891:
For 2x2 games, the set of trembling-hand perfect equilibria coincides with the set of equilibria consisting of two undominated strategies. In the example above, we see that the equilibrium <Down,Right> is imperfect, as Left (weakly) dominates Right for Player 2 and Up (weakly) dominates Down
130:(both pure and mixed) is played with non-zero probability. This is the "trembling hands" of the players; they sometimes play a different strategy, other than the one they intended to play. Then define a strategy set S (in a base game) as being trembling hand perfect if there is a
1013:
The notions of normal-form and extensive-form trembling hand perfect equilibria are incomparable, i.e., an equilibrium of an extensive-form game may be normal-form trembling hand perfect but not extensive-form trembling hand perfect and vice versa. As an extreme example of this,
988:
Alternatively, one may recall that trembles are to be interpreted as modelling mistakes made by the players with some negligible probability when the game is played. Such a mistake would most likely consist of a player making another
537:, player 2 maximizes his expected payoff by placing a minimal weight on R and maximal weight on L. By symmetry, player 1 should place a minimal weight on D and maximal weight on U if player 2 is playing the mixed strategy
1022:
of a two-player extensive form game where no extensive-form trembling hand perfect equilibrium is admissible, i.e., the sets of extensive-form and normal-form trembling hand perfect equilibria for this game are disjoint.
822:
1030:. A normal-form trembling hand perfect equilibrium of an extensive form game may be sequential but is not necessarily so. In fact, a normal-form trembling hand perfect equilibrium does not even have to be
751:
453:
512:
236:
976:
One may interpret the extensive form as being merely a concise description of a normal form game and apply the concepts described above to this normal form game. In the resulting perturbed games, every
883:
is not trembling-hand perfect because player 2 (and, by symmetry, player 1) maximizes his expected payoff by deviating most often to L if there is a small chance of error in the behavior of player 1.
200:
881:
648:
609:
272:
1072:
692:
573:
359:
95:. A trembling hand perfect equilibrium is an equilibrium that takes the possibility of off-the-equilibrium play into account by assuming that the players, through a "slip of the hand" or
391:
845:
535:
1042:
Myerson (1978) pointed out that perfection is sensitive to the addition of a strictly dominated strategy, and instead proposed another refinement, known as
997:
than intended, i.e. a wrong plan for playing the entire game. To capture this, one may define the perturbed game by requiring that every
762:
1005:
is taken with non-zero probability. Limits of equilibria of such perturbed games as the tremble probabilities goes to zero are called
2258:
700:
402:
464:
1098:
Selten, R.: Reexamination of the perfectness concept for equilibrium points in extensive games. Int. J. Game Theory4, 1975, 25–55.
205:
169:
1196:
1125:
2095:
850:
617:
578:
241:
1140:
Myerson, Roger B. "Refinements of the Nash equilibrium concept." International journal of game theory 7.2 (1978): 73-80.
1912:
1245:
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1352:
659:
540:
326:
1821:
2263:
1691:
1362:
1530:
1872:
1290:
1265:
1002:
364:
2222:
1648:
1402:
1392:
1327:
931:
1442:
1422:
1031:
927:
847:, player 1 maximizes his expected payoff by placing a minimal weight on D and maximal weight on U. Hence
993:
than the one intended at some point during play. It would hardly consist of the player choosing another
2156:
1907:
1877:
1535:
1377:
1372:
2192:
2115:
1851:
1407:
1332:
1189:
1019:
2207:
1940:
1826:
1623:
1417:
1235:
981:
of the extensive-form game must be played with non-zero probability. This leads to the notion of a
2010:
1015:
830:
520:
150:
The mixed strategy extension of any finite normal-form game has at least one perfect equilibrium.
