mixed strategies, 43
- rationalizability, 54

- constraints in extensive game
- Best response function,
**15** - Best response to belief
- action not strictly dominated, Lemma 60.1
- action not weakly dominated, Exercise 64.2

- Biological example, Example 49.2, 49
- Bondareva-Shapley theorem, Proposition 262.1
- BoS,
*see*Bach or Stravinsky? - Bounded rationality, 6, 164
- Breakdown in bargaining, 129
- Burning money game, Example 111.1

- Card game, Exercise 217.3
- Centipede game, 106
- Chain-store game, 105
- perturbation, Example 239.1

- Chance moves in extensive game
- imperfect information, 201
- perfect information, 101

- Chess, 6, 100
- Chicken, 30
- Choice rule/function,
**178**- monotonic,
**Definition 186.1** - no veto power,
**Definition 187.1**

- monotonic,
- Choice theory, 4
- Choice under uncertainty, 4, Exercise 71.2
- Clarke-Groves game forms, 183
- Coalescing of moves
- equivalence of extensive games, 207
- sequential equilibrium, Example 226.2
- trembling hand perfect equilibrium, Exercise 252.2

- Coalition, Definition 257.1
- Coalitional game
- nontransferable payoff,
**Definition 268.2**- bargaining set, kernel, 284, 298
- core,
**Definition 268.3** - exchange economy,
**269** - Shapley value, 298

- solutions,
*see*solution - transferable payoff,
**Definition 257.1**- balanced,
**262** - balanced contributions property,
**Definition 291.1** - bargaining set,
**Definition 282.1** - cohesive,
**Definition 258.1** - convex,
**Exercise 260.4** - core,
**Definition 258.2** - cost-sharing, 296
- excess of a coalition, 283
- feasible payoff vector/profile,
**258** - imputation,
**278** - kernel,
**Definition 284.1** - nonemptiness of bargaining set and kernel, Corollary 288.3
- nonemptiness of nucleolus, Proposition 288.1
- nonempty core, Proposition 262.1
- nucleolus,
**Definition 286.1** - objection,
*see*objection, counterobjection - Shapley value,
**Definition 291.2** - simple,
**Exercise 261.1** - stable set,
**Definition 279.1** - superadditive,
**258** - zerosum,
**Exercise 261.2**

- balanced,

- nontransferable payoff,
- Coalitional vs. noncooperative games, 2, 255
- Cohesive coalitional game,
**Definition 258.1** - Common beliefs, 222
- Common knowledge,
**Definition 73.1**,**Definition 73.2** - Communication, 113
- Comparative statics of risk aversion in Nash bargaining, Proposition 304.1
- Competitive equilibrium
- exchange economy,
**269**- and core, 271-274
- existence, 270

- and game theory, 3
- market with transferable payoff,
**266**- and core, 265-268
- existence, Exercise 267.2

- exchange economy,
- Competitive payoff, 266
- Completely mixed strategy, 224
- Complexity of machine, 165
- Concave function,
**7** - Consequences, set of
- coalitional game,
**Definition 268.2** - implementation theory, 178
- strategic game, 12

- coalitional game,
- Consistency
- of beliefs with strategies, 221
- of strategy with history, 213
- structural,
**Definition 228.1**

- Consistent assessment,
**Definition 224.2**- and structural consistency, 228-231

- Constituent game of repeated game, 136
- Constraints on beliefs, 221-222
- Continuous preference relation,
**7** - Convergence of core and competitive equilibrium
- exchange economy, Proposition 273.1
- market with transferable payoff, 267

- Convex coalitional game,
**Exercise 260.4**- core and Shapley value, Exercise 295.5

- Convexity of Nash bargaining problem, Definition 300.1
- Cooperative game,
*see*coalitional game - Coordinated attack problem, 85
- Coordination game, Example 16.1
- Core
- convergence to competitive equilibrium, 267, Proposition 273.1
- equal treatment in, Lemma 272.2
- exchange economy,
**271**- and competitive equilibrium, 271-274

