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Example of Index: Essentials of Game Theory GTessentials MOCL003.cls May 30, 2008 20:36 85 Index !-Nash equilibrium, 27, 27–28 common-payoff game, 4, 5, 10 common-prior assumption, 58 action, 1, 3, 4–7, 10–16, 19–21, 23, 25–27, constant-sum game 31–33, 35, 36, 38, 39, 41, 42, 45, 46, coalitional, 71, 76 50, 51, 53, 54, 57, 61, 62, 64–67, 69 noncooperative, 5 action profile, 3, 4, 10, 13, 19, 20, 53, 63 convex game, 71, 76, 77 additive game, 71 Coordination game, 5, 59 alpha-beta pruning, 39 core, 75, 76, 77 average reward, 51, 52–55 correlated equilibrium, 24, 25, 26 Backoff game, 2 descendant, 32, 37 backward induction, 35, 38, 39, 50, 67, 80 dominant solvable, see solvable by iterated Battle of the Sexes game, 6, 7, 12, 15, 24, 25, elimination 59 dominant strategy, 20, 21, 43, 44, 50, 67, 68 Bayes’ rule, 47 dominated strategy, 20, 21, 22, 24, 28, 79 Bayes–Nash equilibrium, 64, 65, 67 dummy player, 5, 73 ex post, see ex post equilibrium Bayesian game, 3, 57, 58, 59, 60, 61, 62–67, efficiency 79, 80 coalitional, 72, 73 behavioral strategy empirical frequency, 14 extensive form game, 43, 44, 45 epistemic type, 58, 61 stochastic game, 54 equilibrium, see solution concept best response, 10, 11, 13, 14, 16, 18, 19, 21, equilibrium in dominant strategies, 20 23, 24, 27, 28, 30, 34, 36, 44–46, 52, evolutionarily stable strategy, 28–30 64, 66 weak, 29 in a Bayesian game, 64, 66 ex post equilibrium, 67 expected utility, 7, 8, 16, 17, 25, 47, 62–64, Centipede game, 39, 50, 80 66 characteristic function, 70, 73 ex ante, 63, 64, 65 Church–Rosser property, 22 ex interim, 63, 64 coalitional game theory, 1, 69–77, 81 ex post, 62, 63 coalitional game with transferable utility, 69 expectimax algorithm, 67 GTessentials MOCL003.cls May 30, 2008 20:36 86 INDEX extensive form game, 31–48, 80 Markov strategy, 54 imperfect information, 41, 41–48, 60 Matching Pennies game, 5, 6, 13, 17, 18, 23, perfect information, 32, 31–41, 80 59 with chance nodes, 60–61, 67 matrix form game, see normal form game maximum regret, 19, 20 feasible payoff, 55, 72 maxmin strategy, 15, 16–19 fixed-point theorem, 13 maxmin value, 15, 16–18 folk theorem, 51, 52, 55, 80 mechanism design, 21, 62 fully mixed strategy, 7, 26, 27, 46, 47 minimax algorithm, 39 future discounted reward, 51, 53 minimax regret, 18, 19, 20, 79 minmax strategy, 15, 16, 17, 18, 52 game in matrix form, see normal form game minmax value, 16, 17, 18, 52, 55 game in strategic form, see normal form mixed strategy, 7, 8, 11–15, 17, 20–22, 24, game 26, 28–30, 34, 35, 43–45, 52, 62, 63, game of incomplete information, see Bayesian 67, 79 game support of, 7, 11, 12, 14, 30 game tree, see extensive form game, perfect mixed-strategy profile, 7, 8, 16, 27, 46, 47, information 63, 64, 67 Hawk–Dove game, 29, 80 Nash equilibrium, 11, 9–76 history, 32, 50, 54 !-, see !