Ε-Competitive Equilibrium, 35 Ε-Core, 378, 380 Ε-Nash Equilibrium

Cambridge University Press 978-0-521-89943-7 - Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations Yoav Shoham and Kevin Leyton-brown Index More information

Index

-competitive equilibrium, 35 AGV mechanism, see Arrow; d’ -core, 378, 380 Aspremont-Gerard-Varet (AGV) -Nash equilibrium, 83, 84, 180, 204 mechanism algorithmic mechanism design, 294, 296, absolute continuity, 201, 202, 203 312 absorbing state, 197 all-or-nothing bid, 336 ABT algorithm, 9, 10, 11, 13, 15–17 alpha-beta pruning, 120–123, 165 accessibility relation, 395, 398, 399, alternativeness relation, 398 401–403, 405, 413, 414, 417, 442 167 182 achievable match, 305 anonymity, , , 220, 257 achievement goal, 442, 444 anonymous learning rule, 220 action, 1, 19, 23–26, 45, 47–49, 53, 55, Anti-Coordination game, 198, 199, 215 56–59, 61, 63, 64, 71, 72, 76, 78, 79, anytime property, 27 82, 83, 87, 88, 91–95, 99–103, 106, appeal function, 293 109–111, 113–115, 117–121, 123, approval voting, 245, 255, 257 125, 126, 128–131, 133, 137, 141, arc consistency, 4 143, 144, 146, 148, 149, 153–156, Arrow’s impossibility theorem, 248 159–173, 175–177, 179–184, 186, Arrow; d’Aspremont–Gerard-Varet´ 188–192, 196–199, 205–210, (AGV) mechanism, 288, 289, 212–216, 219, 223, 225, 227, 235, 312 237, 262–265, 272, 297, 307, 308, ascending combinatorial auction, 359 310, 318, 358, 367, 390, 410–412, ascending-auction algorithm, 40,42 437, 440, 441, 443, 445 assignment problem, 29, 30–32, 34, 35, action graph, 182, 183, 188 37, 38 action profile, 55, 56, 61, 71, 76, 110, asymmetric auction, 329 148, 153, 155, 162, 167–171, 179, asymptotically stable state, 215, 216, 180, 182, 196, 197, 206–209, 263, 218 265, 272 asynchronous backtracking, see ABT action-graph game (AGG), 176, 181, 183, algorithm 188 asynchronous dynamic programming, activity rule, 347, 358 19–21 additive game, 370 asynchronous forward checking, 16 admissible heuristic, 21 advisor-optimal matching, 304 atomic bid, 353, 354–356 affiliated values, 335, 357 auction affine independence, 65 ascending combinatorial, see affine maximizer, 291, 292 ascending combinatorial auction agency, 439 combinatorial, see combinatorial agent-based simulation, 212, 219 auction Agent-Oriented Programming (AOP), continuous double, see continuous 238, 239 double auction AGM postulate, 428, 429, 430, 432, Dutch, see Dutch auction 433 elimination, see elimination auction AGoal, 442, 444 English, see English auction

473

© in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-89943-7 - Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations Yoav Shoham and Kevin Leyton-brown Index More information

