902:
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
141:(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
1024:
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,
999:
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
548:, 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
1033:
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.
833:
1041:. 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
762:
464:
523:
247:
987:
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
894:
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.
211:
892:
659:
620:
283:
703:
584:
370:
106:. 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
402:
856:
546:
1053:
Myerson (1978) pointed out that perfection is sensitive to the addition of a strictly dominated strategy, and instead proposed another refinement, known as
2269:
1207:
1136:
2106:
1008:
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
773:
1923:
1256:
1016:
is taken with non-zero probability. Limits of equilibria of such perturbed games as the tremble probabilities goes to zero are called
1742:
1561:
1176:
711:
413:
475:
1109:
Selten, R.: Reexamination of the perfectness concept for equilibrium points in extensive games. Int. J. Game Theory4, 1975, 25–55.
216:
1363:
1832:
180:
2274:
1373:
1702:
861:
628:
589:
252:
1883:
1301:
1276:
1083:
1013:
2233:
1659:
1413:
1403:
1338:
1151:
Myerson, Roger B. "Refinements of the Nash equilibrium concept." International journal of game theory 7.2 (1978): 73-80.
942:
1453:
1433:
1042:
938:
1918:
2167:
1888:
1546:
1388:
1383:
670:
551:
337:
2203:
2126:
1862:
1418:
1343:
1200:
1030:
2218:
1951:
1837:
1634:
1428:
1246:
2021:
1026:
2223:
1822:
1792:
1448:
1236:
375:
2157:
2248:
2228:
2208:
1827:
1732:
1591:
1541:
1536:
1468:
1438:
1358:
1286:
1038:
1009:
1005:
1001:
989:
946:
111:
858:, player 1 maximizes his expected payoff by placing a minimal weight on D and maximal weight on U. Hence
1266:
1004:
than the one intended at some point during play. It would hardly consist of the player choosing another
1707:
1692:
2041:
2026:
1913:
1908:
1812:
1797:
1762:
1727:
1326:
1271:
1193:
2198:
1817:
1767:
1604:
1531:
1511:
1368:
1251:
992:
of the extensive-form game must be played with non-zero probability. This leads to the notion of a
980:
971:
841:
531:
161:
The mixed strategy extension of any finite normal-form game has at least one perfect equilibrium.
2177:
2036:
1867:
1847:
1697:
1576:
1481:
1408:
1353:
1054:
67:
2162:
2131:
2086:
1981:
1852:
1807:
1782:
1712:
1586:
1516:
1506:
1398:
1348:
1296:
1172:
1166:
1132:
2243:
2238:
2172:
2136:
2116:
2076:
2046:
2001:
1956:
1941:
1898:
1752:
1393:
1330:
1316:
1281:
1124:
1092:
919:
174:
170:
99:
57:
38:
2141:
2101:
2056:
1971:
1966:
1687:
1639:
1526:
1291:
1261:
1231:
1074:
961:
146:
103:
82:
17:
2006:
979:
There are two possible ways of extending the definition of trembling hand perfection to
134:
strategies are allowed to be played. A totally mixed strategy is a mixed strategy where
2081:
2071:
2061:
1996:
1986:
1976:
1961:
1757:
1737:
1722:
1717:
1677:
1644:
1629:
1624:
1614:
1423:
665:
332:
131:
1079:"A Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games"
2263:
2121:
2111:
2066:
2051:
2031:
1857:
1802:
1777:
1649:
1619:
1609:
1596:
1501:
1443:
1378:
1311:
2096:
2091:
1946:
1521:
2213:
2016:
2011:
1991:
1787:
1772:
1581:
1551:
1486:
1476:
1306:
1241:
1217:
923:
145:
