598:
equilibrium no player's strategy is strictly dominated, in a PBE, for any information set no player's strategy is strictly dominated beginning at that information set. That is, for every belief that the player could hold at that information set there is no strategy that yields a greater expected payoff for that player. Unlike the above solution concepts, no player's strategy is strictly dominated beginning at any information set even if it is off the equilibrium path. Thus in PBE, players cannot threaten to play strategies that are strictly dominated beginning at any information set off the equilibrium path.
31:
624:
another player is (i.e. there is imperfect and asymmetric information), that player may form a belief of what type that player is by observing that player's past actions. Hence the belief formed by that player of what the probability of the opponent being a certain type is based on the past play of
597:
In a
Bayesian game a strategy determines what a player plays at every information set controlled by that player. The requirement that beliefs are consistent with strategies is something not specified by subgame perfection. Hence, PBE is a consistency condition on players' beliefs. Just as in a Nash
521:
For example, consider a dynamic game with an incumbent firm and a potential entrant to the industry. The incumbent has a monopoly and wants to maintain its market share. If the entrant enters, the incumbent can either fight or accommodate the entrant. If the incumbent accommodates, the entrant will
517:
In some games, there are multiple Nash equilibria, but not all of them are realistic. In dynamic games, backward induction can be used to eliminate unrealistic Nash equilibria. Backward induction assumes that players are rational and will make the best decisions based on their future expectations.
525:
The best response for the incumbent if the entrant enters is to accommodate, and the best response for the entrant if the incumbent accommodates is to enter. This results in a Nash equilibrium. However, if the incumbent chooses to fight, the best response for the entrant is to not enter. If the
529:
However, this second Nash equilibrium can be eliminated by backward induction because it relies on a noncredible threat from the incumbent. By the time the incumbent reaches the decision node where it can choose to fight, it would be irrational to do so because the entrant has already entered.
628:
Kohlberg and
Mertens (1986) introduced the solution concept of Stable equilibrium, a refinement that satisfies forward induction. A counter-example was found where such a stable equilibrium did not satisfy backward induction. To resolve the problem
66:
is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are
567:. In these cases, subgame perfection can be used. The eliminated Nash equilibrium described above is subgame imperfect because it is not a Nash equilibrium of the subgame that starts at the node reached once the entrant has entered.
585:, a game of imperfect information may have only one subgame – itself – and hence subgame perfection cannot be used to eliminate any Nash equilibria. A perfect Bayesian equilibrium (PBE) is a specification of players' strategies
307:
594:). In particular, the intuition of PBE is that it specifies player strategies that are rational given the player beliefs it specifies and the beliefs it specifies are consistent with the strategies it specifies.
526:
entrant does not enter, it does not matter what the incumbent chooses to do. Hence, fight can be considered a best response for the incumbent if the entrant does not enter, resulting in another Nash equilibrium.
780:
589:
about which node in the information set has been reached by the play of the game. A belief about a decision node is the probability that a particular player thinks that node is or will be in play (on the
403:
when there is some other strategy available to the player that always has a higher payoff, regardless of the strategies that the other players choose. (Strictly dominated strategies are also important in
499:) in which every strategy played by every agent (agent i) is a best response to every other strategy played by all the other opponents (agents j for every j≠i) . A strategy by a player is a
242:
503:
to another player's strategy if there is no other strategy that could be played that would yield a higher pay-off in any situation in which the other player's strategy is played.
349:
559:
A generalization of backward induction is subgame perfection. Backward induction assumes that all future play will be rational. In subgame perfect equilibria, play in every
82:
to narrow down the solutions. Each successive solution concept presented in the following improves on its predecessor by eliminating implausible equilibria in richer games.
378:
134:
620:
is so called because just as backward induction assumes future play will be rational, forward induction assumes past play was rational. Where a player does not know what
823:
Mertens, Jean-François, 1989. "Stable
Equilibria - A reformulation. Part 1 Basic Definitions and Properties," Mathematics of Operations Research, Vol. 14, No. 4, Nov.