474 Index

auction (cont.) BDI theories, 233, 438 first-price, see first-price auction behavioral strategy generalized first-price, see generalized extensive-form game, 127, 128, 132 first-price auction stochastic game, 154 generalized second-price, see belief generalized second-price auction arbitration, 430, 432, 433, 436 Japanese, see Japanese auction contraction, 431, 436 auction expansion, 431, 436 kth-price auction, see kth-price fusion, 241, 426, 430, 433, 435, 436, auction 445 multiunit, see multiunit auction revision, 124, 414, 415, 417, 426, optimal, see optimal auction 427–432, 436, 445 periodic double, see periodic double self-coherent, see self-coherent belief auction update, 200, 426, 431, 445 position, see position auction belief set, 428, 433 random sampling, see random belief state, 431, 433, 434 sampling auction dominating, 434, 435 reverse, see reverse auction pedigreed, 434, 435 sealed-bid, see sealed-bid auction Bellman equations, 23, 456 second-price, see second-price auction best response, 61, 62, 64, 73, 75, 76, simultaneous ascending, see 78–80, 83, 84, 88, 92–94, 104, 116, simultaneous ascending auction 118, 124, 127, 132, 133, 136, 137, two-sided, see two-sided auction 145–147, 151–153, 162–164, 168, Vickrey, see second-price auction 170, 191, 192, 194–196, 201, 203, auction theory, 262, 315–365 204, 210–212, 214, 216, 218, 224, autocompatibility, 211 227, 297, 319, 322, 325 average reward, 144, 145, 146, 153–156, in a Bayesian game, 162, 163, 164, 190 224, 227, 297, 319, 322, 325 bidding language, 341, 352, 353, babbling equilibrium, 224 355–357, 359, 365 Backoff game, 54 all-or-nothing bid, see all-or-nothing backward induction, 117, 119, 120, 121, bid 123, 124, 139, 143, 149, 165, 185, atomic bid, see atomic bid 427 divisible bid, see divisible bid balanced game, 311 OR bid, see OR bid balanced matrix, 351 OR* bid, see OR* bid balanced set, 376 OR-of-XOR bid, see OR-of-XOR bid Barcan formula, 400 XOR bid, see XOR bid bargaining set, 389 bidding ring, 330, 331–333 Battle of the Sexes game, 58, 59, 62, 72, bidding rule, 28, 265, 317 81, 158 bijective, 69 Bayes’ rule, 138, 200, 227, 450 Borda voting, 245, 246, 247, 258 Bayes–Nash equilibrium, 162, 163, 165, Braess’ paradox, 175, 188 264, 265, 267, 268, 289, 321 branch-and-bound search, 454 ex post, see ex post equilibrium Brouwer’s fixed-point theorem, 68, Bayes–Nash incentive compatibility, 266, 69 289 budget balance, 273, 275, 282–284, Bayesian game, 55, 82, 85, 142, 156, 157, 287–289, 299, 300, 312, 331, 333, 158, 159, 160, 161–163, 165, 166, 338, 342, 343, 349, 363, 372, 373, 187, 191, 228, 262–265, 268, 271, 375 272, 318, 344, 424 ex ante, 274 Bayesian game setting, 263, 264, 272 strict, 372 Bayesian learning, 200 weak, 273, 275, 283, 284, 289, 338, Bayesian updating, 200, 201, 203, 204 342, 343, 349, 372

Index 475

call market, 361, 362, 363 conditional utility independence, 272 capability, 437, 439 Condorcet condition, 242, 243, 244, 246 cartel, 330, 331, 332 Condorcet winner, 243, 244, 246 Centipede game, 124, 139, 143 conﬁguration (of an action-graph game), centroid, 68,69 182, 183 characteristic function, 368, 372 congestion game, 142, 166, 167–174, Chernoff bounds, 208 178, 182, 187 chess, 13, 21, 120, 123, 139, 147, 211 nonatomic, 170–174, 187 Chicken game, 192 consecutive ones property, 351 choice rule, 251, 252, 272, 289, 290 consistency, 195, 401, 413, 415, 431 choice-set monotonicity, 282, 283 constant-sum game chronological backtracking, 8 coalitional, 370, 377 Church–Rosser property, 79 noncooperative, 57 Clarke tax, 280 constraint satisfaction problem (CSP), 2, click-through rate, 345, 346 3–9, 11, 13, 17, 91, 181, 452 coalition logic, 436, 437, 445 continuous double auction (CDA), 361, coalitional game 363 in partition form, 389 contract with nontransferable utility, 388 cluster, 28 with transferable utility, 368 multiagent, 28 coalitional game theory, 47, 299, swap, 28 367–391, 437 contract net, 27, 28, 29, 45 coalitional structure, 370, 371, 389, contraction, see belief contraction 390 convergence, 193 collusion, 285, 330, 332, 349, 358, 364 conversational implicature, 231, 232 combinatorial auction, 312, 315, 344, convex combination, 64 348, 346–361, 364, 377, 378 convex game, 370, 377, 387 commitment, 26, 311, 336, 348, 362, 438, convexity, 64 439, 442 cooperative principle, 230, 234 common belief, 90, 413, 425, 444, 445 Coordination game, 57, 102, 158, 191, probabilistic, 424 224 common knowledge, 124, 143, 156, 160, coordination graph, 26 164, 232, 292, 308, 328, 393, 403, core, 311, 367, 374, 375, 376–386, 405, 406, 410–412, 423, 424, 443, 388–390 444 correlated equilibrium, 81, 82, 110, 111, common prior, 156, 158, 160, 318, 422, 179, 193 423, 424 cumulative voting, 244, 245 common value, 333, 335, 364 common-payoff game, 56, 57, 61, 233, default reasoning, 426 234 defeasible, 414 common-prior assumption, 157, 425 degenerate game, 93 compactness, 67, 69, 71 demand curve, 296 compensation and penalty mechanism, demand query, 359 294, 295, 296 descendant, 114, 119 competitive equilibrium, 31, 33, 35, 38, descriptive theory, 192, 193 39, 40, 42, 297, 298 desire, 233, 438, 439, 441, 446 -, see -competitive equilibrium detail-free auction, 330, 343 complementarity, 37, 347 dialog system, 235, 239, 438 complementarity condition, 92,93 direct mechanism, 265, 266, 267, 273, completely labeled subsimplex, 66, 67, 69 276, 306, 307, 319, 357, 358, concurrent dynamic backtracking, 16 360 conditional probability, 185, 429, 450 disambiguation, 233 conditional strategy, 25 discriminatory pricing rule, 336 conditional strict dominance, 100 divisible bid, 336