of perturbed games that converge to the base game in which there is a series of
115:
91:
42:
1842:
1496:
1128:
1078:
130:. A perturbed game is a copy of a base game, with the restriction that only
1747:
1667:
1491:
287:
2182:
1682:
142:
138:
1185:
1903:
1893:
1571:
1096:
1672:
828:{\displaystyle 0(\varepsilon )+2(1-\varepsilon )=2-2\varepsilon }
1189:
1037:
An extensive-form trembling hand perfect equilibrium is also a
757:{\displaystyle 1\varepsilon +2(1-\varepsilon )=2-\varepsilon }
459:{\displaystyle 1(1-\varepsilon )+2\varepsilon =1+\varepsilon }
518:{\displaystyle 0(1-\varepsilon )+2\varepsilon =2\varepsilon }
242:{\displaystyle \langle {\text{Down}},{\text{Right}}\rangle }
469:
Player 2's expected payoff from playing the strategy R is:
625:
However, similar analysis fails for the strategy profile
206:{\displaystyle \langle {\text{Up}},{\text{Left}}\rangle }
887:{\displaystyle \langle {\text{D}},{\text{R}}\rangle }
864:
844:
776:
714:
673:
654:{\displaystyle \langle {\text{D}},{\text{R}}\rangle }
631:
615:{\displaystyle \langle {\text{U}},{\text{L}}\rangle }
592:
554:
534:
478:
416:
378:
340:
278:{\displaystyle \langle {\text{U}},{\text{L}}\rangle }
255:
219:
183:
2191:
2150:
1932:
1876:
1658:
1560:
1467:
1325:
1224:
967:
957:
952:
934:
929:
913:
78:
73:
63:
53:
48:
32:
886:
850:
827:
756:
697:
653:
614:
578:
540:
517:
458:
396:
364:
277:
241:
205:
155:All completely mixed Nash equilibria are perfect.
914:Extensive-form trembling hand perfect equilibrium
1018:extensive-form trembling hand perfect equilibria
705:. Player 1's expected payoff from playing U is:
33:(Normal form) trembling hand perfect equilibrium
1165:Osborne, Martin J.; Rubinstein, Ariel (1994).
994:normal-form trembling hand perfect equilibrium
767:Player 1's expected payoff from playing D is:
407:Player 2's expected payoff from playing L is:
331:Assume player 1 (the row player) is playing a
1201:
698:{\displaystyle (\varepsilon ,1-\varepsilon )}
579:{\displaystyle (1-\varepsilon ,\varepsilon )}
365:{\displaystyle (1-\varepsilon ,\varepsilon )}
8:
881:
865:
648:
632:
609:
593:
272:
256:
236:
220:
200:
184:
1121:Stability and Perfection of Nash Equilibria
1208:
1194:
1186:
27:Variant of Nash equilibrium in game theory
876:
868:
863:
843:
775:
713:
672:
643:
635:
630:
604:
596:
591:
553:
533:
477:
415:
377:
339:
267:
259:
254:
231:
223:
218:
195:
187:
182:
1066:
910:
397:{\displaystyle 0<\varepsilon <1}
169:The game represented in the following
29:
7:
1084:International Journal of Game Theory
1257:First-player and second-player win
907:Equilibria of extensive form games
324:Trembling hand perfect equilibrium
96:trembling hand perfect equilibrium
25:
2270:Game theory equilibrium concepts
1364:Coalition-proof Nash equilibrium
1171:. MIT Press. pp. 246–254.
1374:Evolutionarily stable strategy
898:Equilibria of two-player games
807:
795:
786:
780:
739:
727:
692:
674:
573:
555:
494:
482:
432:
420:
359:
341:
1:
1302:Simultaneous action selection
664:Assume player 2 is playing a
98:is a type of refinement of a
2234:List of games in game theory
1414:Quantal response equilibrium
1404:Perfect Bayesian equilibrium
1339:Bayes correlated equilibrium
943:Perfect Bayesian equilibrium
851:{\displaystyle \varepsilon }
541:{\displaystyle \varepsilon }
1703:Optional prisoner's dilemma
1434:Self-confirming equilibrium
939:Subgame perfect equilibrium
838:For all positive values of
622:is trembling-hand perfect.
285:is trembling-hand perfect.
