1324:
those having a (scarce) left shoe, and 0 to those owning an (oversupplied) right shoe. No coalition can block this outcome, because no left shoe owner will accept less than 10, and any imputation that pays a positive amount to any right shoe owner must pay less than 10000 in total to the other players, who can get 10000 on their own. So, there is just one imputation in the core.
33:
1314:
game with the following characteristic function: Each man has three gloves, that is one pair with a market value of €5. Together, they have 6 gloves or 3 pair, having a market value of €15. Since the singleton coalitions (consisting of a single man) are the only non-trivial coalitions of the game all
1335:
The
Walrasian equilibria of an exchange economy in a general equilibrium model, will lie in the core of the cooperation game between the agents. Graphically, and in a two-agent economy (see Edgeworth Box), the core is the set of points on the contract curve (the set of Pareto optimal allocations)
1323:
For the moment ignore shoe sizes: a pair consists of a left and a right shoe, which can then be sold for €10. Consider a game with 2001 players: 1000 of them have 1 left shoe, 1001 have 1 right shoe. The core of this game is somewhat surprising: it consists of a single imputation that gives 10 to
1344:
When alternatives are allocations (list of consumption bundles), it is natural to assume that any nonempty subsets of individuals can block a given allocation. When alternatives are public (such as the amount of a certain public good), however, it is more appropriate to assume that only the
1295:
1309:
Mr A and Mr B are knitting gloves. The gloves are one-size-fits-all, and two gloves make a pair that they sell for €5. They have each made three gloves. How to share the proceeds from the sale? The problem can be described by a
111:
a feasible allocation if the members of that coalition can generate more value among themselves than they are allocated in the original allocation. As such, that coalition is not incentivized to stay with the grand coalition.
102:
where no coalition of agents can benefit by breaking away from the grand coalition. One can think of the core corresponding to situations where it is possible to sustain cooperation among all agents. A coalition is said to
1133:
1315:
possible distributions of this sum belong to the core, provided both men get at least €5, the amount they can achieve on their own. For instance (7.5, 7.5) belongs to the core, but so does (5, 10) or (9, 6).
1300:
If there are more than two miners and there is an even number of miners, then the core consists of the single payoff where each miner gets 1/2. If there is an odd number of miners, then the core is empty.
1327:
The message remains the same, even if we increase the numbers as long as left shoes are scarcer. The core has been criticized for being so extremely sensitive to oversupply of one type of player.
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states that, given additional assumptions, the limit of the core as the number of consumers goes to infinity is a set of
Walrasian equilibria.
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1736:
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1459:
1290:{\displaystyle v(S)={\begin{cases}|S|/2,&{\text{if }}|S|{\text{ is even}};\\(|S|-1)/2,&{\text{if }}|S|{\text{ is odd}}.\end{cases}}}
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coalitions that are large enough can block a given alternative. The collection of such large ("winning") coalitions is called a
1393:. A necessary and sufficient condition for the core to be nonempty for all profile of preferences, is provided in terms of the
2424:
1965:
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miners, who have discovered large bars of gold. If two miners can carry one piece of gold, then the payoff of a coalition
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of a game if there is no coalition that can improve upon it. The core is then the set of all feasible allocations.
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1577:(1963). "Some applications of linear programming methods to the theory of cooperative games (In Russian)".
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1547:"A note on the weak core of simple games with ordinary preferences and uncountable alternatives"
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is odd. A game that proposes to divide one unit of a good among a coalition having at least (
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lying between each of the agents' indifference curves defined at the initial endowments.
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2015:
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Mathematical
Psychics: An Essay on the Application of Mathematics to the Moral Sciences
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is based on the idea that only winning coalitions can reject an alternative
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is the set of imputations that are not dominated by any other imputation.
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Multiagent
Systems: Algorithmic, Game-Theoretic, and Logical Foundations
2495:
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2163:
1105:+1)/2 members has an empty core. That is, no stable coalition exists.