563:
is rational (specifically a Nash equilibrium). Backward induction can only be used in terminating (finite) games of definite length and cannot be applied to games with
52:
108:
161:
185:
522:
enter and gain profit. If the incumbent fights, it will lower its prices, run the entrant out of business (incurring exit costs), and damage its own profits.
78:
Many solution concepts, for many games, will result in more than one solution. This puts any one of the solutions in doubt, so a game theorist may apply a
2046:
250:
581:
Sometimes subgame perfection does not impose a large enough restriction on unreasonable outcomes. For example, since subgames cannot cut through
979:
930:
876:
814:
1878:
1695:
1230:
1028:
779:
Govindan, Srihari & Robert Wilson, 2008. "Refinements of Nash
Equilibrium," The New Palgrave Dictionary of Economics, 2nd Edition.
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1333:
853:
844:
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641:
1135:
518:
This eliminates noncredible threats, which are threats that a player would not carry out if they were ever called upon to do so.
1604:
796:
1145:
684:
1474:
1655:
1073:
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582:
2005:
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34:
Selected equilibrium refinements in game theory. Arrows point from a refinement to the more general concept (i.e., ESS
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1975:
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1990:
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1793:
630:
1995:
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1008:
664:
542:
395:
1929:
2020:
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1980:
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1504:
1363:
1313:
1308:
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in the name of this solution concept alludes to the fact that players update their beliefs according to
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1479:
1464:
412:
483:(a strategy profile specifies a strategy for every player, e.g. in the above prisoners' dilemma game (
2041:
1813:
1798:
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68:
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1970:
1589:
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1303:
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1140:
1023:
653:
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113:
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1934:
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1120:
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388:
37:
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concept, probably the first solution concept satisfying both forward and backward induction.
93:
2015:
2010:
1944:
1908:
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72:
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1033:
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537:
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905:
Evolutionary stability in extensive two-person games – correction and further development
625:
that opponent being rational. A player may elect to signal his type through his actions.
30:
1853:
1843:
1833:
1768:
1758:
1748:
1733:
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1509:
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are eliminated from the set of strategies that might feasibly be played. A strategy is
170:
2035:
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1823:
1803:
1629:
1574:
1549:
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1293:
17:
1985:
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1323:
1258:
1248:
1078:
1013:
989:
735:
59:
609:. They calculate probabilities given what has already taken place in the game.
302:{\displaystyle F:\Gamma \rightarrow \bigcup \nolimits _{G\in \Gamma }2^{S_{G}}}
1614:
1268:
829:
1519:
1439:
1263:
868:
745:
530:
Therefore, backward induction eliminates this unrealistic Nash equilibrium.
799:," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
1954:
1454:
682:
Cho, I-K.; Kreps, D. M. (1987). "Signaling Games and Stable
Equilibria".
957:
918:
Multiagent
Systems: Algorithmic, Game-Theoretic, and Logical Foundations
1675:
1665:
1343:
715:
560:
405:
824:
806:
Essentials of Game Theory: A Concise, Multidisciplinary
Introduction
707:
423:
for both players because either player is always better off playing
393:
In this solution concept, players are assumed to be rational and so
1444:
916:
961:
804:
830:
An evolutionary analysis of backward and forward induction
786:
Evolutionary stable strategies: a review of basic theory
770:
Oddness of the number of equilibrium points: a new proof
357:
315:
253:
197:
173:
142:
116:
96:
40:
891:
Evolutionary stability in extensive two-person games
809:. San Rafael, CA: Morgan & Claypool Publishers.
27:
Formal rule for predicting how a game will be played
1963:
1922:
1704:
1648:
1430:
1332:
1239:
1097:
996:
948:
Evolutionary stable sets in mixed-strategist models
795:
Kohlberg, Elon & Jean-François
Mertens, 1986. "
640:Forward induction yields a unique solution for the
372:
343:
301:
236:
179:
155:
128:
102:
46:
939:Thomas, B. (1985a) On evolutionary stable sets.