102:that was first proposed by
2291:
2168:Principal variation search
1884:Aumann's agreement theorem
1547:Strategy-stealing argument
1459:Trembling hand equilibrium
1389:Markov perfect equilibrium
1384:Mertens-stable equilibrium
18:Trembling hand equilibrium
2204:Combinatorial game theory
1863:Princess and monster game
1419:Quasi-perfect equilibrium
1344:Bayesian Nash equilibrium
1129:10.1007/978-3-642-96978-2
918:
322:
114:, albeit with negligible
37:
2219:Evolutionary game theory
1952:Antoine Augustin Cournot
1838:Guess 2/3 of the average
1635:Strictly determined game
1429:Satisfaction equilibrium
1247:Escalation of commitment
1119:Van Damme, Eric (1987).
1049:Problems with perfection
2224:Glossary of game theory
1823:Stackelberg competition
1449:Strong Nash equilibrium
1168:A Course in Game Theory
2249:Tragedy of the commons
2229:List of game theorists
2209:Confrontation analysis
1919:Sprague–Grundy theorem
1439:Sequential equilibrium
1359:Correlated equilibrium
1039:sequential equilibrium
947:Sequential equilibrium
888:
852:
829:
758:
699:
655:
616:
580:
542:
519:
460:
398:
366:
279:
243:
207:
173:has two pure strategy
110:may choose unintended
2275:Non-cooperative games
2022:Jean-François Mertens
1027:Jean-François Mertens
889:
853:
830:
759:
700:
656:
617:
581:
543:
520:
461:
399:
367:
280:
244:
208:
2151:Search optimizations
2027:Jennifer Tour Chayes
1914:Revelation principle
1909:Purification theorem
1848:Nash bargaining game
1813:Bertrand competition
1798:El Farol Bar problem
1763:Electronic mail game
1728:Lewis signaling game
1272:Hierarchy of beliefs
981:extensive form games
972:Extensive form games
862:
842:
774:
712:
671:
629:
590:
552:
532:
528:For small values of
476:
414:
376:
338:
253:
217:
181:
149:that converge to S.
2199:Bounded rationality
1818:Cournot competition
1768:Rock paper scissors
1743:Battle of the sexes
1733:Volunteer's dilemma
1605:Perfect information
1532:Dominant strategies
1369:Epsilon-equilibrium
1252:Extensive-form game
2178:Paranoid algorithm
2158:Alpha–beta pruning
2037:John Maynard Smith
1868:Rendezvous problem
1708:Traveler's dilemma
1698:Gift-exchange game
1693:Prisoner's dilemma
1610:Large Poisson game
1577:Bargaining problem
1482:Backward induction
1454:Subgame perfection
1409:Proper equilibrium
1097:10.1007/BF01766400
1055:proper equilibrium
884:
848:
825:
754:
695:
651:
612:
576:
538:
515:
456:
394:
362:
275:
239:
203:
171:normal form matrix
68:Proper equilibrium
2257:
2256:
2163:Aspiration window
2132:Suzanne Scotchmer
2087:Oskar Morgenstern
1982:Donald B. Gillies
1924:Zermelo's theorem
1853:Induction puzzles
1808:Fair cake-cutting
1783:Public goods game
1713:Coordination game
1587:Intransitive game
1517:Forward induction
1399:Pareto efficiency
1379:Gibbs equilibrium
1349:Berge equilibrium
1297:Simultaneous game
1138:978-3-642-96980-5
977:
976:
879:
871:
646:
638:
607:
599:
329:
328:
270:
262:
234:
226:
198:
190:
88:
87:
16:(Redirected from
2282:
2244:Topological game
2239:No-win situation
2137:Thomas Schelling
2117:Robert B. Wilson
2077:Merrill M. Flood
2047:John von Neumann
1957:Ariel Rubinstein
1942:Albert W. Tucker
1793:War of attrition
1753:Matching pennies
1394:Nash equilibrium
1317:Mechanism design
1282:Normal-form game
1237:Cooperative game
1210:
1203:
1196:
1187:
1182:
1152:
1149:
1143:
1142:
1116:
1110:
1107:
1101:
1100:
1071:
920:Solution concept
911:
893:
891:
890:
885:
880:
877:
872:
869:
857:
855:
854:
849:
834:
832:
831:
826:
763:
761:
760:
755:
704:
702:
701:
696:
660:
658:
657:
652:
647:
644:
639:
636:
621:
619:
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613:
608:
605:
600:
597:
585:
583:
582:
577:
547:
545:
544:
539:
524:
522:
521:
516:
465:
463:
462:
457:
403:
401:
400:
395:
371:
369:
368:
363:
288:
284:
282:
281:
276:
271:
268:
263:
260:
249:. However, only
248:
246:
245:
240:
235:
232:
227:
224:
212:
210:
209:
204:
199:
196:
191:
188:
100:Nash equilibrium
58:Nash Equilibrium
39:Solution concept
30:
21:
2290:
2289:
2285:
2284:
2283:
2281:
2280:
2279:
2260:
2259:
2258:
2253:
2187:
2173:max^n algorithm
2146:
2142:William Vickrey
2102:Reinhard Selten
2057:Kenneth Binmore
1972:David K. Levine
1967:Daniel Kahneman
1934:
1928:
1904:Negamax theorem
1894:Minimax theorem
1872:
1833:Diner's dilemma
1688:All-pay auction
1654:
1640:Stochastic game
1592:Mean-field game
1563:
1556:
1527:Markov strategy
1463:
1329:
1321:
1292:Sequential game
1277:Information set
1262:Game complexity
1232:Congestion game
1220:
1214:
1179:
1164:
1161:
1159:Further reading
1156:
1155:
1150:
1146:
1139:
1118:
1117:
1113:
1108:
1104:
1073:
1072:
1068:
1063:
1051:
1043:subgame perfect
1014:information set
962:Reinhard Selten
909:
900:
860:
859:
840:
839:
772:
771:
710:
709:
669:
668:
627:
626:
588:
587:
550:
549:
530:
529:
474:
473:
412:
411:
374:
373:
336:
335:
251:
250:
215:
214:
179:
178:
175:Nash equilibria
167:
147:Nash equilibria
126:First define a
124:
104:Reinhard Selten
83:Reinhard Selten
28:
23:
22:
15:
12:
11:
5:
2288:
2286:
2278:
2277:
2272:
2262:
2261:
2255:
2254:
2252:
2251:
2246:
2241:
2236:
2231:
2226:
2221:
2216:
2211:
2206:
2201:
2195:
2193:
2189:
2188:
2186:
2185:
2180:
2175:
2170:
2165:
2160:
2154:
2152:
2148:
2147:
2145:
2144:
2139:
2134:
2129:
2124:
2119:
2114:
2109:
2107:Robert Axelrod
2104:
2099:
2094:
2089:
2084:
2082:Olga Bondareva
2079:
2074:
2072:Melvin Dresher
2069:
2064:
2062:Leonid Hurwicz
2059:
2054:
2049:
2044:
2039:
2034:
2029:
2024:
2019:
2014:
2009:
2004:
1999:
1997:Harold W. Kuhn
1994:
1989:
1987:Drew Fudenberg
1984:
1979:
1977:David M. Kreps
1974:
1969:
1964:
1962:Claude Shannon
1959:
1954:
1949:
1944:
1938:
1936:
1930:
1929:
1927:
1926:
1921:
1916:
1911:
1906:
1901:
1899:Nash's theorem
1896:
1891:
1886:
1880:
1878:
1874:
1873:
1871:
1870:
1865:
1860:
1855:
1850:
1845:
1840:
1835:
1830:
1825:
1820:
1815:
1810:
1805:
1800:
1795:
1790:
1785:
1780:
1775:
1770:
1765:
1760:
1758:Ultimatum game
1755:
1750:
1745:
1740:
1738:Dollar auction
1735:
1730:
1725:
1723:Centipede game
1720:
1715:
1710:
1705:
1700:
1695:
1690:
1685:
1680:
1678:Infinite chess
1675:
1670:
1664:
1662:
1656:
1655:
1653:
1652:
1647:
1645:Symmetric game
1642:
1637:
1632:
1630:Signaling game
1627:
1625:Screening game
1622:
1617:
1615:Potential game
1612:
1607:
1602:
1594:
1589:
1584:
1579:
1574:
1568:
1566:
1558:
1557:
1555:
1554:
1549:
1544:
1542:Mixed strategy
1539:
1534:
1529:
1524:
1519:
1514:
1509:
1504:
1499:
1494:
1489:
1484:
1479:
1473:
1471:
1465:
1464:
1462:
1461:
1456:
1451:
1446:
1441:
1436:
1431:
1426:
1424:Risk dominance
1421:
1416:
1411:
1406:
1401:
1396:
1391:
1386:
1381:
1376:
1371:
1366:
1361:
1356:
1351:
1346:
1341:
1335:
1333:
1323:
1322:
1320:
1319:
1314:
1309:
1304:
1299:
1294:
1289:
1284:
1279:
1274:
1269:
1267:Graphical game
1264:
1259:
1254:
1249:
1244:
1239:
1234:
1228:
1226:
1222:
1221:
1215:
1213:
1212:
1205:
1198:
1190:
1184:
1183:
1177:
1160:
1157:
1154:
1153:
1144:
1137:
1111:
1102:
1065:
1064:
1062:
1059:
1050:
1047:
1022:
1021:
997:
975:
974:
969:
965:
964:
959:
955:
954:
950:
949:
936:
932:
931:
927:
926:
916:
915:
908:
905:
903:for Player 1.