- and generalized stable set, Exercise 280.5
- market with transferable payoff,
**264**- and competitive equilibrium, 265-268

- nontransferable payoff game,
**Definition 268.3** - and stable sets, Proposition 279.2
- transferable payoff game,
**Definition 258.2**- nonemptiness, Proposition 262.1

- Correlated equilibrium,
**Definition 45.1**- knowledge, Exercise 81.1
- rationalizability, Lemma 56.2

- Cost-sharing in coalitional game, 296
- Counterobjection in coalitional game
- bargaining set, 281
- kernel, 284
- Nash solution, 302
- nucleolus, 286
- Shapley value, 290

- Cournot duopoly
- rationalizability, Exercise 56.4

- Covariance with positive affine transformations (Nash solution), Exercise 309.1
- Crazy players, 239
- Credible objection in coalitional game, 278
- Cycling phase of machine game,
**171**

- Deductive interpretation, 5
- Dictatorial choice rule,
**181** - Disagreement outcome in Nash solution, Definition 300.1
- Discounting
- bargaining game of alternating offers, 119, 122, Example 125.1
- Nash folk theorem, Proposition 145.2
- perfect folk theorem, Proposition 151.1
- preferences,
**137** - repeated game,
**139** - structure of subgame perfect equilibria of repeated game, 153-154

- Dominance solvable, Exercise 63.2
- Dominant action, Example 18.3
- Dominant strategy equilibrium of strategic game,
**Definition 181.1** - Dominated action,
*see*weakly dominated action, strictly dominated action - Dove,
*see*Hawk-Dove - DSE (dominant strategy equilibrium),
**Definition 181.1** - DUM (Shapley value), 292
- Dummy player in coalitional game, Exercise 280.4
- axiom of Shapley value, 292

- Dynamic adjustment process, 52

- Edgeworth box, 270
- Education, Spence's model, Example 237.2
- refinement of equilibria, Example 246.1

- Eductive interpretation, 5
- Efficiency in coalitional game, 290
- Pareto (Nash solution), 305

- Efficient agreement (bargaining), 122, 125
- Electronic mail game, 81-84
- Elimination of dominated actions,
*see*iterated elimination - Endowment in market, 264
- Enforceable payoff profile/outcome,
**143** - Environment (implementation theory),
**179** - e-equilibrium, Exercise 108.1
- Equal treatment in core, Lemma 272.2
- Equilibrium,
*see*solution - Equilibrium, competitive, 266
- Equivalence of extensive games
- coalescing of moves, 207
- framing effects, 209
- inflation-deflation, 205
- interchange of moves, 208
- one-player games, Exercise 208.1
- superfluous moves, 206

- Equivalence of mixed and behavioral strategies, 214
- ESS (evolutionarily stable strategy), 50
- Event, 69
- self-evident,
**Definition 73.2**

- self-evident,
- Evolutionarily stable strategy,
**Definition 49.1**- existence, Exercise 51.1

- Evolutionary equilibrium, 48
- Evolutive interpretation, 5
- Excess of a coalition, 283
- Exchange economy,
**269**- core,
**271**

- core,
- Exchange game (Bayesian), Exercise 28.1
- Existence
- evolutionarily stable strategy, Exercise 51.1
- mixed strategy equilibrium, Proposition 33.1, 33
- Nash equilibrium, Proposition 20.3
- sequential equilibrium, Corollary 253.2
- subgame perfect equilibrium, Proposition 99.2
- trembling hand perfect equilibrium, Proposition 249.1, Corollary 253.2

- Exogenous uncertainty in extensive game
- imperfect information, 200
- perfect information, 101

- Extensive game,
**Definition 200.1**- behavioral strategy,
**Definition 212.1** - chance moves, 101, 201
- equivalence principles
- addition of superfluous move, 206
- coalescing of moves, 207
- inflation-deflation, 205
- interchange of moves, 208