476 Index

dominance solvable, see solvable by expected utility, 48, 53, 59, 60, 72–74, iterated elimination 81, 87, 88, 92, 99, 100, 109, 111, dominant strategy, 77, 104, 127, 143, 133–135, 138, 161, 163, 177, 179, 147, 149, 166, 173, 175, 190, 223, 185, 225, 269 227, 264–267, 276–279, 281, 284, ex ante, 162, 163 288–291, 294, 305–307, 309, 310, ex interim, 161, 162, 164, 280, 312, 319–321, 326, 328, 332, 334, 321–324, 331, 334, 335, 339, 345, 339, 346, 358, 377, 426, 436 346 dominated strategy, 77, 78–80, 84, 85, 87, ex post, 161 106, 109, 112, 199, 436 ExpectedUtility problem, 177–180, domination 183, 185 strict, 77, 79, 107 expectimax algorithm, 165 very weak, 77, 79, 106, 108 exposure problem, 347, 348 weak, 77, 79, 106, 108 extensive-form game, 113–139 double auction, 315, 361 of imperfect information, 113, 125, dual operator, 398 125–139, 159, 234 dual problem, 32, 452 of perfect information, 114, 113–124, dummy player, 372, 373 225 Dutch auction, 316, 317, 321, 337, with chance nodes, 158–159, 165, 184, 339 185 multiunit, 337 external regret, 210 dynamic programming, 19, 20, 21, 45, false-name bidding, 349 352 feasibility program, 91, 99, 100, 104, 108, 111 E3 algorithm, 208, 222 feasible assignment, 30, 31, 35 economic efficiency, see efficiency feasible payoff, 155, 372 efficiency, 273, 274, 276, 278, 288, 289, feasibly truthful, 293 291, 297–300, 323, 329, 330, 357, fictitious play, 191, 195, 196–200, 209, 361 210, 221, 222 coalitional, 372, 373, 377, 378 filtering algorithm, 4, 6–8 elimination auction, 317, 364 finite-state automaton, 148, 148–153 empirical frequency, 64, 193, 210 first-price auction, 317, 321–328, English auction, 31, 315, 316, 317, 331–333, 335, 336, 340, 345, 348, 319–321, 335, 337, 339, 346 349, 364 multiunit, 337 fitness, 213, 214 entailment, 395, 417, 457 fixed-point axiom, 406 entry cost, 327, 328 fixed-point theorem, 68–85 epistemic type, 157, 159, 160, 263 focal point, 225, 235 equilibrium, see solution concept folk theorem, 145, 145–147, 155, 187, equilibrium in dominant strategies, 77, 308 227, 264 frugal mechanism, 285, 286 Euclidean accessibility relation, 402 fully mixed strategy, 59, 83, 137, 138, 216 evaluation function, 123 fusion, see belief fusion event space, 449 future discounted reward, 144, 146, 153, evolutionarily stable strategy (ESS), 86, 155, 156, 205 216, 217–218 futures market, 363 weak, 217 GALA, 176, 186, 187, 188 ex ante budget balance, see budget GAMBIT, 112 balance, ex ante game in strategic form, see normal-form ex post equilibrium, 165, 265, 305, 358 game excess of a coalition, 380 game network, 188 exchange, 361 game of incomplete information, see expansion, see belief expansion Bayesian game