855:
to the one above, states that the core is a set of payoff allocations
1475:
Gillies, D. B. (1959). "Solutions to general non-zero-sum games". In
1053:
2264:
1722:
1781:
1351:
core of a simple game with respect to a profile of preferences
26:
143:
considered it an interesting concept, they only worked with
1283:
842:
is the set of imputations that are not strongly-dominated.
127:
The idea of the core already appeared in the writings of
1424:- instrumental in proving the non-emptiness of the core.
47:
1706:. Vol. I. Amsterdam: Elsevier. pp. 397–412.
1507:
Shapley, L. S.; Shubik, M. (1969). "On Market Games".
1454:. Vol. I. Amsterdam: Elsevier. pp. 355–395.
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1694:Peleg, B (1992). "Axiomatizations of the Core". In
1442:Kannai, Y. (1992). "The core and balancedness". In
1052:The core is a set which satisfies a system of weak
42:
may be too technical for most readers to understand
1704:Handbook of Game Theory with Economic Applications
1452:Handbook of Game Theory with Economic Applications
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1422:Knaster–Kuratowski–Mazurkiewicz–Shapley theorem
151:. The modern definition of the core is due to
1793:
1666:. New York: Academic Press. pp. 77–117.
8:
1751:"The Usefulness of Core Theory in Economics"
1045:The core is always well-defined, but can be
1007:{\displaystyle \sum _{i\in C}x_{i}\geq v(C)}
634:{\displaystyle \sum _{i\in C}y_{i}\leq v(C)}
1800:
1786:
1778:
1721:Shoham, Yoav; Leyton-Brown, Kevin (2009).
1535:due to the contribution of Mr. E. Kohlberg
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70:Learn how and when to remove this message
54:, without removing the technical details.
946:{\displaystyle \sum _{i\in N}x_{i}=v(N)}
1485:Contributions to the Theory of Games IV
1434:
1599:(1967). "On balanced sets and cores".
1331:The core in general equilibrium theory
883:{\displaystyle x\in \mathbb {R} ^{N}}
681:{\displaystyle x\in \mathbb {R} ^{N}}
276:{\displaystyle x\in \mathbb {R} ^{N}}
52:make it understandable to non-experts
7:
1660:"Cooperative Behavior and Stability"
115:An allocation is said to be in the
1849:First-player and second-player win
1640:Edgeworth, Francis Ysidro (1881).
1601:Naval Research Logistics Quarterly
1491:Studies. Vol. 40. Princeton:
25:
1664:Game Theory for Economic Analysis
1071:: the core of a game is nonempty
131:, at the time referred to as the
2867:Game theory equilibrium concepts
1956:Coalition-proof Nash equilibrium
1756:Journal of Economic Perspectives
1373:in favor of another alternative
1056:inequalities. Hence the core is
31:
1545:Yu, Chaowen (8 December 2020).
1082:has the core property, but not
400:{\displaystyle x_{i}\leq y_{i}}
221:denotes the set of players and
1966:Evolutionarily stable strategy
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805:{\displaystyle x_{i}<y_{i}}
628:
622:
512:{\displaystyle x_{i}<y_{i}}
188:
176:
1:
1894:Simultaneous action selection
1014:for all subsets (coalitions)
2826:List of games in game theory
2006:Quantal response equilibrium
1996:Perfect Bayesian equilibrium
1931:Bayes correlated equilibrium
1523:10.1016/0022-0531(69)90008-8
1312:characteristic function form
1033:{\displaystyle C\subseteq N}
712:if there exists a coalition
559:by threatening to leave the
307:if there exists a coalition
2295:Optional prisoner's dilemma
2026:Self-confirming equilibrium
732:, such that each player in
327:, such that each player in
2883:
2760:Principal variation search
2476:Aumann's agreement theorem
2139:Strategy-stealing argument
2051:Trembling hand equilibrium
1981:Markov perfect equilibrium
1976:Mertens-stable equilibrium
1729:Cambridge University Press
1658:Ichiishi, Tatsuro (1983).