- exogenous uncertainty, 101, 200
- imperfect information,
**Definition 200.1** - machine game, Exercise 174.1
- mixed strategy,
**Definition 212.1** - outcome,
**213**,**223** - perfect and imperfect recall,
**Definition 203.3** - perfect Bayesian equilibrium,
**Definition 232.1** - perfect information,
**Definition 89.1**- Nash equilibrium,
**Definition 93.1** - no indifference condition,
**Exercise 100.2** - outcome,
**93** - reduced strategic form,
**Definition 95.1** - simultaneous moves, 102
- strategic form,
**Definition 94.1** - strategy,
**Definition 92.1** - subgame,
**Definition 97.1** - subgame perfect equilibrium,
**Definition 97.2**

- Nash equilibrium,
- pure strategy,
**Definition 203.1** - sequential equilibrium,
*see*sequential equilibrium - simultaneous moves, 202
- solutions,
*see*solution - vs. strategic game, 3
- trembling hand perfect equilibrium,
**Definition 251.1**

- behavioral strategy,
- Extensive game form with perfect information,
**90**, 179 - External stability in coalitional game, Definition 279.1

- Feasible payoff profile
- coalitional game,
**258** - strategic game,
**139**

- coalitional game,
- Fictitious play, 52
- Finite extensive game,
**90** - Finite horizon extensive game,
**90**- examples, 105

- Finite strategic game,
**11** - Finitely repeated game,
**155**- Nash equilibrium, 155-157
- Nash folk theorem, Proposition 156.1
- perfect folk theorem, Proposition 160.1
- subgame perfect equilibrium, 157-160

- First mover advantage in bargaining game, 126
- First price auction, Exercise 18.2
- Fixed point theorem, Lemma 20.1
- Folk theorem,
*see*Nash folk theorem, perfect folk theorem - Forget, players who do so, 204
- Forward induction, 110-114
- Framing effects, 209
- Full dimensionality in repeated game, 151

- Game form
- extensive, 201
- extensive, with perfect information, 90

- Game theory and competitive equilibrium, 3
- Gibbard-Satterthwaite theorem, Proposition 181.2
- Groves mechanism, 184
- Guess the average, Exercise 35.1
- rationalizability, Exercise 56.5

- Guessing right, Exercise 36.1

- Hats, puzzle of, 71
- Hawk-Dove, Example 16.3, Example 49.2
- History in extensive game
- imperfect information, Definition 200.1
- perfect information, Definition 89.1

- Homogeneous weighted majority game,
**Exercise 289.2**

- IIA (Nash solution axiom), 306
- Impatience in bargaining game, 126
- Imperfect information
- extensive game,
**Definition 200.1** - strategic game, 24

- extensive game,
- Imperfect information in game models, 199
- Imperfect recall, 203
- Implementable choice rule,
**Definition 179.1** - Implementation theory, 177-196
- dominant strategy implementation, 180-185
- Nash implementation, 185-191
- and Nash solution, 311
- subgame perfect equilibrium, 191-195
- virtual SPE-implementation,
**192**

- Imputation,
**278** - Increasing function,
**7** - Independence of irrelevant alternatives (Nash solution), 306, Exercise 309.1
- Individually rational
*see*enforceable, 143- strict (Nash solution), Exercise 309.2

- Indivisible good, market for
- core, Example 260.1
- Shapley value, Example 294.4
- stable set, Exercise 280.2

- Infinitely repeated game,
**Definition 137.1**- complexity, 164
- Nash equilibrium, 143-146
- subgame perfect equilibrium, 146-154

- Inflation-deflation principle, 205
- Information
- more is better, Exercise 71.2
- more may hurt, Exercise 28.2, Exercise 48.1

- Information function,
**Definition 68.1**- partitional,
**Definition 68.2**

- partitional,
- Information partition
- correlated equilibrium, Definition 45.1
- extensive game with imperfect information, Definition 200.1

- Information set, Definition 200.1
- interpretation, 205
- nonordered, Example 223.1, Exercise 229.1

- Initial history, 90
- Interchange of moves
- equivalence of extensive games, 208

- Interchangeable equilibria
- extensive game with perfect information, Exercise 100.2
- strictly competitive game, 23