Index 477

game tree, see extensive-form game of ex interim, 274, 288, 289 perfect information ex post, 274, 283, 284, 338, 343, 349 games of asymmetric information, 228 individually rational matching, 303 GAMUT, 112 induced normal form, 113, 119, 130, 132, generalized ﬁrst-price auction (GFP), 345 136, 163–165, 178 generalized second-price auction (GSP), inessential game, 370 345 information change operators, 436 generalized Vickrey auction, see Groves information dissemination rule, 28 mechanism information market, 362 goal, 439, 440–446 information set grain of truth, 202 in a Bayesian game, 158–161, 184 graphical game, 90, 176, 179, 180, in an extensive-form game, 125, 126, 181–183, 188 128–134, 136–138, 148 greedy allocation scheme, 360, 361 integer program, 28, 29, 36, 37, 39, 341, Gricean maxims, 230, 231 349, 350, 451, 453, 453–454 Groves mechanism, 276, 277, 280, 282, intention, 224, 225, 230, 233, 236, 407, 284, 288, 289, 291, 292, 294, 295, 421, 438, 439, 440–446 300, 312, 319 interchangeable agents, 372 Groves-based mechanism, 292, 293, 312 interior, 69, 70, 94 gullibility rule, 428 interior-point method, 453 interpretation, 234, 235, 356, 357, 394, Hannan consistency, 195, 206 395, 397, 398, 400, 401, 416, 417, Harper identity, 431 422, 432, 457, 458 Hawk–Dove game, 217, 222 interpretation complexity, 356, 357 highest cumulative reward (HCR), 220 iterated belief revision, 436 history, 114, 143, 146, 148, 152, 154, 191, 194, 200–204, 206, 220, 221, Japanese auction, 316, 318, 320, 334, 404, 405, 406, 408 335, 337, 359 homeomorphism, 69,70 multiunit, 337 homotopy method, 104, 112 Job Hunt game, 226 hyper-resolution, 6, 7, 8, 10–12 joint intention, 444, 445 hyperstable set, 86 joint persistent goal, 444, 445 illocutionary act, 230 joint probability, 82, 83, 179, 450 imperfect-information game, see k-face, 65 extensive-form game of imperfect k-implementation, 310, 313 information KB-model, 416, 427–429 implementation KB-structure, 416 in Bayes–Nash equilibrium, 264 kernel, 389 in dominant strategies, 264, 265, 267, KQML, 237, 239 312 Kripke model, 395, 398, 399, 400, 416 in ex post equilibrium, 265 Kripke structure, 398, 399, 402, 403, 405, implementation theory, 262 406, 412, 413, 421 implicature, 231 kth-price auction, 317 imputation, 372, 373, 375 incentive compatibility in dominant learning and teaching, 189, 190, 210 strategies, 266 learning real-time A∗ (LRTA∗), 21 independence of irrelevant alternatives least core, 378, 379, 380 (IIA), 248, 251, 256 Lemke–Howson algorithm, 91, 92, independent private value (IPV), 319, 93–96, 98, 99, 104, 111, 129, 136 320, 333, 337, 364 Levi identity, 431 indirect speech act, 232 lexicographic disutility for complexity, individual rationality, 282, 295, 303, 342, 150, 151 372, 373 lexicographic probability system (LPS), ex ante, 289 430