2212:
1811:
1781:
1437:
1225:
2237:
2217:
2197:
2146:
1816:
1721:
1580:
1525:
1457:
1427:
1347:
1275:
1027:
998:
994:
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935:
100:
1155:
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1255:
276:
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2015:
1902:
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1801:
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1716:
1315:
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8:
2187:
1806:
1756:
1593:
1520:
1500:
1357:
1240:
969:
960:
1846:
968:
There are two possible ways of extending the definition of trembling hand perfection to
123:
strategies are allowed to be played. A totally mixed strategy is a mixed strategy where
2166:
2025:
1856:
1836:
1686:
1565:
1470:
1397:
1342:
1043:
56:
1068:"A Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games"
2151:
2120:
2075:
1970:
1841:
1796:
1771:
1701:
1575:
1505:
1495:
1387:
1337:
1285:
1161:
1121:
2232:
2227:
2161:
2125:
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2065:
2035:
1990:
1945:
1930:
1887:
1741:
1382:
1319:
1305:
1270:
1113:
1081:
908:
163:
159:
88:
46:
27:
2130:
2090:
2045:
1960:
1955:
1676:
1628:
1515:
1280:
1250:
1220:
1063:
950:
135:
92:
71:
1995:
134:
of perturbed games that converge to the base game in which there is a series of
2070:
2060:
2050:
1985:
1975:
1965:
1950:
1746:
1726:
1711:
1706:
1666:
1633:
1618:
1613:
1603:
1412:
654:
321:
120:
1117:
1067:
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2110:
2100:
2055:
2040:
2020:
1791:
1766:
1638:
1608:
1598:
1585:
1490:
1432:
1367:
1300:
119:. A perturbed game is a copy of a base game, with the restriction that only
2085:
2080:
1935:
1510:
2202:
2005:
2000:
1980:
1776:
1761:
1570:
1540:
1475:
1465:
1295:
1230:
1206:
912:
104:
80:
31:
1174:
1831:
1485:
1085:
1736:
1656:
1480:
2171:
1671:
131:
127:
1892:
1882:
1560:
817:{\displaystyle 0(\varepsilon )+2(1-\varepsilon )=2-2\varepsilon }
1026:
An extensive-form trembling hand perfect equilibrium is also a
746:{\displaystyle 1\varepsilon +2(1-\varepsilon )=2-\varepsilon }
448:{\displaystyle 1(1-\varepsilon )+2\varepsilon =1+\varepsilon }
1661:
507:{\displaystyle 0(1-\varepsilon )+2\varepsilon =2\varepsilon }
231:{\displaystyle \langle {\text{Down}},{\text{Right}}\rangle }
458:
Player 2's expected payoff from playing the strategy R is:
614:
However, similar analysis fails for the strategy profile
195:{\displaystyle \langle {\text{Up}},{\text{Left}}\rangle }
895:
876:{\displaystyle \langle {\text{D}},{\text{R}}\rangle }
853:
833:
765:
703:
662:
643:{\displaystyle \langle {\text{D}},{\text{R}}\rangle }
620:
604:{\displaystyle \langle {\text{U}},{\text{L}}\rangle }
581:
543:
523:
467:
405:
367:
329:
267:{\displaystyle \langle {\text{U}},{\text{L}}\rangle }
244:
208:
172:
875:
839:
816:
745:
686:
642:
603:
567:
529:
506:
447:
385:
353:
266:
230:
194:
144:All completely mixed Nash equilibria are perfect.
1153:
903:Extensive-form trembling hand perfect equilibrium
886:
2250:
1007:extensive-form trembling hand perfect equilibria
694:. Player 1's expected payoff from playing U is:
22:(Normal form) trembling hand perfect equilibrium
1154:Osborne, Martin J.; Rubinstein, Ariel (1994).
983:normal-form trembling hand perfect equilibrium
756:Player 1's expected payoff from playing D is:
396:Player 2's expected payoff from playing L is:
320:Assume player 1 (the row player) is playing a
1190:
687:{\displaystyle (\varepsilon ,1-\varepsilon )}
568:{\displaystyle (1-\varepsilon ,\varepsilon )}
354:{\displaystyle (1-\varepsilon ,\varepsilon )}
870:
854:
637:
621:
598:
582:
261:
245:
225:
209:
189:
173:
1110:Stability and Perfection of Nash Equilibria
1037:
1197:
1183:
16:Variant of Nash equilibrium in game theory
1204:
1107:
2251:
1062:
386:{\displaystyle 0<\varepsilon <1}
158:The game represented in the following
1178:
1073:International Journal of Game Theory
13:
1246:First-player and second-player win
1147:
896:Equilibria of extensive form games
313:Trembling hand perfect equilibrium
85:trembling hand perfect equilibrium
14:
2275:
2259:Game theory equilibrium concepts
1353:Coalition-proof Nash equilibrium
1160:. MIT Press. pp. 246–254.