- Interchangeable players in coalitional game, 292
- Internal stability in coalitional game, Definition 279.1
- Interpretation
- forward induction, 112
- information set, 205
- mixed strategy Nash equilibrium, 37-44
- solutions, 5
- state of the world, 67
- strategic game, 13
- strategy in extensive game, 103

- Introductory phase of machine game,
**171** - Investment race, Exercise 35.2
- Irrational players, 239
- Irrelevant alternatives, independence of, 306
- Iterated elimination
- forward induction, 110-114
- and rationalizable actions, Proposition 61.2
- strictly dominated actions,
**Definition 60.2** - subgame perfect equilibrium, 108
- weakly dominated actions, 62
- and subgame perfect equilibrium, 108

- Judgment of Solomon,
*see*Solomon's predicament

- Kakutani's fixed point theorem, Lemma 20.1
- Kalai-Smorodinsky solution,
**310** - Kernel of coalitional game,
**Definition 284.1**- and bargaining set, Lemma 285.1
- and nucleolus, Lemma 287.1

- Knowledge
- common,
**Definition 73.1**,**Definition 73.2** - mutual, 73

- common,
- Knowledge and solution concepts, 76-81
- Knowledge function,
**69**,**70** - Kuhn's theorem, Proposition 99.2
- in game with chance moves, Exercise 102.1
- in game with simultaneous moves, Exercise 103.3

- Leader-follower game, Example 97.3
- Learning, 52
- Lexicographic minimality in nucleolus of coalitional game, Lemma 286.2
- Lexicographic preferences in machine game,
**165**, 172-174 - Limit of means
- Nash folk theorem, Proposition 144.3
- perfect folk theorem, Proposition 146.2
- preferences,
**138** - repeated game,
**139**

- Location game, Example 18.6
- iterated elimination of dominated actions, Exercise 63.1
- rationalizable actions, Exercise 57.1

- Long- and short-lived players in infinite game, Exercise 148.1

- Machine,
**140**,**164**- complexity, 165

- Machine game,
**Definition 165.1**- cycling/introductory phases,
**171** - extensive game and complexity, Exercise 174.1
- lexicographic preferences,
**165** - structure of equilibria, 168-174

- cycling/introductory phases,
- Majority game, Example 295.3, Exercise 295.4
- bargaining set, Example 282.2
- core, Example 259.1, Example 260.3
- kernel, Example 285.2
- stable set, Example 279.3
- weighted,
**Exercise 289.2**- nucleolus, Exercise 289.2
- Shapley value, Example 294.1

- Marginal contribution of player in coalitional game, 291
- Market for indivisible good
- core, Example 260.1
- Shapley value, Example 294.4
- stable set, Exercise 280.2

- Market with transferable payoff,
**263**- bargaining set, Exercise 283.1
- core,
**264**- nonempty, Proposition 264.2

- Markovian machine, 143
- Matching pennies, Example 17.1
- Maxminimizer,
**Definition 21.2**, 209 - Mechanism design,
*see*implementation theory - Memory, poor (extensive games that model), 204
- Message
- in Beer or Quiche game, Example 244.2
- in signaling game, 237

- Minmax payoff,
**143** - Mistakes, 247
- Mixed extension
- strategic game,
**Definition 32.1** - strictly competitive, 36

- strategic game,
- Mixed strategy
- as belief, 43
- extensive game
- imperfect information,
**Definition 212.1** - perfect information, 93

- imperfect information,
- naïve interpretation, 37
- outcome equivalence with behavioral strategy, 214
- as pure strategy in extended game, 39
- strategic game, 32

- Mixed strategy equilibrium
- approachable, 42
- and correlated equilibrium, Proposition 45.3
- extensive game,
**216** - Harsanyi's model, 41-43
- interpretation, 37-44
- knowledge requirements, Proposition 78.1
- as steady state, 38
- strategic game,
**Definition 32.3**, Definition 44.1

- Monotonic choice rule,
**Definition 186.1** - Mutation, 49
- Mutual knowledge, 73
- My aunt and I (coalitional game)
- bargaining set, Example 282.3
- generalization, Example 295.3
- kernel, Example 285.3