973:
237:{\displaystyle \Pi _{G\in \Gamma }2^{S_{G}};}
110:be the class of all games and, for each game
8:
980:
966:
958:
915:Shoham, Yoav; Leyton-Brown, Kevin (2009).
803:Leyton-Brown, Kevin; Shoham, Yoav (2008).
697:
633:introduced what game theorists now call
356:
335:
314:
291:
286:
270:
252:
223:
218:
202:
196:
172:
147:
141:
115:
95:
39:
797:On the Strategic Stability of Equilibria
668:
429:
427:, regardless of what his opponent does.
383:Rationalizability and iterated dominance
29:
828:Noldeke, G. & Samuelson, L. (1993)
411:.) For example, in the (single period)
7:
774:International Journal of Game Theory
191:is an element of the direct product
344:{\displaystyle F(G)\subseteq S_{G}}
267:
1029:First-player and second-player win
491:) specifies that prisoner 1 plays
364:
277:
260:
209:
199:
123:
97:
25:
845:Evolution and the Theory of Games
2047:Game theory equilibrium concepts
1136:Coalition-proof Nash equilibrium
549:Subgame perfect Nash equilibrium
1146:Evolutionarily stable strategy
834:Games & Economic Behaviour
790:Theoretical Population Biology
685:Quarterly Journal of Economics
325:
319:
263:
1:
1074:Simultaneous action selection
396:strictly dominated strategies
373:{\displaystyle G\in \Gamma .}
2006:List of games in game theory
1186:Quantal response equilibrium
1176:Perfect Bayesian equilibrium
1111:Bayes correlated equilibrium
744:. Cambridge, Massachusetts:
571:Perfect Bayesian equilibrium
129:{\displaystyle G\in \Gamma }
1475:Optional prisoner's dilemma
1206:Self-confirming equilibrium
555:Subgame perfect equilibrium
2063:
1940:Principal variation search
1656:Aumann's agreement theorem
1319:Strategy-stealing argument
1231:Trembling hand equilibrium
1161:Markov perfect equilibrium
1156:Mertens-stable equilibrium
923:Cambridge University Press
659:Trembling hand equilibrium
635:Mertens-stable equilibrium
574:
552:
510:
472:
386:
1976:Combinatorial game theory
1635:Princess and monster game
1191:Quasi-perfect equilibrium
1116:Bayesian Nash equilibrium
419:is strictly dominated by
1991:Evolutionary game theory
1724:Antoine Augustin Cournot
1610:Guess 2/3 of the average
1407:Strictly determined game
1201:Satisfaction equilibrium
1019:Escalation of commitment
479:A Nash equilibrium is a
47:{\displaystyle \subset }
1996:Glossary of game theory
1595:Stackelberg competition
1221:Strong Nash equilibrium
865:A course in game theory
784:Hines, W. G. S. (1987)
665:The Intuitive Criterion
543:Stackelberg competition
103:{\displaystyle \Gamma }
2021:Tragedy of the commons
2001:List of game theorists
1981:Confrontation analysis
1691:Sprague–Grundy theorem
1211:Sequential equilibrium
1131:Correlated equilibrium
538:Monetary policy theory
374:
345:
303:
238:
181:
157:
130:
104:
55:
48:
1794:Jean-François Mertens
631:Jean-François Mertens
565:imperfect information
495:and prisoner 2 plays
443:Prisoner 1 Cooperate
375:
346:
304:
239:
182:
158:
156:{\displaystyle S_{G}}
131:
105:
49:
33:
1923:Search optimizations
1799:Jennifer Tour Chayes
1686:Revelation principle
1681:Purification theorem
1620:Nash bargaining game
1585:Bertrand competition
1570:El Farol Bar problem