1363:Evolutionarily stable strategy
1134:
1101:
1092:
1056:
887:Equilibria of two-player games
796:
784:
775:
769:
728:
716:
681:
663:
562:
544:
483:
471:
421:
409:
348:
330:
1:
1291:Simultaneous action selection
1049:
653:Assume player 2 is playing a
110:
87:is a type of refinement of a
2223:List of games in game theory
1403:Quantal response equilibrium
1393:Perfect Bayesian equilibrium
1328:Bayes correlated equilibrium
932:Perfect Bayesian equilibrium
840:{\displaystyle \varepsilon }
530:{\displaystyle \varepsilon }
7:
1692:Optional prisoner's dilemma
1423:Self-confirming equilibrium
928:Subgame perfect equilibrium
827:For all positive values of
611:is trembling-hand perfect.
274:is trembling-hand perfect.
91:that was first proposed by
10:
2280:
2157:Principal variation search
1873:Aumann's agreement theorem
1536:Strategy-stealing argument
1448:Trembling hand equilibrium
1378:Markov perfect equilibrium
1373:Mertens-stable equilibrium
153:
2193:Combinatorial game theory
2180:
2139:
1921:
1865:
1852:Princess and monster game
1647:
1549:
1456:
1408:Quasi-perfect equilibrium
1333:Bayesian Nash equilibrium
1314:
1213:
1118:10.1007/978-3-642-96978-2
956:
946:
941:
923:
918:
907:
902:
311:
103:, albeit with negligible
67:
62:
52:
42:
37:
26:
21:
2208:Evolutionary game theory
1941:Antoine Augustin Cournot
1827:Guess 2/3 of the average
1624:Strictly determined game
1418:Satisfaction equilibrium
1236:Escalation of commitment
1108:Van Damme, Eric (1987).
1038:Problems with perfection
2213:Glossary of game theory
1812:Stackelberg competition
1438:Strong Nash equilibrium
1157:A Course in Game Theory
2238:Tragedy of the commons
2218:List of game theorists
2198:Confrontation analysis
1908:Sprague–Grundy theorem
1428:Sequential equilibrium
1348:Correlated equilibrium
1028:sequential equilibrium
936:Sequential equilibrium
877:
841:
818:
747:
688:
644:
605:
569:
531:
508:
449:
387:
355:
268:
232:
196:
162:has two pure strategy
99:may choose unintended
2264:Non-cooperative games
2011:Jean-François Mertens
1016:Jean-François Mertens
878:
842:
819:
748:
689:
645:
606:
570:
532:
509:
450:
388:
356:
269:
233:
197:
2140:Search optimizations
2016:Jennifer Tour Chayes
1903:Revelation principle
1898:Purification theorem
1837:Nash bargaining game
1802:Bertrand competition
1787:El Farol Bar problem
1752:Electronic mail game
1717:Lewis signaling game
1261:Hierarchy of beliefs
970:extensive form games
961:Extensive form games
851:
831:
763:
701:
660:
618:
579:
541:
521:
517:For small values of
465:
403:
365:
327:
242:
206:
170:
138:that converge to S.