- Naïve interpretation of mixed strategy, 37
- Nash bargaining
- and bargaining game of alternating offers, 310-311
- comparative statics of risk aversion, Proposition 304.1
- independence of irrelevant alternatives, 306
- Pareto efficiency, 305
- problem,
**Definition 300.1** - symmetry, Definition 305.1

- Nash equilibrium
- Bayesian game,
**Definition 26.1** - behavioral strategies,
**216** - and correlated equilibrium, Proposition 45.3
- existence for strategic game, Proposition 20.3
- extensive game with perfect information,
**Definition 93.1** - finitely repeated game, 155-157
- infinitely repeated game, 143-146
- interchangeability, 23
- knowledge requirements, Proposition 77.1
- mixed strategy of extensive game,
**216** - mixed strategy of strategic game,
**Definition 32.3**, 43 - strategic game,
**Definition 14.1**- and maxminimizers, Proposition 22.2

- and trembling hand perfect equilibrium, 248

- Bayesian game,
- Nash folk theorem
- discounting criterion, Proposition 145.2
- finitely repeated game, Proposition 156.1
- limit of means criterion, Proposition 144.3

- Nash implementation, 185-191
- revelation principle, Lemma 185.2

- Nash solution,
**Definition 301.2**- axiomatic definition, 305-310
- exact implementation, 311

- Nature, moves of,
*see*chance moves - Negotiation,
*see*bargaining game of alternating offers, Nash bargaining - Never-best response,
**Definition 59.1** - No indifference condition,
**Exercise 100.2** - No veto power,
**Definition 187.1** - Non-redundancy in Nash bargaining problem, Definition 300.1
- Noncooperative vs. coalitional games, 2, 255
- Nondecreasing function,
**7** - Nonempty core
- coalitional game, Proposition 262.1
- market with transferable payoff, Proposition 264.2

- Nonordered information sets, Example 223.1, Exercise 229.1
- Nontransferable payoff coalitional game,
**Definition 268.2** - Normal form game,
*see*strategic game - Nucleolus of coalitional game,
**Definition 286.1**- and kernel, Lemma 287.1

- Objection in coalitional game
- bargaining set, 281
- kernel, 284
- Nash solution, 302
- nucleolus, 285
- Shapley value, 290
- stable set, 278

- One deviation property
- sequential equilibrium, Exercise 227.1
- subgame perfect equilibrium, Lemma 98.2
- bargaining game, Exercise 123.1
- game with chance moves, Exercise 102.1
- game with simultaneous moves, Exercise 103.3
- infinitely repeated game with discounting, Lemma 153.1

- Opting out (bargaining), 128
- Outcome
- extensive game
- imperfect information,
**213**,**223** - perfect information,
**93**

- imperfect information,
- implementation theory, 178
- strategic game, 11

- extensive game
- Outcome-equivalence of mixed and behavioral strategies, 214
- Outcome-equivalent strategies, 94
- Output function of machine,
**140**,**164** - Outside option
- in bargaining, 128
- in BoS, Example 110.1

- Outside option principle, 129
- Overtaking
- perfect folk theorem, Proposition 149.1
- preferences,
**139** - repeated game,
**139**

- PAR (Nash solution axiom), 305
- Paradoxes in finite horizon games, 105
- Paratroopers, 170
- Pareto efficiency,
**7**- axiom of Nash solution, 305

- Pareto frontier of agreement set, 122
- Parliament, coalitional game model, Example 295.3, Exercise 295.4
- Partition of a set,
**7** - Partitional information function,
**Definition 68.2** - Payoff function, 13
- Payoff profile
- repeated game
- discounting,
**138** - limit of means,
**138**

- discounting,
- strategic game,
**139**

- repeated game
- Perfect Bayesian equilibrium,
**Definition 232.1**- and sequential equilibrium, Proposition 234.1