478 Index

linear complementarity problem (LCP), Shapley value, see Shapley value 91, 92, 111, 135, 136 mechanism linear program, 28–30, 32, 35, 39, 45, Vickrey–Clarke–Groves (VCG) , see 87–89, 92, 96, 107–110, 132–136, Vickrey–Clarke–Groves (VCG) 155, 156, 179, 207, 350–352, 375, mechanism 376, 378–380, 385, 451, 451–454, mechanism design, 29, 77, 161, 176, 262, 456 261–313, 315, 318, 358, 368 relaxation, 39, 350, 454 minimax algorithm, 120, 121, 165 linkage principle, 335 minimax regret, 75, 76,85 local learning rule, 220 minimax-Q, 206, 207, 208 locally envy free, 346 minimum ratio test, 96, 97 locutionary act, 229 minmax strategy, 72, 73, 74, 75, 87, 88, logical omniscience, 401, 413 105, 135, 145, 146 lottery, 49, 50–53, 269, 270 minmax value, 72, 73, 74, 145, 146, 155 machine game, 149, 150–152 minority game, 167 makespan, 294, 295, 296 mixed strategy, 59, 60, 61, 63, 64, 69, 71, marginal contribution net (MC-net), 386 72, 74, 76, 78, 80, 82, 83, 85, 88, marginal probability, 450 92–95, 100, 106–111, 116, 124, 127, market clearing rule, 28 128, 145, 152, 161, 162, 165, 191, Markov decision problem (MDP), 19, 23, 195–199, 210, 214–218 27, 45, 153, 155, 156, 187, 204, 205, support of, 59, 61, 63, 64, 71, 92, 93, 207, 222, 455, 455–456 99–101, 105, 112, 216, 218 Markov game, 153 mixed-integer program, 453 Markov perfect equilibrium (MPE), mixed-strategy profile, 59, 60, 69, 73, 83, 154 84, 104, 107, 137, 138, 161, 162, Markov strategy, 154 165, 177, 179, 211, 216 matching, 303 mixing time, 208 Matching Pennies game, 57, 58, 63, 64, modal operator, 395, 397, 399, 401, 415, 74, 75, 80, 158, 193, 196–198, 206, 427, 437, 438, 441 208 model maximum regret, 76 first-order logic, 458 maxmin fairness, 275 propositional logic, 457 maxmin strategy, 72, 73–76, 105, Modus Ponens, 399, 401, 413, 457 206–208 money pump, 50 maxmin value, 72–74, 146, 221 monotonicity, 51, 52, 251, 252–254, 297, mechanism, 263, 315, 316, 318, 319, 323, 299 324, 329, 330, 332, 333, 338, 339, monotonicity rule, 429 342–346, 348, 349, 352, 357–361, Moore machine, 148 363, 365, 369, 374, 377 multi-issue representation, 385, 386, 387, Arrow; d’Aspremont–Gerard-Varet´ 391 (AGV), see Arrow; multiagent influence diagrams (MAIDs), d’Aspremont–Gerard-Varet´ 183 mechanism multiagent MDP, 23, 24,27 Groves, see Groves mechanism multicast cost sharing, 298, 301, 312, 369 Groves-based, see Groves-based multicast routing, 298, 299 mechanism multicast routing tree, 299 proportional allocation, see multiunit auctions, 336, 337–340, 344, proportional allocation mechanism 349 quasilinear, 272, 273–276, 280, 289, mutation, 213 292, 294, 296, 299, 318, 371 myopic best-response, 168 direct, 272, 276, 280, 289, 292, 299 second-chance, see second-chance n-simplex, 65 mechanism Nanson’s method, 245

Index 479

Nash equilibrium, 62, 60–71, 73, 74, partition model, 393, 394, 395–398, 77–87, 89–91, 93, 98–106, 110–113, 400–404, 410–415, 418, 422, 425 116, 117, 119, 120, 123, 127, 128, payment rule, 265, 272, 280, 290, 336, 134–137, 142, 144–147, 150, 151, 339, 343 154, 155, 157, 159, 163, 164, payoff function, 55, 129, 130, 132, 143, 167–173, 178, 179, 181, 185, 186, 153, 160, 165, 191, 388 188, 190, 193, 196–199, 201, 202, perfect equilibrium, see trembling-hand 206, 209, 215, 216, 218, 234, 297, perfect equilibrium 298, 310, 375, 376, 436 perfect recall, 128, 129, 131, 133, -, see -Nash equilibrium 137–139 strict, 62,63 perfect-information game, see weak, 62,63 extensive-form game of perfect Necessitation, 399, 401, 413 information 402 negative introspection, , 413, 415, 425 performative, 230, 237 neighborhood relation, 179 periodic double auction, 361 no externalities, 346 perlocutionary act, 230 no fun in gambling, 50 96 no negative externalities, 282, 283 pivot algorithms, no single-agent effect, 283, 284, 287, 288 pivot mechanism, see Groves mechanism no-regret, 193, 195, 200, 209, 210, 211, 222 plan, 439, 440, 443 Nogood, 6, 7, 8, 10–16 plurality voting, 241, 242, 243, 244, 246, nonatomic congestion game, see 258 congestion game, nonatomic with elimination, 245, 246 nondictatorship, 249, 251, 252, 255 polynomial type, 177, 178, 179 nonlinear complementarity problem, 102 pooling equilibrium, 229 nonmonotonic logic, 445 Popper function, 430 nonmonotonic reasoning, 426, 429 position auction, 344, 345, 346, 364 nonranking voting, 244 generalized first-price, see generalized nonstandard probability, 430 first-price auction normal-form game, 47, 53, 55, 55–60, 72, generalized second-price, see 113, 116, 117, 119, 127, 130, 132, generalized second-price auction 135–137, 142, 163–165, 177–179, positive introspection, 402, 425 181, 197, 199 possible world, 394, 395, 398, 399, 400, nucleolus, 367, 378, 379, 380 404–406, 409, 411, 412, 414, 416, observability, 191 421, 422, 424, 433 online auction, 255, 308, 320, 339, 344 possible-worlds structure, see Kripke open-outcry auction, 317, 339 structure optimal auction, 329, 330 potential game, 168, 169, 170, 187, 199 optimal policy, 23, 24, 205, 207, 208, exact, 168 455, 456 ordinal, 169 optimal single price, 342, 343 weighted, 169 optimal strategy, 60, 194, 228 pre-imputation, 372, 373 OR bid, 353, 354, 356 prediction market, 362, 363, 365 OR* bid, 355, 356 preference ordering, 150, 243, 245, 248, OR-of-XOR bid, 355 250–252, 262, 301–303, 305, 306 order book, 361, 362 preference profile, 243, 248–254, 256, order statistic, 325 257, 268, 306 pairwise elimination, 245, 247 preferences, 47, 49, 50, 53, 241–244, Pareto domination, 61, 77, 247 246–249, 251, 252, 254–256, Pareto efficiency (PE), 248, 251–254 261–263, 265, 267–269, 271, 273, Pareto optimality, 60, 61, 77, 85, 101, 290, 291, 301, 303–306, 318, 344, 102, 111, 223 see also strict Pareto 388, 436 efficiency prescriptive theory, 192

