Index absorbing state 104 Centipede Game with threat 105 admissible imputations 223 Centipede Game (Game 6.4) 106 Agency (Game 6.2) 92–94 characteristic function see coalition all-or-nothing offer 184 function anonymous (solutions) 128 classical game theory 45 anticoordination game 39, 59–62, coalition for production and sale 196 74–6, 83, 160 coalition function 6, 18, 20, 30, 38, 43, arm-wrestling 70, 83 125, 148, 159 Arrow impossibility theorem 112, coalition structure 6, 22, 169 257 coalitional egoism 131 Arrow, Kenneth 112, 257 coalition-proof equilibrium 47, 64 assurance principle 31–2, 38, 41, 125, Coalitions among colleges (Game 8.4) 159 138 assurance value 31, 125, 159 collective threats 243–4 auction 120 commitment 154–63, 208 Aumann, Robert 3, 6, 27, 38, 42–4, 47, commitment, revocable 144 53, 64, 67, 72, 98 Complementary Market Entry (Game Aumann’s Game (Game 5.2) 77 5.3) 80 conditional transfer 144 backward induction 42, 47, 87, 149, Condorcet 112, 257 170 Conflict among Three Nations (Game bargaining 32, 37–8, 128–9, 174–8, 4.7) 63 241–5, 256–65 considerable solutions 169–71, 181, 186 bargaining power 38, 126, 159, 174–7, constant-sum game 58 182, 191, 192, 200–202, 207–8, consumers’ cooperatives 30, 137, 187 231, 254, 256–65 consumers’ surplus 90, 189, 213 basic subgame 87 contestability 147 Battle of the Sexes (Game 3.2) 39 contingent claims 80 Bayesian decision making 42 contingent fee 92 Bayesian Nash Equilibrium 111 contingent strategy 12, 36, 56, 78 behavior strategies 13, 15, 35, 56, 86, cooperative games 4, 17–22, 40, 125– 141 40, 167 behavioral game theory 45 coordination games 39, 59–62, 74–6 biform games 47, 167–75 core 36, 44, 117, 125–8, 131, 132–7, Borda, de 112 147–52, 171–5, 204–14 bounded rationality 67, 160 core assignment algorithm 131, 168, bridge (card game) 22 245 burnt bannock 75 corner solution 199, 228, 229, 233, 237, 238 candidate solution 5, 30, 45, 151, 169, correlated strategy (equilibrium) 39, 181, 205, 223 45, 70–85, 143
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Roger A. McCain - 9781784710903 Downloaded from Elgar Online at 10/02/2021 05:42:06AM via free access 290 Game theory and public policy correlated strategy, game illustrating Gibbard-Satterthwaite Theorem 113–5, (Game 9.1) 143 161–2 covariance under strategic equivalence grand coalition 18 127, 131 grim trigger 100 custom 60, 82 custom of the sea 76 Harsanyi, John 38, 42, 45 holdout behavior 168 decisive voting procedure 113, 115 Holmes, Sherlock (fictional character) deferred acceptance 117 27, 56–7 deviation 150–52, 205, 208, 210, 212, honesty 158–9 213, 224 Hurwicz, Leonid 109 distributive weights 187, 197 hybrid solution 54 Dodgson, C.L. 112 dominance cycles 30, 224, 258 ideal rationality 157–60, 167, 208 dominant strategy 40, 50–52, 55 imbedded coalition 22 dominant strategy equilibrium 51–2, imbedded game 16, 94–6, 109–10, 111 148–52 duopoly 40, 96–103 imperfect recall 8, 22–3, 35, 141–63 Duopoly Game (Game 6.6) 96–103 implementation theory 109 imputation 126–7, 181 economic planning agency 82 incentive compatibility 110, 257 efficiency wage theory 176, 242 incredible threat 91 efficient allocation of resources within independence of irrelevant alternatives a coalition 183, 187–9 113, 129 effort, disutility of, 92, 184–5 individual rationality 128 elections 112–5 industrial organization 40, 121 Entry Game (Game 2.2) 10 information set 11, 35 evolution 42–6, 53, 66–8 inframarginal transfer 186 exchange games 132–6, 143–8 interactive decision theory 3, 5, 8, 9, 27 excise tax 193–4 intermediate case 227–9, 232–3 expenditure function 186 Intersection Game, The (Game 4.6) extended core 207–8 61–2, 74, 83 extensive form 10, 86–108, 141–3 intertemporal inconsistency (in externality 6, 21, 41, 47, 90, 171, decision-making) 154 218 irreversible events 103 iterated elimination of dominated FCS (feasible coalition structure) strategies 33, 55 games 169–70, 205–7 Fender-Bender Game, The (Game 4.5) Jevons, Stanley 79 60–61, 82 film industry 136 Kuhn, Harold 13, 22–3, 35–6, 141, 148 Final Problem, The (Game 4.3) 57 labor markets 215–21, 227–32 firm modeled as cooperative coalition law of one price 143, 147, 184 180–203 Lindow man 75 focal equilibrium (Schelling point) linear games 261–3 39–40, 61 Luce, R. Duncan 36–8, 72, 128 folk theorem 44, 97–104 foresight 37, 224 majority rule 256–74 forgiving trigger strategy rule 100 marginal productivity 208–10