- Perfect folk theorem
- discounting criterion, Proposition 151.1
- finitely repeated game, Proposition 160.1
- limit of means criterion, Proposition 146.2
- overtaking criterion, Proposition 149.1

- Perfect information extensive game,
**Definition 89.1**- strategic form,
**Definition 94.1**

- strategic form,
- Perfect recall,
**Definition 203.3** - Perturbed game
- chain-store, Example 239.1
- mixed and pure strategies, 42
- trembling hand perfect equilibrium, 247

- Phases of equilibrium of machine game,
**171** - f,
*see*Shapley value - Plan of action vs. strategy, 103
- Planner (implementation theory), 177
- Player function in extensive game
- imperfect information, Definition 200.1
- perfect information, Definition 89.1

- Pollute the lake, Exercise 261.3
- Pooling equilibrium in Spence's model, Example 237.2
- eliminated by refinement, Example 246.1

- Pre-trial negotiation, Exercise 246.2
- Preference relation,
**7**- repeated game, 137

- Prior belief
- in Bayesian game, Definition 25.1
- and posterior belief, 75

- Prisoner's dilemma, Example 16.2
- equilibria of machine game, Example 166.2, 169, 172
- grim strategy in repeated game, Example 141.1
- complexity, Example 166.1

- infinitely vs. finitely repeated game, 134
- modified in finitely repeated game, 159
- rationalizability, 56

- Probability measure,
**7** - Production economy
- core, Exercise 259.3
- core convergence, Exercise 268.1
- nucleolus, Exercise 289.1
- Shapley value, Exercise 295.2

- Production function, 264
- Profile,
**7** - Proper equilibrium, 254
- Punishment
- limited length of time, Proposition 146.2
- punishing the punisher, Proposition 149.1
- rewarding players who punish, 150, 159
- trigger strategies, 143

- Pure strategy
- extensive game,
**Definition 203.1** - strategic game,
**32**

- extensive game,
- Purification of mixed strategy equilibrium, 39
- Puzzle of the hats, 71

- Quasi-concave preference relation,
**7**,**20**

- Rational choice, 4
- Rational, individually,
*see*enforceable, 143 - Rationalizability, 53
- independence vs. correlation in beliefs, 57
- and iterated elimination of strictly dominated actions, Proposition 61.2
- knowledge requirements, Proposition 80.1

- Rationalizable action,
**Definition 54.1**,**Definition 55.1** - Recall, 203
- Reduced strategic form,
**Definition 95.1** - Reduced strategy, 94
- Refinements of sequential equilibrium, 243-246
- Relative probabilities, 254
- Renegotiation, 161
- Repeated game
- constituent game, 136
- finite,
**155** - finite vs. infinite, 134
- forms of preference relation, 137-139
- infinite,
**Definition 137.1** *see also*finitely repeated game, infinitely repeated game

- Reputation, 238-243
- Restrictions on beliefs, 243-246
- Revelation principle
- DSE implementation, Lemma 181.4
- Nash implementation, Lemma 185.2

- Reversal of beliefs, Example 236.1
- Risk of breakdown in bargaining, 129
- and Nash solution, Proposition 310.3

- Risk, comparative statics (Nash bargaining), Proposition 304.1

*S**see*coalition*S*-feasible payoff vector,**258**- Second price auction, Exercise 18.3
- imperfect information, Example 27.1

- Self-evident event,
**Definition 73.2** - Selten's horse
- sequential equilibria, Example 225.2
- trembling hand perfect equilibria, Example 252.1

- Separating equilibrium, Example 237.2, Example 246.1
- Sequential equilibrium,
**Definition 225.1**- assessment,
**Definition 222.1** - belief system, 223
- coalescing of moves, Example 226.2
- existence, Corollary 253.2
- and perfect Bayesian equilibrium, Proposition 234.1
- refinements, 243-246
- restrictions on beliefs, 243-246
- reversal of beliefs, Example 236.1
- and structural consistency, 228-231
- and trembling hand perfect equilibrium, Proposition 251.2

- assessment,
- Sequential rationality, 221, 223,
**Definition 224.1** - Shapley value,
**Definition 291.2**- axiomatic characterization, 292
- objections and counterobjections, 289