480 Index

price of anarchy, 172, 173, 174–176, 188, rational learning, 193, 200, 201–204, 275, 298 209, 221 minimization, 275 rational programming, 237, 239 price taker, 297 rationality of a learning rule, 195 primal problem, 32, 452 rationalizable strategy, 79, 80, 81 principle of optimality, 19 reachability relation, 398 prioritization rule, 428 realism, 193 Prisoner’s Dilemma game, 54, 56, 58, 77, realization plan, 131, 132, 133, 135 79, 80, 116, 126, 141–144, 147–150, of βi , 131 152, 153, 158, 159, 187, 191, 194, realization probability, 131 196, 200–204, 210, 211, 213, 222, reﬂexive accessibility relation, 402 223, 330 regret, 76, 193, 195, 200, 209, 210, 211, privacy, 272 222 probability density function, 328, 329, regret matching, 210 449 reinforcement learning, 194, 204, 205, probably approximately correct (PAC) 209, 221 learning, 207 relaxation method, 350 production economy, 32 repeated game, 64, 72, 141–153, 155, proper equilibrium, 83 167, 187, 190–201, 203, 204, 206, proper labeling, 65, 66, 68, 69 210, 211, 213–215, 222, 344 proper simple game, 371 replicator dynamic, 212, 213, 214–216, proportional allocation mechanism, 296, 218–220, 222 297, 298, 312 representation theorem, 399 proxy bidding, 320 request for quote, 327 pruning, 4, 121, 165, 352 revealing equilibrium, 225 pseudonymous bidding, 349 revelation principle, 265, 266, 267, 278, pure coordination game, 56,57 290, 305, 311, 358 pure strategy, 58, 59, 61, 63, 64, 71, 74, revenue maximization, 274 78, 80–82, 88, 93, 99, 100, 103, 106, revenue minimization, 275 107, 109–111, 115, 116, 126–130, revenue monotonicity, 286, 287, 312 134, 137, 152, 161, 163, 195, 198, reverse auction, 317, 327 209, 210, 213, 218, 436 ring center, 330, 331, 332 pure-strategy proﬁle, 58, 59, 106, 107, risk attitude, 269, 270, 271, 318, 320, 110, 163, 167, 197, 198 321, 326 risk averse, 270, 271, 320, 326 Q-learning, 204, 205, 206–209, 222 risk neutral, 269, 271, 272, 318, 320, quasi-partition, 413, 414, 416 321, 324, 326, 329, 330, 339 quasilinear mechanism, see mechanism, risk seeking, 271, 320, 326 quasilinear Rochambeau game, see Rock, Paper, quasilinear preferences, 268, 269, 271, Scissors game 275, 291, 318 Rock, Paper, Scissors game, 57, 58, 199 quasilinear utility functions, 268, 288 rules of conversation, 230

R-max algorithm, 207, 222 safety, 211 random sampling auction, 342, 343 safety of a learning rule, 195 optimal price, 343, 364 sample space, 449, 450 ranked independence of irrelevant Santa Fe Bar problem, 167 alternatives (RIIA), 257 scheduling problem, 19, 36, 37–40, 45, ranking rule, 255, 256–259 294, 296 ranking systems setting, 255 sealed-bid auction, 316, 317, 318–320, ranking voting, 245 322, 324, 328, 329, 335, 336, 348 rational balance, 439 multiunit, 336 rational consequence relation, 429 second-chance mechanism, 293, 312