Roger A. McCain - 9781784710903 Downloaded from Elgar Online at 10/02/2021 05:42:06AM via free access Index 291 market entry 10, 79, 90–92 partition 21, 28, 37 Marx, Karl 120, 149 partition function 22, 41, 47 Maskin, Eric 5, 43, 79, 101, 109–11, patent rights 88 115, 167 perfect equilibrium 43, 87–9, 104–5, maximin 29, 31, 33, 35 156–9 McKinsey’s Game (Game 3.1) 34 perfect rationality 157–61 messaging service model 215–21 Pigou, A.C. 112 middle ground 167–70 poison gas 100 military draft 73 Political economy 148 military rank 83 Pollution Game, The (Game 4.1) 52, 83 Mill, J.S. 112 pragmatism 4, 50, 89–90 minimum wage 230–31 price discrimination 135, 145, 184 mixed strategy 29, 39, 57 Prisoner’s Dilemma 12, 33, 37, 42, 46 monopoly 42, 143–7, 171, 190–93, production function 196 232–5 production game 152 monopoly, natural 135 production, games with 135–7 monopoly price regulation 192–3 productivity, idiosyncratic 170 monopoly restriction of output 147 profit 210–12 monopsony 121, 227–32 proper subgame 16 Morgenstern, Oskar 12, 45, 56–7 public good 20, 75 Myerson, Roger 43, 109 public good production game (Game 2.5) 20, 126–7 Nash equilibrium 5, 32, 36–9, 47, public policy process 4 50–69, 86, 111, 141–3 Nash, John 32, 39, 96 Raiffa, Howard 37–8, 72, 128 Nash program 33 rationality constraint 182, 209, 246, nested game 16, 92 263–5 noncomparable utility 262 rationality constraint, idiosyncratic 263 nonconstant-sum games 29 rationalizable strategies 44, 62 noncooperative game theory 4, 9–17, reciprocity 106 32–6, 167 reciprocity, third-party 106 non-envious division 110 reciprocity, negative 106 non-transferable utility (NTU) 25, 132, recontracting 126, 204–5 168 reduced game 55, 87 normal form 11–16, 28 refinement (of a partition) 21 Normandy invasion game (Game 2.6) refinement (of Nash equilibrium) 43, 23–4, 58 65–6 normative economics 112 rhetorical interpretation (of nucleolus 41, 51, 130–33, 178, 241 cooperative game solutions) 132 null coalition 18 Ricardian corn economy 149–52 riparian rights 94 opportunism 94 roundabout production 105 optimism/pessimism 174, 208 Rousseau, J.-J. 19
Pareto dominance 51, 66, 81 Schelling, Thomas 3, 39, 51, 61, 91, 153 Pareto optimality 119, 129–30, 169, Selten, Reinhard 14, 41, 43, 45, 48, 88, 181, 183, 187–9, 262 141, 153 Pareto, Vilfredo 112 Selten’s Horse (Game 2.3) 14, 88 Parking Garage Game (Game 5.1) separability, additive 185–7 70–74 Shapley, Lloyd 33, 36, 44, 109
Roger A. McCain - 9781784710903 Downloaded from Elgar Online at 10/02/2021 05:42:06AM via free access 292 Game theory and public policy
Shapley-Roth matching algorithm 40, surplus 174, 177, 181, 183, 189, 200, 117 215 Shapley value 36, 40, 51, 129–30, 137, symmetrical election games 260 178 shareholder democracy 265–6 Talmud, Babylonian 27 side payment 18, 30, 71, 126, 142, Terrorist vs. Defender (Game 4.4) 58–9 184–5, 192 tit for tat 44, 99 side payments 18, 23, 71, 126, 142, 184, tradeable emissions controls 116–7 192 transferable utility (TU) 18, 23, 30, Simon, Herbert 66 128, 135, 170, 180–94, 260 simultaneous ascending auction 121 transfers, game of 144–6 singleton coalitions 18 trembling hand equilibrium 43, 86 Smith, Adam 27 trigger strategy rule 99–100 social contract 149, 161 two-by-two games 9, 24 social dilemma 50–53 Two-Person Game (Game 9.2) 156 social mechanism design 5, 109–24 types (of agents in mechanism design) sophisticated rationality 158–60 110 stability interpretation (of cooperative game solutions) 131 uncertainty 17, 224 Stag Hunt, Game 2.4 19 utility 16, 18, 27, 112, 184 state transition matrix 101 utility, normalization of, 185–7 state variable 52 utopian 109 stoplight 74 strategically equivalent games 127 value of a coalition 18 strategic form see normal form Vickrey auction 120 strategic investment to deter entry von Neumann and Morgenstern (Game 6.1) 90–91 solution set 31–2 strategic voting 112, 257 von Neumann, John 12, 23, 27–32, 97, strategy-proof election rules 114 122 strong equilibrium 64 voting 42, 112–6, 256–74 subgame 16, 35 subgame perfect equilibrium 43, 86–8, water 9, 50, 54–6 90 Water Game, The (Game 2.1) 9, 50–51, subjective probability 58 53 successor function 205, 224 weak domination 87 sunspot 79 weakness of will 153 superadditivity 6, 20, 22, 31, 43, welfare triangle 146 125–39 supergame 38, 98 zero-sum game 29–30
Roger A. McCain - 9781784710903 Downloaded from Elgar Online at 10/02/2021 05:42:06AM via free access