1510:Journal of Economic Theory
1493:Princeton University Press
2796:Combinatorial game theory
2455:Princess and monster game
2011:Quasi-perfect equilibrium
1936:Bayesian Nash equilibrium
1340:The core in voting theory
1069:Bondareva–Shapley theorem
956:Coalitional rationality:
147:where the core is always
2811:Evolutionary game theory
2544:Antoine Augustin Cournot
2430:Guess 2/3 of the average
2227:Strictly determined game
2021:Satisfaction equilibrium
1839:Escalation of commitment
2816:Glossary of game theory
2415:Stackelberg competition
2041:Strong Nash equilibrium
1687:A Course in Game Theory
1551:SSRN Electronic Journal
1075:the game is "balanced".
243:characteristic function
84:cooperative game theory
2841:Tragedy of the commons
2821:List of game theorists
2801:Confrontation analysis
2511:Sprague–Grundy theorem
2031:Sequential equilibrium
1951:Correlated equilibrium
1613:10.1002/nav.3800140404
1407:Cooperative bargaining
1387:
1367:
1291:
1034:
1008:
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831:{\displaystyle i\in C}
806:
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726:
706:
692:by another imputation
682:
635:
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459:that strictly-prefers
453:
452:{\displaystyle i\in C}
427:
426:{\displaystyle i\in C}
401:
361:
341:
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287:by another imputation
277:
235:
215:
195:
2614:Jean-François Mertens
1646:. London: C. K. Paul.
1489:Annals of Mathematics
1397:for the simple game.
1388:
1368:
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1080:Walrasian equilibrium
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194:{\displaystyle (N,v)}
2743:Search optimizations
2619:Jennifer Tour Chayes
2506:Revelation principle
2501:Purification theorem
2440:Nash bargaining game
2405:Bertrand competition
2390:El Farol Bar problem
2355:Electronic mail game
2320:Lewis signaling game
1864:Hierarchy of beliefs
1681:Osborne, Martin J.;
1579:Problemy Kybernetiki
1560:10.2139/ssrn.3225500
1377:
1357:
1134:
1119:Consider a group of
1088:Edgeworth conjecture
1018:
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851:Another definition,
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165:transferable utility
2791:Bounded rationality
2410:Cournot competition
2360:Rock paper scissors
2335:Battle of the sexes
2325:Volunteer's dilemma
2197:Perfect information
2124:Dominant strategies
1961:Epsilon-equilibrium
1844:Extensive-form game
1770:10.1257/jep.8.2.151
433:) and there exists
2770:Paranoid algorithm
2750:Alpha–beta pruning
2629:John Maynard Smith
2460:Rendezvous problem
2300:Traveler's dilemma
2290:Gift-exchange game
2285:Prisoner's dilemma
2202:Large Poisson game
2169:Bargaining problem
2074:Backward induction
2046:Subgame perfection
2001:Proper equilibrium
1622:10338.dmlcz/135729
1575:Bondareva, Olga N.
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690:strongly-dominated
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2862:Cooperative games
2849:
2848:
2755:Aspiration window
2724:Suzanne Scotchmer
2679:Oskar Morgenstern
2574:Donald B. Gillies
2516:Zermelo's theorem
2445:Induction puzzles
2400:Fair cake-cutting
2375:Public goods game
2305:Coordination game
2179:Intransitive game
2109:Forward induction
1991:Pareto efficiency
1971:Gibbs equilibrium
1941:Berge equilibrium
1889:Simultaneous game
1747:Telser, Lester G.
1738:978-0-521-89943-7
1713:978-0-444-88098-7
1696:Aumann, Robert J.
1683:Rubinstein, Ariel
1597:Shapley, Lloyd S.
1495:. pp. 47–85.
1461:978-0-444-88098-7
1444:Aumann, Robert J.