1535:Electronic mail game
1500:Lewis signaling game
1044:Hierarchy of beliefs
859:Osborne, Martin J.;
669:Cho & Kreps 1987
435:Prisoner 2 Cooperate
355:
313:
251:
195:
171:
140:
114:
94:
69:equilibrium concepts
38:
1971:Bounded rationality
1590:Cournot competition
1540:Rock paper scissors
1515:Battle of the sexes
1505:Volunteer's dilemma
1377:Perfect information
1304:Dominant strategies
1141:Epsilon-equilibrium
1024:Extensive-form game
946:Thomas, B. (1985b)
654:Extensive form game
1950:Paranoid algorithm
1930:Alpha–beta pruning
1809:John Maynard Smith
1640:Rendezvous problem
1480:Traveler's dilemma
1470:Gift-exchange game
1465:Prisoner's dilemma
1382:Large Poisson game
1349:Bargaining problem
1254:Backward induction
1226:Subgame perfection
1181:Proper equilibrium
642:burning money game
513:Backward induction
507:Backward induction
454:Prisoner 1 Defect
438:Prisoner 2 Defect
413:prisoners' dilemma
401:strictly dominated
370:
341:
299:
234:
177:
153:
126:
100:
56:
44:
2029:
2028:
1935:Aspiration window
1904:Suzanne Scotchmer
1859:Oskar Morgenstern
1754:Donald B. Gillies
1696:Zermelo's theorem
1625:Induction puzzles
1580:Fair cake-cutting
1555:Public goods game
1485:Coordination game
1359:Intransitive game
1289:Forward induction
1171:Pareto efficiency
1151:Gibbs equilibrium
1121:Berge equilibrium
1069:Simultaneous game
952:Theor. Pop. Biol.
932:978-0-521-89943-7
878:978-0-262-65040-3
861:Rubinstein, Ariel
840:Maynard Smith, J.
816:978-1-59829-593-1
618:Forward induction
613:Forward induction
466:
465:
389:Rationalizability
180:{\displaystyle G}
165:strategy profiles
86:Formal definition
18:Forward induction
16:(Redirected from
2054:
2016:Topological game
2011:No-win situation
1909:Thomas Schelling
1889:Robert B. Wilson
1849:Merrill M. Flood
1819:John von Neumann
1729:Ariel Rubinstein
1714:Albert W. Tucker
1565:War of attrition
1525:Matching pennies
1166:Nash equilibrium
1089:Mechanism design
1054:Normal-form game
1009:Cooperative game
982:
975:
968:
959:
936:
882:
820:
759:
727:
701:
592:equilibrium path
583:information sets
481:strategy profile
475:Nash equilibrium
469:Nash equilibrium
430:
409:game-tree search
379:
377:
376:
371:
350:
348:
347:
342:
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339:
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189:solution concept
186:
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135:
133:
132:
127:
109:
107:
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101:
73:Nash equilibrium
71:, most famously
64:solution concept
53:
51:
50:
45:
21:
2062:
2061:
2057:
2056:
2055:
2053:
2052:
2051:
2032:
2031:
2030:
2025:
1959:
1945:max^n algorithm
1918:
1914:William Vickrey
1874:Reinhard Selten
1829:Kenneth Binmore
1744:David K. Levine
1739:Daniel Kahneman
1706:
1700:
1676:Negamax theorem
1666:Minimax theorem
1644:
1605:Diner's dilemma
1460:All-pay auction
1426:
1412:Stochastic game
1364:Mean-field game
1335:
1328:
1299:Markov strategy
1235:
1101:
1093:
1064:Sequential game
1049:Information set
1034:Game complexity
1004:Congestion game
992:
986:
933:
914:
909:Math. Soc. Sci.
895:Math. Soc. Sci.