- Short-lived players in infinite game, Exercise 148.1
- Shouting game in implementation, 188, 189
- Signal function in Bayesian game, Definition 25.1
- Signaling game,
**237**- pooling equilibrium, Example 237.2
- eliminated by refinement, Example 246.1

- separating equilibrium, Example 237.2, Example 246.1

- pooling equilibrium, Example 237.2
- Simple coalitional game,
**Exercise 261.1**- core, Exercise 261.1
- stable sets, Exercise 280.1

- Simultaneous moves in extensive game
- imperfect information, 202
- perfect information, 102

- Solomon's predicament, Example 186.3, Example 190.1, Example 191.2
- Solution
- for coalitional games
- bargaining set,
**Definition 282.1** - core (nontransferable payoff),
**Definition 268.3** - core (transferable payoff),
**Definition 258.2** - general idea, 255
- kernel,
**Definition 284.1** - Nash solution,
**Definition 301.2** - nucleolus,
**Definition 286.1** - Shapley value,
**Definition 291.2** - stable sets,
**Definition 279.1**

- bargaining set,
- deductive interpretation, 5
- for extensive games
- perfect Bayesian equilibrium,
**Definition 232.1** - sequential equilibrium,
**Definition 225.1** - subgame perfect equilibrium,
**Definition 97.2** - trembling hand perfect equilibrium,
**Definition 251.1**

- perfect Bayesian equilibrium,
- general idea, 2
- implementation theory, 179
- steady state interpretation, 5
- for strategic games
- correlated equilibrium,
**Definition 45.1** - dominant strategy equilibrium,
**Definition 181.1** - evolutionary equilibrium,
**Definition 49.1** - iterated elimination of strictly dominated actions,
**Definition 60.2** - mixed strategy equilibrium,
**Definition 32.3** - Nash equilibrium,
**Definition 14.1** - rationalizability,
**Definition 54.1** - trembling hand perfect equilibrium,
**Definition 248.1**

- correlated equilibrium,

- for coalitional games
- SPE,
*see*subgame perfect equilibrium - Spence's model of education, Example 237.2
- refinement of equilibria, Example 246.1

- Split-the-pie game, Example 120.1
- subgame perfect equilibrium, Example 125.1

- Stable set of coalitional game,
**Definition 279.1**- and core, Proposition 279.2
- generalized, Exercise 280.5

- Stackelberg game, Example 97.3
- Standard of behavior in coalitional game, 279
- State of machine,
**140**,**164** - State of the world, 67
- Stationarity of strategies in bargaining game, 126
- Steady state interpretation, 5, 14
- Strategic form
- agent strategic form,
**250** - extensive game with perfect information,
**Definition 94.1**

- agent strategic form,
- Strategic game,
**Definition 11.1**- Bayesian,
**Definition 25.1** - dominant strategy equilibrium,
**Definition 181.1** - examples, 15-19
- existence of Nash equilibrium, Proposition 20.3
- vs. extensive game, 3
- form of extensive game, Definition 94.1
- imperfect information, 24
- interpretation, 13
- mixed extension,
**Definition 32.1** - as reduced strategic form,
**Definition 95.1** - solutions,
*see*solution - strictly competitive,
**Definition 21.1** - symmetric, Exercise 20.4
- tabular representation, 13
- trembling hand perfect equilibrium,
**Definition 248.1**

- Bayesian,
- Strategic game form, 178
- Strategy
- equilibrium structure in repeated game, 134, 163
- extensive game
- imperfect information,
**Definition 203.1** - interpretation, 103
- perfect information,
**Definition 92.1** - perfect information and chance moves, 102
- perfect information and simultaneous moves, 102
- vs. plan of action, 103

- imperfect information,
- as machine in repeated game, 140
- stationarity in bargaining game, 126

- Strict equilibrium, 50
- Strict individual rationality
- Nash bargaining, Exercise 309.2

- Strict individual rationality (strict enforceability), 143
- Strictly competitive strategic game, Example 17.1,
**Definition 21.1**- value,
**23**