1417:Pareto efficiency
1412:Welfare economics
1386:{\displaystyle y}
1366:{\displaystyle x}
1305:Example 2: Gloves
1275:
1257:
1207:
1189:
1115:Example 1: Miners
963:
902:
765:{\displaystyle y}
752:strictly-prefers
745:{\displaystyle C}
725:{\displaystyle C}
705:{\displaystyle y}
590:
576:{\displaystyle C}
552:{\displaystyle y}
532:{\displaystyle C}
472:{\displaystyle y}
360:{\displaystyle y}
340:{\displaystyle C}
320:{\displaystyle C}
300:{\displaystyle y}
234:{\displaystyle v}
214:{\displaystyle N}
80:
79:
72:
16:(Redirected from
2874:
2836:Topological game
2831:No-win situation
2729:Thomas Schelling
2709:Robert B. Wilson
2669:Merrill M. Flood
2639:John von Neumann
2549:Ariel Rubinstein
2534:Albert W. Tucker
2385:War of attrition
2345:Matching pennies
1986:Nash equilibrium
1909:Mechanism design
1874:Normal-form game
1829:Cooperative game
1802:
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1689:. The MIT Press.
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1319:Example 3: Shoes
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168:cooperative game
129:Edgeworth (1881)
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2765:max^n algorithm
2738:
2734:William Vickrey
2694:Reinhard Selten
2649:Kenneth Binmore
2564:David K. Levine
2559:Daniel Kahneman
2526:
2520:
2496:Negamax theorem
2486:Minimax theorem
2464:
2425:Diner's dilemma
2280:All-pay auction
2246:
2232:Stochastic game
2184:Mean-field game
2155:
2148:
2119:Markov strategy
2055:
1921:
1913:
1884:Sequential game
1869:Information set
1854:Game complexity
1824:Congestion game
1812:
1806:
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1654:
1652:Further reading
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1403:
1395:Nakamura number
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1097:players, where
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896:
868:
857:
856:
848:
814:
813:
792:
779:
774:
773:
754:
753:
734:
733:
714:
713:
694:
693:
666:
655:
654:
651:
606:
585:
584:
565:
564:
561:grand coalition
541:
540:
521:
520:
499:
486:
481:
480:
461:
460:
435:
434:
409:
408:
387:
374:
369:
368:
349:
348:
347:weakly-prefers
329:
328:
309:
308:
289:
288:
261:
250:
249:
223:
222:
203:
202:
171:
170:
161:
125:
98:allocations or
76:
65:
59:
56:
48:help improve it
45:
36:
32:
23:
22:
15:
12:
11:
5:
2880:
2878:
2870:
2869:
2864:
2854:
2853:
2847:
2846:
2844:
2843:
2838:
2833:
2828:
2823:
2818:
2813:
2808:
2803:
2798:
2793:
2787:
2785:
2781:
2780:
2778:
2777:
2772:
2767:
2762:
2757:
2752:
2746:
2744:
2740:
2739:
2737:
2736:
2731:
2726:
2721:
2716:
2711:
2706:
2701:
2699:Robert Axelrod
2696:
2691:
2686:
2681:
2676:
2674:Olga Bondareva
2671:
2666:
2664:Melvin Dresher
2661:
2656:
2654:Leonid Hurwicz
2651:
2646:
2641:
2636:
2631:
2626:
2621:
2616:
2611:
2606:
2601:
2596:
2591:
2589:Harold W. Kuhn
2586:
2581:
2579:Drew Fudenberg
2576:
2571:
2569:David M. Kreps
2566:
2561:
2556:
2554:Claude Shannon
2551:
2546:
2541:
2536:
2530:
2528:
2522:
2521:
2519:
2518:
2513:
2508:
2503:
2498:
2493:
2491:Nash's theorem
2488:
2483:
2478:
2472:
2470:
2466:
2465:
2463:
2462:
2457:
2452:
2447:
2442:
2437:
2432:
2427:
2422:
2417:
2412:
2407:
2402:
2397:
2392:
2387:
2382:
2377:
2372:
2367:
2362:
2357:
2352:
2350:Ultimatum game
2347:
2342:
2337:
2332:
2330:Dollar auction
2327:
2322:
2317:
2315:Centipede game
2312:
2307:
2302:
2297:
2292:
2287:
2282:
2277:
2272:
2270:Infinite chess
2267:
2262:
2256:
2254:
2248:
2247:
2245:
2244:
2239:
2237:Symmetric game
2234:
2229:
2224:
2222:Signaling game
2219:
2217:Screening game
2214:
2209:
2207:Potential game
2204:
2199:
2194:
2186:
2181:
2176:
2171:
2166:
2160:
2158:
2150:
2149:
2147:
2146:
2141:
2136:
2134:Mixed strategy
2131:
2126:
2121:
2116:
2111:
2106:
2101:
2096:
2091:
2086:
2081:
2076:
2071:
2065:
2063:
2057:
2056:
2054:
2053:
2048:
2043:
2038:
2033:
2028:
2023:
2018:
2016:Risk dominance
2013:
2008:
2003:
1998:
1993:
1988:
1983:
1978:
1973:
1968:
1963:
1958:
1953:
1948:
1943:
1938:
1933:
1927:
1925:
1915:
1914:
1912:
1911:
1906:
1901:
1896:
1891:
1886:
1881:
1876:
1871:
1866:
1861:
1859:Graphical game
1856:
1851:
1846:
1841:
1836:
1831:
1826:
1820:
1818:
1814:
1813:
1807:
1805:
1804:
1797:
1790:
1782:
1776:
1775:
1763:(2): 151–164.
1743:
1737:
1718:
1712:
1691:
1678:
1672:
1653:
1650:
1649:
1648:
1635:
1632:
1629:
1628:
1607:(4): 453–460.
1588:
1566:
1537:
1498:
1467:
1460:
1433:
1432:
1430:
1427:
1426:
1425:
1419:
1414:
1409:
1402:
1399:
1382:
1362:
1341:
1338:
1332:
1329:
1320:
1317:
1306:
1303:
1298:
1297:
1284:
1279:
1270:
1266:
1262:
1253:
1251:
1248:
1244:
1240:
1237:
1234:
1230:
1226:
1222:
1218:
1215:
1214:
1211:
1202:
1198:
1194:
1185:
1183:
1180:
1176:
1171:
1167:
1163:
1159:
1158:
1156:
1151:
1148:
1145:
1142:
1139:
1116:
1113:
1111:
1108:
1107:
1106:
1091:
1076:
1073:if and only if
1065:
1050:
1042:
1041:
1029:
1026:
1023:
1003:
1000:
997:
994:
991:
986:
982:
976:
973:
970:
966:
954:
942:
939:
936:
933:
930:
925:
921:
915:
912:
909:
905:
892:
891:
877:
872:
867:
864:
847:
844:
827:
824:
821:
799:
795:
791:
786:
782:
761:
741:
721:
701:
675:
670:
665:
662:
653:An imputation
650:
647:
630:
627:
624:
621:
618:
613:
609:
603:
600:
597:
593:
572:
548:
528:
506:
502:
498:
493:
489:
468:
448:
445:
442:
422:
419:
416:
394:
390:
386:
381:
377:
356:
336:
316:
296:
270:
265:
260:
257:
230:
210:
190:
187:
184:
181:
178:
160:
157:
145:zero-sum games
135:. Even though
133:contract curve
124:
121:
78:
77:
39:
37:
30:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2879:
2868:
2865:
2863:
2860:
2859:
2857:
2842:
2839:
2837:
2834:
2832:
2829:
2827:
2824:
2822:
2819:
2817:
2814:
2812:
2809:
2807:
2804:
2802:
2799:
2797:
2794:
2792:
2789:
2788:
2786:
2784:Miscellaneous
2782:
2776:
2773:
2771:
2768:
2766:
2763:
2761:
2758:
2756:
2753:
2751:
2748:
2747:
2745:
2741:
2735:
2732:
2730:
2727:
2725:
2722:
2720:
2719:Samuel Bowles
2717:
2715:
2714:Roger Myerson
2712:
2710:
2707:
2705:
2704:Robert Aumann
2702:
2700:
2697:
2695:
2692:
2690:
2687:
2685:
2682:
2680:
2677:
2675:
2672:
2670:
2667:
2665:
2662:
2660:
2659:Lloyd Shapley
2657:
2655:
2652:
2650:
2647:
2645:
2644:Kenneth Arrow
2642:
2640:
2637:
2635:
2632:
2630:
2627:
2625:
2624:John Harsanyi
2622:
2620:
2617:
2615:
2612:
2610:
2607:
2605:
2602:
2600:
2597:
2595:
2594:Herbert Simon
2592:
2590:
2587:
2585:
2582:
2580:
2577:
2575:
2572:
2570:
2567:
2565:
2562:
2560:
2557:
2555:
2552:
2550:
2547:
2545:
2542:
2540:
2537:
2535:
2532:
2531:
2529:
2523:
2517:
2514:
2512:
2509:
2507:
2504:
2502:
2499:
2497:
2494:
2492:
2489:
2487:
2484:
2482:
2479:
2477:
2474:
2473:
2471:
2467:
2461:
2458:
2456:
2453:
2451:
2448:
2446:
2443:
2441:
2438:
2436:
2433:
2431:
2428:
2426:
2423:
2421:
2418:
2416:
2413:
2411:
2408:
2406:
2403:
2401:
2398:
2396:
2395:Fair division
2393:
2391:
2388:
2386:
2383:
2381:
2378:
2376:
2373:
2371:
2370:Dictator game
2368:
2366:
2363:
2361:
2358:
2356:
2353:
2351:
2348:
2346:
2343:
2341:
2338:
2336:
2333:
2331:
2328:
2326:
2323:
2321:
2318:
2316:
2313:
2311:
2308:
2306:
2303:
2301:
2298:
2296:
2293:
2291:
2288:
2286:
2283:
2281:
2278:
2276:
2273:
2271:
2268:
2266:
2263:
2261:
2258:
2257:
2255:
2253:
2249:
2243:
2242:Zero-sum game
2240:
2238:
2235:
2233:
2230:
2228:
2225:
2223:
2220:
2218:
2215:
2213:
2212:Repeated game
2210:
2208:
2205:
2203:
2200:
2198:
2195:
2193:
2191:
2187:
2185:
2182:
2180:
2177:
2175:
2172:
2170:
2167:
2165:
2162:
2161:
2159:
2157:
2151:
2145:
2142:
2140:
2137:
2135:
2132:
2130:
2129:Pure strategy
2127:
2125:
2122:
2120:
2117:
2115:
2112:
2110:
2107:
2105:
2102:
2100:
2097:
2095:
2094:De-escalation
2092:
2090:
2087:
2085:
2082:
2080:
2077:
2075:
2072:
2070:
2067:
2066:
2064:
2062:
2058:
2052:
2049:
2047:
2044:
2042:
2039:
2037:
2036:Shapley value
2034:
2032:
2029:
2027:
2024:
2022:
2019:
2017:
2014:
2012:
2009:
2007:
2004:
2002:
1999:
1997:
1994:
1992:
1989:
1987:
1984:
1982:
1979:
1977:
1974:
1972:
1969:
1967:
1964:
1962:
1959:
1957:
1954:
1952:
1949:
1947:
1944:
1942:
1939:
1937:
1934:
1932:
1929:
1928:
1926:
1924:
1920:
1916:
1910:
1907:
1905:
1904:Succinct game
1902:
1900:
1897:
1895:
1892:
1890:
1887:
1885:
1882:
1880:
1877:
1875:
1872:
1870:
1867:
1865:
1862:
1860:
1857:
1855:
1852:
1850:
1847:
1845:
1842:
1840:
1837:
1835:
1832:
1830:
1827:
1825:
1822:
1821:
1819:
1815:
1811:
1803:
1798:
1796:
1791:
1789:
1784:
1783:
1780:
1771:
1766:
1762:
1758:
1757:
1752:
1748:
1744:
1740:
1734:
1730:
1726:
1725:
1719:
1715:
1709:
1705:
1701:
1697:
1692:
1688:
1684:
1679:
1675:
1673:0-12-370180-5
1669:
1665:
1661:
1656:
1655:
1651:
1645:
1644:
1638:
1637:
1633:
1623:
1618:
1614:
1610:
1606:
1602:
1598:
1592:
1589:
1584:
1580:
1576:
1570:
1567:
1561:
1556:
1552:
1548:
1541:
1538:
1532:
1528:
1524:
1520:
1516:
1512:
1511:
1502:
1499:
1494:
1490:
1486:
1482:
1478:
1477:Tucker, A. W.