879:
858:
817:
802:
756:
732:Fudenberg, Drew
730:
708:10.2307/1885060
699:10.1.1.407.5013
681:
678:
650:
615:
579:
573:
557:
551:
515:
509:
477:
471:
415:(shown below),
391:
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28:
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5:
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1911:
1906:
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1879:Robert Axelrod
1876:
1871:
1866:
1861:
1856:
1854:Olga Bondareva
1851:
1846:
1844:Melvin Dresher
1841:
1836:
1834:Leonid Hurwicz
1831:
1826:
1821:
1816:
1811:
1806:
1801:
1796:
1791:
1786:
1781:
1776:
1771:
1769:Harold W. Kuhn
1766:
1761:
1759:Drew Fudenberg
1756:
1751:
1749:David M. Kreps
1746:
1741:
1736:
1734:Claude Shannon
1731:
1726:
1721:
1716:
1710:
1708:
1702:
1701:
1699:
1698:
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1673:
1671:Nash's theorem
1668:
1663:
1658:
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1650:
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1582:
1577:
1572:
1567:
1562:
1557:
1552:
1547:
1542:
1537:
1532:
1530:Ultimatum game
1527:
1522:
1517:
1512:
1510:Dollar auction
1507:
1502:
1497:
1495:Centipede game
1492:
1487:
1482:
1477:
1472:
1467:
1462:
1457:
1452:
1450:Infinite chess
1447:
1442:
1436:
1434:
1428:
1427:
1425:
1424:
1419:
1417:Symmetric game
1414:
1409:
1404:
1402:Signaling game
1399:
1397:Screening game
1394:
1389:
1387:Potential game
1384:
1379:
1374:
1366:
1361:
1356:
1351:
1346:
1340:
1338:
1330:
1329:
1327:
1326:
1321:
1316:
1314:Mixed strategy
1311:
1306:
1301:
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1286:
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1256:
1251:
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1237:
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1234:
1233:
1228:
1223:
1218:
1213:
1208:
1203:
1198:
1196:Risk dominance
1193:
1188:
1183:
1178:
1173:
1168:
1163:
1158:
1153:
1148:
1143:
1138:
1133:
1128:
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1113:
1107:
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1091:
1086:
1081:
1076:
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1046:
1041:
1039:Graphical game
1036:
1031:
1026:
1021:
1016:
1011:
1006:
1000:
998:
994:
993:
987:
985:
984:
977:
970:
962:
956:
955:
944:
941:J. Math. Biol.
937:
931:
912:
898:
884:
877:
856:
837:
826:
821:
815:
800:
793:
782:
777:
763:
754:
728:
692:(2): 179–221.
677:
674:
673:
672:
661:
656:
649:
646:
614:
611:
607:Bayes' theorem
575:Main article:
572:
569:
553:Main article:
550:
547:
546:
545:
540:
511:Main article:
508:
505:
473:Main article:
470:
467:
464:
463:
458:
455:
451:
450:
447:
444:
440:
439:
436:
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387:Main article:
384:
381:
369:
366:
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338:
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327:
324:
321:
318:
294:
290:
285:
279:
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273:
269:
265:
262:
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247:., a function
233:
226:
222:
217:
211:
208:
205:
201:
176:
163:be the set of
150:
146:
125:
122:
119:
99:
87:
84:
43:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2059:
2048:
2045:
2043:
2040:
2039:
2037:
2022:
2019:
2017:
2014:
2012:
2009:
2007:
2004:
2002:
1999:
1997:
1994:
1992:
1989:
1987:
1984:
1982:
1979:
1977:
1974:
1972:
1969:
1968:
1966:
1964:Miscellaneous
1962:
1956:
1953:
1951:
1948:
1946:
1943:
1941:
1938:
1936:
1933:
1931:
1928:
1927:
1925:
1921:
1915:
1912:
1910:
1907:
1905:
1902:
1900:
1899:Samuel Bowles
1897:
1895:
1894:Roger Myerson
1892:
1890:
1887:
1885:
1884:Robert Aumann
1882:
1880:
1877:
1875:
1872:
1870:
1867:
1865:
1862:
1860:
1857:
1855:
1852:
1850:
1847:
1845:
1842:
1840:
1839:Lloyd Shapley
1837:
1835:
1832:
1830:
1827:
1825:
1824:Kenneth Arrow
1822:
1820:
1817:
1815:
1812:
1810:
1807:
1805:
1804:John Harsanyi
1802:
1800:
1797:
1795:
1792:
1790:
1787:
1785:
1782:
1780:
1777:
1775:
1774:Herbert Simon
1772:
1770:
1767:
1765:
1762:
1760:
1757:
1755:
1752:
1750:
1747:
1745:
1742:
1740:
1737:
1735:
1732:
1730:
1727:
1725:
1722:
1720:
1717:
1715:
1712:
1711:
1709:
1703:
1697:
1694:
1692:
1689:
1687:
1684:
1682:
1679:
1677:
1674:
1672:
1669:
1667:
1664:
1662:
1659:
1657:
1654:
1653:
1651:
1647:
1641:
1638:
1636:
1633:
1631:
1628:
1626:
1623:
1621:
1618:
1616:
1613:
1611:
1608:
1606:
1603:
1601:
1598:
1596:
1593:
1591:
1588:
1586:
1583:
1581:
1578:
1576:
1575:Fair division
1573:
1571:
1568:
1566:
1563:
1561:
1558:
1556:
1553:
1551:
1550:Dictator game
1548:
1546:
1543:
1541:
1538:
1536:
1533:
1531:
1528:
1526:
1523:
1521:
1518:
1516:
1513:
1511:
1508:
1506:
1503:
1501:
1498:
1496:
1493:
1491:
1488:
1486:
1483:
1481:
1478:
1476:
1473:
1471:
1468:
1466:
1463:
1461:
1458:
1456:
1453:
1451:
1448:
1446:
1443:
1441:
1438:
1437:
1435:
1433:
1429:
1423:
1422:Zero-sum game
1420:
1418:
1415:
1413:
1410:
1408:
1405:
1403:
1400:
1398:
1395:
1393:
1392:Repeated game
1390:
1388:
1385:
1383:
1380:
1378:
1375:
1373:
1371:
1367:
1365:
1362:
1360:
1357:
1355:
1352:
1350:
1347:
1345:
1342:
1341:
1339:
1337:
1331:
1325:
1322:
1320:
1317:
1315:
1312:
1310:
1309:Pure strategy
1307:
1305:
1302:
1300:
1297:
1295:
1292:
1290:
1287:
1285:
1282:
1280:
1277:
1275:
1274:De-escalation
1272:
1270:
1267:
1265:
1262:
1260:
1257:
1255:
1252:
1250:
1247:
1246:
1244:
1242:
1238:
1232:
1229:
1227:
1224:
1222:
1219:
1217:
1216:Shapley value
1214:
1212:
1209:
1207:
1204:
1202:
1199:
1197:
1194:
1192:
1189:
1187:
1184:
1182:
1179:
1177:
1174:
1172:
1169:
1167:
1164:
1162:
1159:
1157:
1154:
1152:
1149:
1147:
1144:
1142:
1139:
1137:
1134:
1132:
1129:
1127:
1124:
1122:
1119:
1117:
1114:
1112:
1109:
1108:
1106:
1104:
1100:
1096:
1090:
1087:
1085:
1084:Succinct game
1082:
1080:
1077:
1075:
1072:
1070:
1067:
1065:
1062:
1060:
1057:
1055:
1052:
1050:
1047:
1045:
1042:
1040:
1037:
1035:
1032:
1030:
1027:
1025:
1022:
1020:
1017:
1015:
1012:
1010:
1007:
1005:
1002:
1001:
999:
995:
991:
983:
978:
976:
971:
969:
964:
963:
960:
953:
949:
945:
942:
938:
934:
928:
924:
920:
919:
913:
910:
906:
902:
899:
896:
892:
888:
885:
880:
874:
870:
866:
862:
857:
855:
854:0-521-28884-3
851:
847:
846:
841:
838:
835:
831:
827:
825:
822:
818:
812:
808:
807:
801:
798:
794:
791:
787:
783:
781:
778:
775:
771:
767:
764:
762:
761:Book preview.