- value,
- Strictly dominated action,
**Definition 59.2** - Strictly enforceable payoff profile/outcome,
**143** - Structural consistency, 222,
**Definition 228.1**- and sequential equilibrium, 228-231

- Structure of equilibria of repeated game, 153-154
- complexity, 163
- cycling/introductory phases,
**171**

- Subgame of extensive game with perfect information,
**Definition 97.1** - Subgame perfect equilibrium
- extensive game with imperfect information,
*see*sequential equilibrium - extensive game with perfect information,
**Definition 97.2** - finitely repeated game, Proposition 157.2, Proposition 160.1
- implementation, 191
- Nash solution, 311

- infinitely repeated game, 146-154
- discounting, Proposition 151.1, Proposition 154.1
- limit of means, Proposition 146.2
- overtaking, Proposition 149.1

- interchangeability, Exercise 100.2
- iterated elimination of weakly dominated actions, 108
- virtual SPE-implementation,
**192**

- extensive game with imperfect information,
- Superadditivity of coalitional game,
**258** - Superfluous moves
- equivalence of extensive games, 206

- Support of probability distribution, 32
- SYM (Nash solution axiom), 305
- SYM (Shapley value axiom), 292
- Symmetric bargaining problem,
**Definition 305.1** - Symmetric game, Exercise 20.4
- evolutionary equilibrium, Exercise 51.1

- Symmetry axiom
- Nash solution, 305
- Shapley value, 292

- Symmetry function, Definition 305.1

- Terminal history in extensive game
- imperfect information, Definition 200.1
- perfect information, Definition 89.1

- Three-player bargaining, 130
- Three-player majority game
- bargaining set, Example 282.2
- core, Example 259.1
- kernel, Example 285.2
- stable set, Example 279.3

- Transferable payoff
- coalitional game,
**Definition 257.1** - coalitional game without,
**Definition 268.2** - core,
**Definition 258.2** - market,
**263**

- coalitional game,
- Transition function of machine,
**140**,**164** - Treasure in the mountains, Example 259.2
- Trembling hand perfect equilibrium, 246-253
- extensive game,
**Definition 251.1**- existence, Corollary 253.2
- and sequential equilibrium, Proposition 251.2
- and weakly dominated strategy, 252

- strategic game,
**Definition 248.1**- existence, Proposition 249.1
- and Nash equilibrium, 248
- and weakly dominated strategy, Proposition 248.2

- extensive game,
- Trigger strategy in repeated game, 143
- Truthful implementation,
**Definition 179.2**- and DSE-implementation, Lemma 181.4
- and Nash implementation, Lemma 185.2
- via Groves mechanism, Proposition 184.2

- Type of agent in exchange economy, 272
- Types of players, 24, Definition 231.1

- Uncertainty
- in extensive game
- imperfect information, 200
- perfect information, 101

- in model of rational choice, 4, Exercise 71.2
- about others' characteristics, 24
- about others' knowledge, 29

- in extensive game
- Unique best agreements in Nash bargaining problem, Definition 300.1
- Utility function, 4
*see also*payoff function, 13

- Value
- coalitional game,
**290** - strictly competitive game,
**23**

- coalitional game,
- Veto player in coalitional game,
**Exercise 261.1** - Veto power,
**Definition 187.1** - Virtual SPE-implementation,
**192** - Von Neumann-Morgenstern utility function, 5

- War of attrition, Example 18.4
- Weak separability of preferences in repeated game,
**Definition 137.1** - Weakly dominant action, Exercise 18.3
- Weakly dominated action,
**Definition 62.1**- and trembling hand perfect equilibrium, Proposition 248.2

- Weighted majority game,
**Exercise 289.2**- Shapley value, Example 294.1

- Winning coalition, Exercise 261.1
- Worth of a coalition, Definition 257.1

- Zerosum coalitional game,
**Exercise 261.2**- weighted majority game,
**Exercise 289.2**

- weighted majority game,
- Zerosum strategic game,
**21**