1471:
1468:
1463:
1457:
1453:
1449:
1445:
1438:
1435:
1428:
1423:
1420:
1418:
1415:
1413:
1410:
1408:
1405:
1404:
1400:
1398:
1396:
1380:
1360:
1352:
1348:
1339:
1337:
1330:
1328:
1325:
1318:
1316:
1313:
1304:
1302:
1277:
1264:
1249:
1246:
1242:
1235:
1232:
1224:
1209:
1206: is even
1196:
1181:
1178:
1174:
1165:
1154:
1149:
1143:
1137:
1130:
1129:
1128:
1126:
1122:
1114:
1109:
1104:
1100:
1096:
1093:Let there be
1092:
1089:
1085:
1081:
1077:
1074:
1070:
1066:
1063:
1059:
1055:
1051:
1048:
1044:
1043:
1027:
1024:
1021:
998:
992:
989:
984:
980:
974:
971:
968:
964:
955:
937:
931:
928:
923:
919:
913:
910:
907:
903:
894:
893:
875:
865:
862:
854:
850:
849:
845:
843:
841:
825:
822:
819:
797:
793:
789:
784:
780:
759:
739:
719:
699:
691:
673:
663:
660:
648:
646:
644:
625:
619:
616:
611:
607:
601:
598:
595:
591:
570:
562:
546:
526:
504:
500:
496:
491:
487:
466:
446:
443:
440:
420:
417:
414:
392:
388:
384:
379:
375:
354:
334:
314:
294:
286:
268:
258:
255:
248:
244:
228:
208:
185:
182:
179:
169:
166:
158:
156:
154:
150:
146:
142:
138:
134:
130:
122:
120:
118:
113:
110:
106:
101:
97:
93:
89:
85:
74:
71:
63:
60:February 2024
53:
49:
43:
40:This article
38:
29:
28:
19:
2689:Peyton Young
2684:Paul Milgrom
2599:Hervé Moulin
2539:Amos Tversky
2481:Folk theorem
2192:-player game
2189:
2114:Grim trigger
1945:
1760:
1754:
1727:. New York:
1723:
1703:
1700:Hart, Sergiu
1686:
1663:
1642:
1604:
1600:
1591:
1582:
1578:
1569:
1550:
1540:
1514:
1508:
1505:As noted by
1501:
1484:
1470:
1451:
1448:Hart, Sergiu
1437:
1350:
1346:
1343:
1334:
1326:
1322:
1308:
1299:
1274: is odd
1124:
1120:
1118:
1102:
1098:
1094:
1083:
895:Efficiency:
839:
689:
652:
642:
539:can enforce
284:
162:
132:
126:
116:
114:
108:
105:improve upon
104:
87:
81:
66:
57:
41:
2806:Coopetition
2609:Jean Tirole
2604:John Conway
2584:Eric Maskin
2380:Blotto game
2365:Pirate game
2174:Global game
2144:Tit for tat
2079:Bid shading
2069:Appeasement
1919:Equilibrium
1899:Solved game
1834:Determinacy
1817:Definitions
1810:game theory
1634:Works cited
1517:(1): 9–25.