-Nash equilibrium Bayes–, see Bayes–Nash equilibrium imperfect-information game, see extensive strict, 11, 13 form game, imperfect information weak, 11, 12 imputation, 72, 73, 75 normal form game, 3, 3–9, 15, 31, 34, 35, 43, induced normal form, 31, 64–67 46, 49, 64–67 inessential game, 71 information set optimal strategy, 9 Bayesian game, 59–62 extensive form game, 41, 42, 44–47 Pareto domination, 10, 20 interchangeable agents, 73 Pareto optimality, 9, 10, 20, 79 irreducible stochastic game, 55 payoff function, 3, 49, 53, 61 perfect equilibrium, see trembling-hand Markov decision problem (MDP), 53, perfect equilibrium 80 perfect recall, 44, 45, 46, 48 Markov game, 53 perfect-information game, see extensive form Markov perfect equilibrium (MPE), 54 game, perfect information GTessentials MOCL003.cls May 30, 2008 20:36 INDEX 87 pre-imputation, 72, 73 dominant solvable, see dominant Prisoner’s Dilemma game, 2, 3–4, 6, 20, 22, solvable 23, 35, 42, 43, 49–51, 59, 60, 80 equilibrium in dominant strategies, proper equilibrium, 27 see equilibrium in dominant proper simple game, 71 strategies pure coordination game, 4, 5 maxmin strategies, see maxmin strategy pure strategy, 6, 7, 10–14, 17, 21, 23, 24, minmax strategies, see minmax strategy 26, 32, 33, 35, 42–44, 46, 62, 64, Pareto optimality, see Pareto optimality 65 perfect equilibrium, see trembling-hand pure-strategy profile, 6, 7, 65 perfect equilibrium proper equilibrium, see proper rationalizable strategy, 23, 24 equilibrium regret, 19 rationalizable strategies, see repeated game, 14, 16, 49–53, 55, 80 rationalizable strategy Rochambeau game, see Rock, Paper, Scissors sequential equilibrium, see sequential game equilibrium Rock, Paper, Scissors game, 5, 6 strong Nash equilibrium, see strong Nash equilibrium security level, 15 subgame-perfect equilibrium, see sequential equilibrium, 46, 45–48 subgame-perfect equilibrium Shapley value, 74, 75–77 solvable by iterated elimination, 22 Sharing game, 32, 33 stage game, 49, 50, 51, 53 simple game, 71, 76 stationary strategy, 50, 54 single-controller stochastic game, 54 stochastic game, 53, 54, 55, 80 solution concept, 9, 10, 11, 15, 16, 20, 21, strategic form game, see normal form game 24, 26, 27, 31, 48, 58, 72, 73, 76, strategy 79–81 behavioral, see behavioral strategy coalitional Markov, see Markov strategy core, see core mixed, see mixed strategy Shapley value, see Shapley value pure, see pure strategy noncooperative stationary, see stationary strategy !-Nash equilibrium, see !-Nash trigger, see trigger strategy equilibrium strict domination, 20, 22 Bayes–Nash equilibrium, see strict Pareto efficiency, 10, see Pareto Bayes–Nash equilibrium optimality correlated equilibrium, see correlated strong Nash equilibrium, 76 equilibrium subgame, 31, 35–38, 45–48, 50, 53, 54, 80 GTessentials MOCL003.cls May 30, 2008 20:36 88 INDEX subgame-perfect equilibrium (SPE), 31, 35, trigger strategy, 51 37, 38, 45, 46, 48, 53, 54 type, 58, 61–68 superadditive game, 70, 71 support, see mixed strategy, support of utility function, 1, 3, 9, 32, 39, 60–62, 67 utility theory, 1, 4, 79 TCP user’s game, 2 team games, 4 value of a zero-sum game, 17 tit-for-tat (TfT), 51, 80 very weak domination, 20, 23 traffic, 4 veto player, 76 transferable utility assumption, 69 tree-form game, see extensive form game weak domination, 20, 23 trembling-hand perfect equilibrium, 26, 27 zero-sum game, 5, 10, 17, 39, 54, 71.
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