2188:Bounded rationality
1807:Cournot competition
1757:Rock paper scissors
1732:Battle of the sexes
1722:Volunteer's dilemma
1594:Perfect information
1521:Dominant strategies
1358:Epsilon-equilibrium
1241:Extensive-form game
2167:Paranoid algorithm
2147:Alpha–beta pruning
2026:John Maynard Smith
1857:Rendezvous problem
1697:Traveler's dilemma
1687:Gift-exchange game
1682:Prisoner's dilemma
1599:Large Poisson game
1566:Bargaining problem
1471:Backward induction
1443:Subgame perfection
1398:Proper equilibrium
1086:10.1007/BF01766400
1044:proper equilibrium
873:
837:
814:
743:
684:
640:
601:
565:
527:
504:
445:
383:
351:
264:
228:
192:
160:normal form matrix
57:Proper equilibrium
2246:
2245:
2152:Aspiration window
2121:Suzanne Scotchmer
2076:Oskar Morgenstern
1971:Donald B. Gillies
1913:Zermelo's theorem
1842:Induction puzzles
1797:Fair cake-cutting
1772:Public goods game
1702:Coordination game
1576:Intransitive game
1506:Forward induction
1388:Pareto efficiency
1368:Gibbs equilibrium
1338:Berge equilibrium
1286:Simultaneous game
1127:978-3-642-96980-5
966:
965:
868:
860:
635:
627:
596:
588:
318:
317:
259:
251:
223:
215:
187:
179:
77:
76:
2271:
2233:Topological game
2228:No-win situation
2126:Thomas Schelling
2106:Robert B. Wilson
2066:Merrill M. Flood
2036:John von Neumann
1946:Ariel Rubinstein
1931:Albert W. Tucker
1782:War of attrition
1742:Matching pennies
1383:Nash equilibrium
1306:Mechanism design
1271:Normal-form game
1226:Cooperative game
1199:
1192:
1185:
1176:
1175:
1171:
1141:
1138:
1132:
1131:
1105:
1099:
1096:
1090:
1089:
1060:
909:Solution concept
900:
899:
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869:
866:
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838:
823:
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815:
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533:
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510:
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454:
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451:
446:
392:
390:
389:
384:
360:
358:
357:
352:
277:
273:
271:
270:
265:
260:
257:
252:
249:
238:. However, only
237:
235:
234:
229:
224:
221:
216:
213:
201:
199:
198:
193:
188:
185:
180:
177:
89:Nash equilibrium
47:Nash Equilibrium
28:Solution concept
19:
18:
2279:
2278:
2274:
2273:
2272:
2270:
2269:
2268:
2249:
2248:
2247:
2242:
2176:
2162:max^n algorithm
2135:
2131:William Vickrey
2091:Reinhard Selten
2046:Kenneth Binmore
1961:David K. Levine
1956:Daniel Kahneman
1923:
1917:
1893:Negamax theorem
1883:Minimax theorem
1861:
1822:Diner's dilemma
1677:All-pay auction
1643:
1629:Stochastic game
1581:Mean-field game
1552:
1545:
1516:Markov strategy
1452:
1318:
1310:
1281:Sequential game
1266:Information set
1251:Game complexity
1221:Congestion game
1209:
1203:
1168:
1150:
1148:Further reading
1145:
1144:
1139:
1135:
1128:
1106:
1102:
1097:
1093:
1061:
1057:
1052:
1040:
1032:subgame perfect
1003:information set
951:Reinhard Selten
898:
889:
865:
857:
852:
849:
848:
832:
829:
828:
764:
761:
760:
702:
699:
698:
661:
658:
657:
632:
624:
619:
616:
615:
593:
585:
580:
577:
576:
542:
539:
538:
522:
519:
518:
466:
463:
462:
404:
401:
400:
366:
363:
362:
328:
325:
324:
256:
248:
243:
240:
239:
220:
212:
207:
204:
203:
184:
176:
171:
168:
167:
164:Nash equilibria
156:
136:Nash equilibria
115:First define a
113:
93:Reinhard Selten
72:Reinhard Selten
17:
12:
11:
5:
2277:
2267:
2266:
2261:
2244:
2243:
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2240:
2235:
2230:
2225:
2220:
2215:
2210:
2205:
2200:
2195:
2190:
2184:
2182:
2178:
2177:
2175:
2174:
2169:
2164:
2159:
2154:
2149:
2143:
2141:
2137:
2136:
2134:
2133:
2128:
2123:
2118:
2113:
2108:
2103:
2098:
2096:Robert Axelrod
2093:
2088:
2083:
2078:
2073:
2071:Olga Bondareva
2068:
2063:
2061:Melvin Dresher
2058:
2053:
2051:Leonid Hurwicz
2048:
2043:
2038:
2033:
2028:
2023:
2018:
2013:
2008:
2003:
1998:
1993:
1988:
1986:Harold W. Kuhn
1983:
1978:
1976:Drew Fudenberg
1973:
1968:
1966:David M. Kreps
1963:
1958:
1953:
1951:Claude Shannon
1948:
1943:
1938:
1933:
1927:
1925:
1919:
1918:
1916:
1915:
1910:
1905:
1900:
1895:
1890:
1888:Nash's theorem
1885:
1880:
1875:
1869:
1867:
1863:
1862:
1860:
1859:
1854:
1849:
1844:
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1814:
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1804:
1799:
1794:
1789:
1784:
1779:
1774:
1769:
1764:
1759:
1754:
1749:
1747:Ultimatum game
1744:
1739:
1734:
1729:
1727:Dollar auction
1724:
1719:
1714:
1712:Centipede game
1709:
1704:
1699:
1694:
1689:
1684:
1679:
1674:
1669:
1667:Infinite chess
1664:
1659:
1653:
1651:
1645:
1644:
1642:
1641:
1636:
1634:Symmetric game
1631:
1626:
1621:
1619:Signaling game
1616:
1614:Screening game
1611:
1606:
1604:Potential game
1601:
1596:
1591:
1583:
1578:
1573:
1568:
1563:
1557:
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1547:
1546:
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1533:
1531:Mixed strategy
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1413:Risk dominance
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1258:
1256:Graphical game
1253:
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1228:
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1201:
1194:
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1142:
1133:
1126:
1100:
1091:
1054:
1053:
1051:
1048:
1039:
1036:
1011:
1010:
986:
964:
963:
958:
954:
953:
948:
944:
943:
939:
938:
925:
921:
920:
916:
915:
905:
904:
897:
894:
892:for Player 1.
888:
885:
872:
864:
856:
836:
825:
824:
813:
810:
807:
804:
801:
798:
795:
792:
789:
786:
783:
780:
777:
774:
771:
768:
754:
753:
742:
739:
736:
733:
730:
727:
724:
721:
718:
715:
712:
709:
706:
683:
680:
677:
674:
671:
668:
665:
655:mixed strategy
639:
631:
623:
600:
592:
584:
564:
561:
558:
555:
552:
549:
546:
526:
515:
514:
503:
500:
497:
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479:
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470:
456:
455:
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435:
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414:
411:
408:
382:
379:
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370:
350:
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344:
341:
338:
335:
332:
322:mixed strategy
316:
315:
309:
308:
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302:
298:
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291:
287:
286:
283:
280:
263:
255:
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155:
152:
117:perturbed game
112:
109:
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69:
65:
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60:
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54:
50:
49:
44:
40:
39:
35:
34:
24:
23:
15:
9:
6:
4:
3:
2:
2276:
2265:
2262:
2260:
2257:
2256:
2254:
2239:
2236:
2234:
2231:
2229:
2226:
2224:
2221:
2219:
2216:
2214:
2211:
2209:
2206:
2204:
2201:
2199:
2196:
2194:
2191:
2189:
2186:
2185:
2183:
2181:Miscellaneous
2179:
2173:
2170:
2168:
2165:
2163:
2160:
2158:
2155:
2153:
2150:
2148:
2145:
2144:
2142:
2138:
2132:
2129:
2127:
2124:
2122:
2119:
2117:
2116:Samuel Bowles
2114:
2112:
2111:Roger Myerson