Index 481

second-price auction, 312, 317, 319–322, social welfare function, 244, 247–249, 325–331, 334, 335, 338, 339, 349, 252–255 364, 377 social welfare maximization, 273 security level, 72 solution concept, 43, 60, 61, 62, 71, 73, self-coherent belief, 424 76, 78, 81, 83, 85, 87, 110, 113, 139, self-committing utterance, 224 157, 179, 193, 217, 264, 297, 367, self-play, 194, 195, 201, 209, 211, 212 371, 372, 376, 378, 381, 389, 390, self-revealing utterance, 224 436 selﬁsh routing, 172, 173–176, 187, 262, coalitional game theory 296, 298 -core, see -core Semantic Web, 237 core, see core sensor network, 1,2,3 least core, see least core separating equilibrium, 229 nucleolus, see nucleolus sequence, 129, 130–134, 136 Shapley value, see Shapley value sequence form, 129, 130, 132, 134, 136, noncooperative game theory 139, 165, 178, 187 -Nash equilibrium, sequence-form payoff function, 130 see -Nash equilibrium sequential auction, 339, 364 Bayes–Nash equilibrium, sequential equilibrium, 137, 136–139 see Bayes–Nash equilibrium serial accessibility relation, 401 correlated equilibrium, serial model, 401 see correlated equilibrium set packing problem, 37, 350 equilibrium in dominant strategies, see equilibrium in dominant shadow price, 32 strategies Shapley value, 299, 300, 367, 373, 374, ex post equilibrium, 377, 381–383, 385–387, 390 see ex post equilibrium Shapley value mechanism, 299–300 hyperstable set, see hyperstable set Shapley’s Almost-Rock-Paper-Scissors maxmin strategies, game, 199 see maxmin strategy Sharing game, 114, 115 minmax strategies, shill bid, 349 see minmax strategy signaling game, 223, 227, 228, 233, 234, Nash equilibrium, 238 see Nash equilibrium 288 simple exchange, Pareto optimality, simple game, 370, 371, 377 see Pareto optimality simplex algorithm, 96, 453 perfect equilibrium, simplicial subdivision, 65, 66, 103, 104, see trembling-hand perfect 178 equilibrium simplotope, 69, 104 proper equilibrium, simultaneous ascending auction, 348, see proper equilibrium 358 rationalizable strategies, single-minded, 360 see rationalizable strategy single-parameter valuation, 292 sequential equilibrium, single-sided auction, 273, 283, 315, 361 see sequential equilibrium slack variable, 88, 89, 91–93 solvable by iterated elimination, Smith set, 244, 245, 259 see solvable by iterated smooth ﬁctitious play, 200, 210 elimination social choice correspondence, 243 stable equilibrium, social choice function, 243, 244, 247, see stable equilibrium 248, 251, 252, 254, 264–268, 276, strong equilibrium, 278, 284, 290–292, 301, 358 see strong equilibrium social choice problem, 241, 255 subgame-perfect equilibrium, social convention, 43, 44, 219, 220, 221 see subgame-perfect equilibrium social law, 19, 43, 44, 45, 219, 307, 313 solvable by iterated elimination, 79, 199