757:
755:9780262061414
751:
747:
743:
742:
737:
733:
729:
725:
721:
717:
713:
709:
705:
700:
695:
691:
687:
686:
680:
679:
675:
670:
666:
662:
660:
657:
655:
652:
651:
647:
645:
643:
638:
636:
632:
626:
623:
619:
612:
610:
608:
604:
599:
595:
593:
588:
584:
578:
577:Bayesian game
570:
568:
566:
562:
556:
548:
544:
541:
539:
536:
535:
534:
531:
527:
523:
519:
514:
506:
504:
502:
501:best response
498:
494:
490:
486:
482:
476:
468:
462:
459:
456:
453:
452:
448:
445:
442:
441:
437:
434:
432:
431:
428:
426:
422:
418:
414:
410:
407:
402:
398:
397:
390:
382:
380:
367:
361:
358:
336:
332:
328:
322:
316:
292:
288:
283:
274:
271:
257:
254:
246:
231:
224:
220:
215:
206:
203:
190:
174:
166:
148:
144:
120:
117:
85:
83:
81:
76:
74:
70:
65:
61:
41:
32:
19:
1869:Peyton Young
1864:Paul Milgrom
1779:Hervé Moulin
1719:Amos Tversky
1661:Folk theorem
1372:-player game
1369:
1294:Grim trigger
1102:
951:
940:
921:. New York:
917:
908:
894:
864:
843:
833:
805:
789:
773:
766:Harsanyi, J.
740:
736:Tirole, Jean
689:
683:
639:
627:
621:
617:
616:
602:
600:
596:
591:
586:
580:
558:
532:
528:
524:
520:
516:
496:
492:
488:
484:
478:
460:
424:
420:
416:
394:
392:
244:
188:
89:
79:
77:
63:
57:
2042:Game theory
1986:Coopetition
1789:Jean Tirole
1784:John Conway
1764:Eric Maskin
1560:Blotto game
1545:Pirate game
1354:Global game
1324:Tit for tat
1259:Bid shading
1249:Appeasement
1099:Equilibrium
1079:Solved game
1014:Determinacy
997:Definitions
990:game theory
943:22:105–115.
792:31:195–272.
741:Game Theory
587:and beliefs
60:game theory
2036:Categories
1630:Trust game
1615:Kuhn poker
1284:Escalation
1279:Deterrence
1269:Cheap talk
1241:Strategies
1059:Preference
988:Topics of
954:28:332–341
911:16:223–266
901:Selten, R.
897:5:269–363.
887:Selten, R.
836:5:425–454.
776:2:235–250.
676:References
533:See also:
446:−0.5, −0.5
309:such that
80:refinement
1814:John Nash
1520:Stag hunt
1264:Collusion
869:MIT Press
746:MIT Press
724:154404556
694:CiteSeerX
493:cooperate
485:cooperate
417:cooperate
365:Γ
362:∈
329:⊆
278:Γ
275:∈
268:⋃
264:→
261:Γ
210:Γ
207:∈
200:Π
124:Γ
121:∈
98:Γ
42:⊂
1955:Lazy SMP
1649:Theorems
1600:Deadlock
1455:Checkers
1336:of games
1103:concepts
863:(1994).
738:(1991).
648:See also
603:Bayesian
351:for all
54:Proper).
1707:figures
1490:Chicken
1344:Auction
1334:Classes
903:(1988)
889:(1983)
842:(1982)
768:(1973)
716:1885060
561:subgame
449:−10, 0
406:minimax
929:
875:
852:
813:
752:
722:
714:
696:
497:defect
489:defect
461:−2, −2
457:0, −10
425:defect
421:defect
136:, let
1445:Chess
1432:Games
720:S2CID
712:JSTOR
1126:Core
927:ISBN
873:ISBN
850:ISBN
811:ISBN
750:ISBN
622:type
601:The
187:. A
90:Let
62:, a
1705:Key
848:.
704:doi
690:102
667:" (
245:i.e
167:of
58:In
2038::
1440:Go
950:.
925:.
907:.
893:.
871:.
867:.
832:.
788:.
772:.
748:.
734:;
718:.
710:.
702:.
688:.
644:.
487:,
75:.
1370:n
981:e
974:t
967:v
935:.
883:.
881:.
819:.
758:.
726:.
706::
671:)
663:"
368:.
359:G
337:G
333:S
326:)
323:G
320:(
317:F
293:G
289:S
284:2
272:G
258::
255:F
232:;
225:G
221:S
216:2
204:G
175:G
149:G
145:S
118:G
20:)
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