2109:
2107:
2104:
2102:
2101:Robert Aumann
2099:
2097:
2094:
2092:
2089:
2087:
2084:
2082:
2079:
2077:
2074:
2072:
2069:
2067:
2064:
2062:
2059:
2057:
2056:Lloyd Shapley
2054:
2052:
2049:
2047:
2044:
2042:
2041:Kenneth Arrow
2039:
2037:
2034:
2032:
2029:
2027:
2024:
2022:
2021:John Harsanyi
2019:
2017:
2014:
2012:
2009:
2007:
2004:
2002:
1999:
1997:
1994:
1992:
1991:Herbert Simon
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:
1920:
1914:
1911:
1909:
1906:
1904:
1901:
1899:
1896:
1894:
1891:
1889:
1886:
1884:
1881:
1879:
1876:
1874:
1871:
1870:
1868:
1864:
1858:
1855:
1853:
1850:
1848:
1845:
1843:
1840:
1838:
1835:
1833:
1830:
1828:
1825:
1823:
1820:
1818:
1815:
1813:
1810:
1808:
1805:
1803:
1800:
1798:
1795:
1793:
1792:Fair division
1790:
1788:
1785:
1783:
1780:
1778:
1775:
1773:
1770:
1768:
1767:Dictator game
1765:
1763:
1760:
1758:
1755:
1753:
1750:
1748:
1745:
1743:
1740:
1738:
1735:
1733:
1730:
1728:
1725:
1723:
1720:
1718:
1715:
1713:
1710:
1708:
1705:
1703:
1700:
1698:
1695:
1693:
1690:
1688:
1685:
1683:
1680:
1678:
1675:
1673:
1670:
1668:
1665:
1663:
1660:
1658:
1655:
1654:
1652:
1650:
1646:
1640:
1639:Zero-sum game
1637:
1635:
1632:
1630:
1627:
1625:
1622:
1620:
1617:
1615:
1612:
1610:
1609:Repeated game
1607:
1605:
1602:
1600:
1597:
1595:
1592:
1590:
1588:
1584:
1582:
1579:
1577:
1574:
1572:
1569:
1567:
1564:
1562:
1559:
1558:
1556:
1554:
1548:
1542:
1539:
1537:
1534:
1532:
1529:
1527:
1526:Pure strategy
1524:
1522:
1519:
1517:
1514:
1512:
1509:
1507:
1504:
1502:
1499:
1497:
1494:
1492:
1491:De-escalation
1489:
1487:
1484:
1482:
1479:
1477:
1474:
1472:
1469:
1467:
1464:
1463:
1461:
1459:
1455:
1449:
1446:
1444:
1441:
1439:
1436:
1434:
1433:Shapley value
1431:
1429:
1426:
1424:
1421:
1419:
1416:
1414:
1411:
1409:
1406:
1404:
1401:
1399:
1396:
1394:
1391:
1389:
1386:
1384:
1381:
1379:
1376:
1374:
1371:
1369:
1366:
1364:
1361:
1359:
1356:
1354:
1351:
1349:
1346:
1344:
1341:
1339:
1336:
1334:
1331:
1329:
1326:
1325:
1323:
1321:
1317:
1313:
1307:
1304:
1302:
1301:Succinct game
1299:
1297:
1294:
1292:
1289:
1287:
1284:
1282:
1279:
1277:
1274:
1272:
1269:
1267:
1264:
1262:
1259:
1257:
1254:
1252:
1249:
1247:
1244:
1242:
1239:
1237:
1234:
1232:
1229:
1227:
1224:
1222:
1219:
1218:
1216:
1212:
1208:
1200:
1195:
1193:
1188:
1186:
1181:
1180:
1177:
1169:
1167:9780262650403
1163:
1159:
1158:
1152:
1151:
1137:
1129:
1123:
1119:
1115:
1111:
1104:
1095:
1087:
1083:
1079:
1075:
1074:
1069:
1065:
1059:
1055:
1047:
1045:
1035:
1033:
1029:
1024:
1021:
1018:has given an
1017:
1008:
1004:
1000:
996:
992:
987:
984:
980:
975:
974:
973:
971:
962:
959:
955:
952:
949:
945:
940:
937:
933:
929:
926:
922:
917:
914:
910:
906:
901:
893:
884:
862:
834:
811:
808:
805:
802:
799:
793:
790:
787:
781:
778:
772:
766:
759:
758:
757:
740:
737:
734:
731:
725:
722:
719:
713:
710:
707:
704:
697:
696:
695:
678:
675:
672:
669:
666:
656:
651:
629:
612:
590:
559:
556:
553:
550:
547:
524:
501:
498:
495:
492:
489:
486:
480:
477:
474:
468:
461:
460:
459:
442:
439:
436:
433:
430:
427:
424:
418:
415:
412:
406:
399:
398:
397:
394:
380:
377:
374:
371:
368:
345:
342:
339:
336:
333:
323:
314:
310:
306:
303:
300:
299:
295:
292:
289:
288:
284:
281:
279:
278:
275:
253:
217:
181:
165:
161:
151:
149:
145:
143:
139:
137:
133:
129:
126:
122:
121:totally mixed
118:
108:
106:
102:
98:
94:
90:
86:
82:
73:
70:
66:
61:
58:
55:
51:
48:
45:
41:
36:
33:
29:
25:
20:
2086:Peyton Young
2081:Paul Milgrom
1996:Hervé Moulin
1936:Amos Tversky
1878:Folk theorem
1589:-player game
1586:
1511:Grim trigger
1447:
1156:
1136:
1109:
1103:
1094:
1080:(1): 25–55.