482 Index

Spence signaling game, 228, 239 substitutes, 37, 40, 347 Sperner’s lemma, 66, 66–69, 90 partial, 347 sponsored search auction, see position strict, 347 auction superadditive game, 370, 381, 384, 391 stable equilibrium, 86 superadditive valuation function, see stable marriage, 303 complementarity stable matching, 303, 304–306, 312 support, see mixed strategy, support of stable sets, 389 support-enumeration method, 100, stable steady state, 215, 216, 218 112 Stackelberg game, 190 symmetric game, 211, 213, 221, 311 Stackelberg routing, 176 synergy representation, 381, 384, 385 Stag Hunt game, 225, 226 targeted learning, 211, 212, 222 stage game, 142, 143, 144, 146, 153, efficient, 211 190, 191, 193–198, 209, 210, targeted optimality, 195, 211 213 TCP user’s game, 54 standard n-simplex, 65 team game, 56 stationary strategy, 143, 154, 193, 195 Tit-for-Tat (TfT), 144 steady state, 197, 198, 214, 215, 216 tit-for-tat (TfT), 144, 148–150, 187, 191, stochastic game, 142, 153, 154–156, 187, 194, 200, 203, 204, 210, 211, 222 191, 194, 195, 204, 205, 208 total preorder, 255, 416, 429, 433, 435 irreducible, 154, 155 total unimodularity, 350, 454 separable reward state independent tractability, 274, 275, 287–289, 359 transition (SR-SIT), 155 traffic, 19, 43, 45, 56, 170, 172–175, 262, single-controller, 155 296, 307 strategic relevance, 185 transferable utility, 271, 367, 368, 388 strategic-form game, see normal-form tree-form game, see extensive-form game game tree-structured bid, 351 strategy trembling-hand perfect equilibrium, 83, behavioral, see behavioral strategy 216 Markov, see Markov strategy trigger strategy, 144, 146, 150, 151, 201, mixed, see mixed strategy 203, 204, 332 pure, see pure strategy truthful, 261, 265, 266–268, 273, stationary, see stationary strategy 276–280, 282–284, 289, 290, trigger, see trigger strategy 292–295, 299, 300, 305, 312, 319, strategy-proof, see incentive 320, 327, 329, 331, 338, 339, 342, compatibility in dominant strategies 343, 345, 346, 348, 349, 358, 359, strict budget balance, see budget balance 361, 364, 377 strict Pareto efficiency, 61, 101, 211, 248, two-sided auction, 361 251, 273 two-sided matching, 301 strictly dominant strategy, 104, 127, type, 157, 159–167, 214, 224, 263–265, 426 267, 268, 272, 273, 292, 294, 295, strong equilibrium, 310, 311, 375 318, 323–325, 424 strong quasi-transitivity, 258 unblocked matching, 303 strong transitivity, 256, 257 unconditional regret, 210 student-optimal matching, 304 uniform pricing rule, 336 subadditive valuation function, see unit resolution, 6 substitutes universal consistency, 195, 209, 222 subgame, 43, 113, 117–120, 122–124, utility function, 40, 47, 48, 49, 52, 53, 55, 133, 134, 136–139, 143, 146, 154, 60, 102, 105, 114, 120, 123, 150, 234 155, 159, 160, 166, 167, 171, 182, subgame-perfect equilibrium (SPE), 113, 183, 243, 262–264, 266–269, 117, 119, 123, 124, 136–139, 146, 271–273, 276, 288, 318, 321 154 utility theory, 47, 49, 50, 85, 263

Index 483

validity, 399, 413, 457 approval, see approval voting valuation, 272, 315, 319, 321–333, 335, Borda, see Borda voting 336, 338–343, 345–350, cumulative, see cumulative voting 352–360 nonranking, see nonranking voting valuation function, 37, 276, 296–298, pairwise elimination, see pairwise 346 elimination nonadditive, 347 plurality, see plurality voting subadditive, see substitutes plurality with elimination, see plurality superadditive, see complementarity with elimination value ranking, see ranking voting affiliated, see affiliated value Wardrop equilibrium, 173, 188 common, see common value weak achievement goal, 444 independent private, see independent weak budget balance, see budget balance, private values weak value iteration, 23, 156, 205, 221, 455, weak monotonicity (WMON), 291 456 weak Pareto efficiency, 251, 252–254 value of a zero-sum game, 74 weak transitivity, 256, 257 stochastic, 206 weak S5, 412 value query, 359 weighted graph game, 381, 382, 383, 390 variable elimination, 25, 26, 27 weighted majority game, 381 VCG mechanism, see weighted matching, 29 Vickrey–Clarke–Groves mechanism weighted voting games, 381, 390 veridity, 401, 412, 415 well-founded total preorder, 416 verification complexity, 356, Wilson doctrine, 330, 343, 364 357 winner determination problem vertex, 44, 65, 66, 94, 453 combinatorial auction, 349 veto player, 377, 381 general multiunit auction, 340 Vickrey auction, see second-price auction winner’s curse, 334 Vickrey–Clarke–Groves (VCG) mechanism, 176, 280, 281–289, XML, 237 295, 298, 300, 301, 312, 319, 338, XOR bid, 354, 355, 356 340, 343, 345, 346, 348, 349, zero-sum game, 57, 61, 73, 74, 87, 105, 357–359, 377, 378 112, 120, 123, 134, 135, 139, 147, virtual valuation, 329 155, 165, 194, 196, 205–207, 222, voting method, 244–246 370