899:
896:
883:
875:
867:
847:
836:
835:
824:
821:
818:
815:
812:
809:
806:
803:
800:
797:
794:
791:
788:
785:
782:
779:
765:
764:
753:
750:
747:
744:
741:
738:
735:
732:
729:
726:
723:
720:
717:
694:
691:
688:
685:
682:
679:
676:
666:mixed strategy
650:
642:
634:
611:
603:
595:
575:
572:
569:
566:
563:
560:
557:
537:
526:
525:
514:
511:
508:
505:
502:
499:
496:
493:
490:
487:
484:
481:
467:
466:
455:
452:
449:
446:
443:
440:
437:
434:
431:
428:
425:
422:
419:
393:
390:
387:
384:
381:
361:
358:
355:
352:
349:
346:
343:
333:mixed strategy
327:
326:
320:
319:
316:
313:
309:
308:
305:
302:
298:
297:
294:
291:
274:
266:
258:
238:
230:
222:
202:
194:
186:
166:
163:
128:perturbed game
123:
120:
86:
85:
80:
76:
75:
71:
70:
65:
61:
60:
55:
51:
50:
46:
45:
35:
34:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2287:
2276:
2273:
2271:
2268:
2267:
2265:
2250:
2247:
2245:
2242:
2240:
2237:
2235:
2232:
2230:
2227:
2225:
2222:
2220:
2217:
2215:
2212:
2210:
2207:
2205:
2202:
2200:
2197:
2196:
2194:
2192:Miscellaneous
2190:
2184:
2181:
2179:
2176:
2174:
2171:
2169:
2166:
2164:
2161:
2159:
2156:
2155:
2153:
2149:
2143:
2140:
2138:
2135:
2133:
2130:
2128:
2127:Samuel Bowles
2125:
2123:
2122:Roger Myerson
2120:
2118:
2115:
2113:
2112:Robert Aumann
2110:
2108:
2105:
2103:
2100:
2098:
2095:
2093:
2090:
2088:
2085:
2083:
2080:
2078:
2075:
2073:
2070:
2068:
2067:Lloyd Shapley
2065:
2063:
2060:
2058:
2055:
2053:
2052:Kenneth Arrow
2050:
2048:
2045:
2043:
2040:
2038:
2035:
2033:
2032:John Harsanyi
2030:
2028:
2025:
2023:
2020:
2018:
2015:
2013:
2010:
2008:
2005:
2003:
2002:Herbert Simon
2000:
1998:
1995:
1993:
1990:
1988:
1985:
1983:
1980:
1978:
1975:
1973:
1970:
1968:
1965:
1963:
1960:
1958:
1955:
1953:
1950:
1948:
1945:
1943:
1940:
1939:
1937:
1931:
1925:
1922:
1920:
1917:
1915:
1912:
1910:
1907:
1905:
1902:
1900:
1897:
1895:
1892:
1890:
1887:
1885:
1882:
1881:
1879:
1875:
1869:
1866:
1864:
1861:
1859:
1856:
1854:
1851:
1849:
1846:
1844:
1841:
1839:
1836:
1834:
1831:
1829:
1826:
1824:
1821:
1819:
1816:
1814:
1811:
1809:
1806:
1804:
1803:Fair division
1801:
1799:
1796:
1794:
1791:
1789:
1786:
1784:
1781:
1779:
1778:Dictator game
1776:
1774:
1771:
1769:
1766:
1764:
1761:
1759:
1756:
1754:
1751:
1749:
1746:
1744:
1741:
1739:
1736:
1734:
1731:
1729:
1726:
1724:
1721:
1719:
1716:
1714:
1711:
1709:
1706:
1704:
1701:
1699:
1696:
1694:
1691:
1689:
1686:
1684:
1681:
1679:
1676:
1674:
1671:
1669:
1666:
1665:
1663:
1661:
1657:
1651:
1650:Zero-sum game
1648:
1646:
1643:
1641:
1638:
1636:
1633:
1631:
1628:
1626:
1623:
1621:
1620:Repeated game
1618:
1616:
1613:
1611:
1608:
1606:
1603:
1601:
1599:
1595:
1593:
1590:
1588:
1585:
1583:
1580:
1578:
1575:
1573:
1570:
1569:
1567:
1565:
1559:
1553:
1550:
1548:
1545:
1543:
1540:
1538:
1537:Pure strategy
1535:
1533:
1530:
1528:
1525:
1523:
1520:
1518:
1515:
1513:
1510:
1508:
1505:
1503:
1502:De-escalation
1500:
1498:
1495:
1493:
1490:
1488:
1485:
1483:
1480:
1478:
1475:
1474:
1472:
1470:
1466:
1460:
1457:
1455:
1452:
1450:
1447:
1445:
1444:Shapley value
1442:
1440:
1437:
1435:
1432:
1430:
1427:
1425:
1422:
1420:
1417:
1415:
1412:
1410:
1407:
1405:
1402:
1400:
1397:
1395:
1392:
1390:
1387:
1385:
1382:
1380:
1377:
1375:
1372:
1370:
1367:
1365:
1362:
1360:
1357:
1355:
1352:
1350:
1347:
1345:
1342:
1340:
1337:
1336:
1334:
1332:
1328:
1324:
1318:
1315:
1313:
1312:Succinct game
1310:
1308:
1305:
1303:
1300:
1298:
1295:
1293:
1290:
1288:
1285:
1283:
1280:
1278:
1275:
1273:
1270:
1268:
1265:
1263:
1260:
1258:
1255:
1253:
1250:
1248:
1245:
1243:
1240:
1238:
1235:
1233:
1230:
1229:
1227:
1223:
1219:
1211:
1206:
1204:
1199:
1197:
1192:
1191:
1188:
1180:
1178:9780262650403
1174:
1170:
1169:
1163:
1162:
1158:
1148:
1145:
1140:
1134:
1130:
1126:
1122:
1115:
1112:
1106:
1103:
1098:
1094:
1090:
1086:
1085:
1080:
1076:
1070:
1067:
1060:
1058:
1056:
1048:
1046:
1044:
1040:
1035:
1032:
1029:has given an
1028:
1019:
1015:
1011:
1007:
1003:
998:
995:
991:
986:
985:
984:
982:
973:
970:
966:
963:
960:
956:
951:
948:
944:
940:
937:
933:
928:
925:
921:
917:
912:
906:
904:
897:
895:
873:
845:
822:
819:
816:
813:
810:
804:
801:
798:
792:
789:
783:
777:
770:
769:
768:
751:
748:
745:
742:
736:
733:
730:
724:
721:
718:
715:
708:
707:
706:
689:
686:
683:
680:
677:
667:
662:
640:
623:
601:
570:
567:
564:
561:
558:
535:
512:
509:
506:
503:
500:
497:
491:
488:
485:
479:
472:
471:
470:
453:
450:
447:
444:
441:
438:
435:
429:
426:
423:
417:
410:
409:
408:
405:
391:
388:
385:
382:
379:
356:
353:
350:
347:
344:
334:
325:
321:
317:
314:
311:
310:
306:
303:
300:
299:
295:
292:
290:
289:
286:
264:
228:
192:
176:
172:
164:
162:
160:
156:
154:
150:
148:
144:
140:
137:
133:
132:totally mixed
129:
121:
119:
117:
113:
109:
105:
101:
97:
93:
84:
81:
77:
72:
69:
66:
62:
59:
56:
52:
47:
44:
40:
36:
31:
19:
2097:Peyton Young
2092:Paul Milgrom
2007:Hervé Moulin
1947:Amos Tversky
1889:Folk theorem
1600:-player game
1597:
1522:Grim trigger
1458:
1167:
1147:
1120:
1114:
1105:
1091:(1): 25–55.