1077:
1071:
1058:
1041:
1025:
1012:
1006:
982:
967:
942:Significance
919:Relationship
890:
826:
755:
652:
613:
516:
457:
395:
319:
312:
157:
147:
146:
141:
140:
124:
116:
114:
96:
84:
78:
63:Significance
38:Relationship
2203:Coopetition
2006:Jean Tirole
2001:John Conway
1981:Eric Maskin
1777:Blotto game
1762:Pirate game
1571:Global game
1541:Tit for tat
1476:Bid shading
1466:Appeasement
1316:Equilibrium
1296:Solved game
1231:Determinacy
1214:Definitions
1207:game theory
947:Proposed by
913:game theory
105:probability
81:game theory
68:Proposed by
53:Superset of
32:game theory
2253:Categories
1847:Trust game
1832:Kuhn poker
1501:Escalation
1496:Deterrence
1486:Cheap talk
1458:Strategies
1276:Preference
1205:Topics of
1064:Selten, R.
1050:References
111:Definition
101:strategies
2031:John Nash
1737:Stag hunt
1481:Collusion
1001:at every
924:Subset of
871:⟩
855:⟨
835:ε
812:ε
806:−
794:ε
791:−
773:ε
741:ε
738:−
726:ε
723:−
708:ε
679:ε
676:−
667:ε
638:⟩
622:⟨
599:⟩
583:⟨
575:. Hence
560:ε
554:ε
551:−
525:ε
502:ε
493:ε
481:ε
478:−
443:ε
431:ε
419:ε
416:−
375:ε
346:ε
340:ε
337:−
262:⟩
246:⟨
226:⟩
210:⟨
190:⟩
174:⟨
166:, namely
43:Subset of
2172:Lazy SMP
1866:Theorems
1817:Deadlock
1672:Checkers
1553:of games
1320:concepts
1066:(1975).
995:strategy
979:strategy
957:Used for
132:sequence
128:strategy
97:tremble,
1924:figures
1707:Chicken
1561:Auction
1551:Classes
1020:example
361:, for
154:Example
148:Note 2:
1164:
1124:
285:Right
1662:Chess
1649:Games
307:2, 2
304:0, 2
301:Down
296:2, 0
293:1, 1
282:Left
222:Right
142:Note:
125:every
1343:Core
1162:ISBN
1122:ISBN
999:move
991:move
378:<
372:<
214:Down
202:and
186:Left
1922:Key
1114:doi
1082:doi
911:in
393:.
290:Up
79:In
30:in
2255::
1657:Go
1120:.
1112:.
1076:.
1070:.
1046:.
1034:.
972:.
934:,
930:,
650:.
178:Up
107:.
83:,
1587:n
1198:e
1191:t
1184:v
1170:.
1130:.
1116::
1088:.
1084::
1078:4
1009:.
985:.
867:R
863:,
859:D
809:2
803:2
800:=
797:)
788:1
785:(
782:2
779:+
776:)
770:(
767:0
735:2
732:=
729:)
720:1
717:(
714:2
711:+
705:1
682:)
673:1
670:,
664:(
634:R
630:,
626:D
595:L
591:,
587:U
563:)
557:,
548:1
545:(
499:2
496:=
490:2
487:+
484:)
475:1
472:(
469:0
440:+
437:1
434:=
428:2
425:+
422:)
413:1
410:(
407:1
381:1
369:0
349:)
343:,
334:1
331:(
258:L
254:,
250:U
218:,
182:,
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