1481:Luce, R. D.
1347:simple game
163:Consider a
141:Morgenstern
137:von Neumann
100:imputations
18:Core-stable
2856:Categories
2450:Trust game
2435:Kuhn poker
2104:Escalation
2099:Deterrence
2089:Cheap talk
2061:Strategies
1879:Preference
1808:Topics of
1585:: 119–139.
1429:References
1084:vice versa
890:satisfying
853:equivalent
846:Properties
247:imputation
159:Definition
2634:John Nash
2340:Stag hunt
2084:Collusion
1531:153498438
1233:−
1025:⊆
990:≥
972:∈
965:∑
911:∈
904:∑
866:∈
840:weak core
823:∈
664:∈
649:Weak core
617:≤
599:∈
592:∑
444:∈
418:∈
385:≤
285:dominated
259:∈
2775:Lazy SMP
2469:Theorems
2420:Deadlock
2275:Checkers
2156:of games
1923:concepts
1749:(1994).
1702:(eds.).
1685:(1994).
1483:(eds.).
1450:(eds.).
1401:See also
1256:if
1188:if
812:for all
563:to form
407:for all
96:feasible
2527:figures
2310:Chicken
2164:Auction
2154:Classes
1110:Example
838:). The
641:). The
519:), and
241:is the
153:Gillies
90:is the
46:Please
1735:
1710:
1670:
1529:
1458:
1349:. The
1086:. The
1078:Every
1062:convex
1058:closed
1054:linear
201:where
123:Origin
86:, the
2265:Chess
2252:Games
1527:S2CID
1047:empty
245:. An
149:empty
109:block
1946:Core
1733:ISBN
1708:ISBN
1668:ISBN
1456:ISBN
1067:The
1060:and
790:<
643:core
497:<
139:and
117:core
88:core
2525:Key
1765:doi
1617:hdl
1609:doi
1555:doi
1519:doi
1127:is
688:is
283:is
107:or
94:of
92:set
82:In
50:to
2858::
2260:Go
1759:.
1753:.
1731:.
1698:;
1662:.
1615:.
1605:14
1603:.
1583:10
1581:.
1553:.
1549:.
1525:.
1513:.
1487:.
1479:;
1446:;
155:.
2190:n
1801:e
1794:t
1787:v
1773:.
1767::
1761:8
1741:.
1716:.
1676:.
1625:.
1619::
1611::
1563:.
1557::
1533:.
1521::
1515:1
1464:.
1381:y
1361:x
1278:.
1269:|
1265:S
1261:|
1250:,
1247:2
1243:/
1239:)
1236:1
1229:|
1225:S
1221:|
1217:(
1210:;
1201:|
1197:S
1193:|
1182:,
1179:2
1175:/
1170:|
1166:S
1162:|
1155:{
1150:=
1147:)
1144:S
1141:(
1138:v
1125:S
1121:n
1103:n
1099:n
1095:n
1064:.
1049:.
1040:.
1028:N
1022:C
1002:)
999:C
996:(
993:v
985:i
981:x
975:C
969:i
953:,
941:)
938:N
935:(
932:v
929:=
924:i
920:x
914:N
908:i
876:N
871:R
863:x
826:C
820:i
798:i
794:y
785:i
781:x
772:(
760:y
740:C
720:C
700:y
674:N
669:R
661:x
629:)
626:C
623:(
620:v
612:i
608:y
602:C
596:i
583:(
571:C
547:y
527:C
505:i
501:y
492:i
488:x
479:(
467:y
447:C
441:i
421:C
415:i
393:i
389:y
380:i
376:x
367:(
355:y
335:C
315:C
295:y
269:N
264:R
256:x
229:v
209:N
189:)
186:v
183:,
180:N
177:(
73:)
67:(
62:)
58:(
44:.
20:)
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