1088:
1082:
1069:
1052:
1036:
1023:
1017:
993:
978:
953:Significance
930:Relationship
901:
837:
766:
663:
624:
527:
468:
406:
330:
323:
168:
158:
157:
152:
151:
135:
127:
125:
107:
95:
89:
74:Significance
49:Relationship
2214:Coopetition
2017:Jean Tirole
2012:John Conway
1992:Eric Maskin
1788:Blotto game
1773:Pirate game
1582:Global game
1552:Tit for tat
1487:Bid shading
1477:Appeasement
1327:Equilibrium
1307:Solved game
1242:Determinacy
1225:Definitions
1218:game theory
958:Proposed by
924:game theory
116:probability
92:game theory
79:Proposed by
64:Superset of
43:game theory
2264:Categories
1858:Trust game
1843:Kuhn poker
1512:Escalation
1507:Deterrence
1497:Cheap talk
1469:Strategies
1287:Preference
1216:Topics of
1075:Selten, R.
1061:References
122:Definition
112:strategies
2042:John Nash
1748:Stag hunt
1492:Collusion
1012:at every
935:Subset of
882:⟩
866:⟨
846:ε
823:ε
817:−
805:ε
802:−
784:ε
752:ε
749:−
737:ε
734:−
719:ε
690:ε
687:−
678:ε
649:⟩
633:⟨
610:⟩
594:⟨
586:. Hence
571:ε
565:ε
562:−
536:ε
513:ε
504:ε
492:ε
489:−
454:ε
442:ε
430:ε
427:−
386:ε
357:ε
351:ε
348:−
273:⟩
257:⟨
237:⟩
221:⟨
201:⟩
185:⟨
177:, namely
54:Subset of
2183:Lazy SMP
1877:Theorems
1828:Deadlock
1683:Checkers
1564:of games
1331:concepts
1077:(1975).
1006:strategy
990:strategy
968:Used for
143:sequence
139:strategy
108:tremble,
1935:figures
1718:Chicken
1572:Auction
1562:Classes
1031:example
372:, for
165:Example
159:Note 2:
1175:
1135:
296:Right
1673:Chess
1660:Games
318:2, 2
315:0, 2
312:Down
307:2, 0
304:1, 1
293:Left
233:Right
153:Note:
136:every
1354:Core
1173:ISBN
1133:ISBN
1010:move
1002:move
389:<
383:<
225:Down
213:and
197:Left
1933:Key
1125:doi
1093:doi
922:in
404:.
301:Up
90:In
41:in
2266::
1668:Go
1131:.
1123:.
1087:.
1081:.
1057:.
1045:.
983:.
945:,
941:,
661:.
189:Up
118:.
94:,
1598:n
1209:e
1202:t
1195:v
1181:.
1141:.
1127::
1099:.
1095::
1089:4
1020:.
996:.
878:R
874:,
870:D
820:2
814:2
811:=
808:)
799:1
796:(
793:2
790:+
787:)
781:(
778:0
746:2
743:=
740:)
731:1
728:(
725:2
722:+
716:1
693:)
684:1
681:,
675:(
645:R
641:,
637:D
606:L
602:,
598:U
574:)
568:,
559:1
556:(
510:2
507:=
501:2
498:+
495:)
486:1
483:(
480:0
451:+
448:1
445:=
439:2
436:+
433:)
424:1
421:(
418:1
392:1
380:0
360:)
354:,
345:1
342:(
269:L
265:,
261:U
229:,
193:,
20:)
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