236:. This theorem is a combination of strategies in which no player can improve their payoff or outcome by changing their strategy, given the strategies of the other players. In other words, a Nash equilibrium is a set of strategies in which each player is doing the best possible, assuming what the others are doing to receive the most optimal outcome for themselves. It is important to note that not all games have a unique nash equilibrium and if they do, it may not be the most desirable outcome. Additionally, the desired outcomes is greatly affected by individuals chosen strategies, and their beliefs on what they believe other players will do under the assumption that players will make the most
33:
276:
present the payoff of both players in the game. For example, the best response of player one is the highest payoff for player one’s move, and vice versa. For player one, they will pick the payoffs from the column strategies. For player two, they will choose their moves based on the two row strategies. Assuming both players do not know the opponents strategies. It is a
140:, the outcome of a game is the ultimate result of a strategic interaction with one or more people, dependant on the choices made by all participants in a certain exchange. It represents the final payoff resulting from a set of actions that individuals can take within the context of the game. Outcomes are pivotal in determining the payoffs and
148:
chosen by involved players and can be represented in a number of ways; one common way is a payoff matrix showing the individual payoffs for each players with a combination of strategies, as seen in the payoff matrix example below. Outcomes can be expressed in terms of monetary value or utility to a specific person. Additionally, a
272:
game-theoretic analysis, when applied to a rational approach, is to provide recommendations on how to make choices against other rational players. First, it reduces the possible outcomes; logical action is more predictable than irrational. Second, it provides a criterion for assessing an economic system's efficiency.
147:
In game theory, a strategy is a set of actions that a player can take in response to the actions of others. Each player’s strategy is based on their expectation of what the other players are likely to do, often explained in terms of probability. Outcomes are dependent on the combination of strategies
275:
In a
Prisoner's Dilemma game between two players, player one and player two can choose the utilities that are the best response to maximise their outcomes. "A best response to a coplayer’s strategy is a strategy that yields the highest payoff against that particular strategy". A matrix is used to
271:
Players are persons who make logical economic decisions. It is assumed that human people make all of their economic decisions based only on the idea that they are irrational. A player's rewards (utilities, profits, income, or subjective advantages) are assumed to be maximised. The purpose of
252:
Many different concepts exist to express how players might interact. An optimal interaction may be one in which no player's payoff can be made greater, without making any other player's payoff lesser. Such a payoff is described as
307:
Equilibria are not always Pareto efficient, and a number of game theorists design ways to enforce Pareto efficient play, or play that satisfies some other sort of social optimality. The theory of this is called
543:
Self-organizing coalitions for managing complexity : agent-based simulation of evolutionary game theory models using dynamic social networks for interdisciplinary applications
330:
288:
Outcome optimisation in game theory has many real world applications that can help predict actions and economic behaviours by other players. Examples of this include
629:
566:
97:
280:
for the first player to choose a payoff of 5 rather than a payoff of 3 because strategy D is a better response than strategy C.
152:
can be used to deduce the actions leading to an outcome by displaying possible sequences of actions and the outcomes associated.
69:
50:
686:
613:
588:
550:
1585:
76:
397:
470:"Belief distorted Nash equilibria: introduction of a new kind of equilibrium in dynamic games with distorted information"
144:
for parties involved. Game theorists commonly study how the outcome of a game is determined and what factors affect it.
1402:
937:
735:
1221:
1040:
116:
83:
842:
268:, where each player plays a strategy such that their payoff is maximized given the strategy of the other players.
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17:
65:
1181:
852:
54:
1020:
1362:
780:
755:
1712:
1138:
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817:
932:
912:
141:
1646:
1397:
1367:
1025:
867:
862:
1682:
1605:
1341:
897:
822:
679:
1697:
1430:
1316:
1113:
907:
725:
130:
1500:
643:
240:
decision for themselves. A common example of the nash equilibrium and undesirable outcomes is the
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8:
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809:
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481:
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232:
350:"Nash Equilibrium: How It Works in Game Theory, Examples, Plus Prisoner's Dilemma"
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260:
Many economists study the ways in which payoffs are in some sort of
32:
1661:
1161:
1382:
1372:
1050:
1151:
257:, and the set of such payoffs is called the Pareto frontier.
230:
A commonly used theorem in relation to outcomes is the
518:"What Is the Prisoner's Dilemma and How Does It Work?"
467:
423:"Nash Equilibrium and the History of Economic Theory"
57:. Unsourced material may be challenged and removed.
1740:
581:Encyclopedia of statistics in behavioral science
468:Wiszniewska-Matyszkiel, Agnieszka (2016-08-01).
583:. Hoboken, N.J.: John Wiley & Sons. 2005.
680:
648:INDUSTRIAL ENGINEERING AND OPERATION RESEARCH
264:. One example of such an equilibrium is the
687:
673:
628:: CS1 maint: location missing publisher (
565:: CS1 maint: location missing publisher (
247:
694:
540:
485:
117:Learn how and when to remove this message
328:
603:
420:
14:
1741:
668:
55:adding citations to reliable sources
26:
606:Game theory : through examples
24:
736:First-player and second-player win
644:"Game Theory and its Applications"
25:
1760:
129:For other uses of "Outcome", see
843:Coalition-proof Nash equilibrium
31:
636:
597:
329:Osbourne, Martin (2000-11-05).
283:
42:needs additional citations for
853:Evolutionarily stable strategy
573:
534:
510:
461:
427:Journal of Economic Literature
414:
390:
366:
342:
332:An Introduction to Game Theory
322:
13:
1:
781:Simultaneous action selection
474:Annals of Operations Research
315:
1713:List of games in game theory
893:Quantal response equilibrium
883:Perfect Bayesian equilibrium
818:Bayes correlated equilibrium
338:. (Draft). pp. 157–161.
7:
1182:Optional prisoner's dilemma
913:Self-confirming equilibrium
541:Burguillo, Juan C. (2018).
402:Corporate Finance Institute
10:
1765:
1647:Principal variation search
1363:Aumann's agreement theorem
1026:Strategy-stealing argument
938:Trembling hand equilibrium
868:Markov perfect equilibrium
863:Mertens-stable equilibrium
421:Myerson, Roger B. (1999).
304:and even social sciences.
128:
66:"Outcome" game theory
1683:Combinatorial game theory
1670:
1629:
1411:
1355:
1342:Princess and monster game
1137:
1039:
946:
898:Quasi-perfect equilibrium
823:Bayesian Nash equilibrium
804:
703:
487:10.1007/s10479-015-1920-7
374:"ICS 180, April 17, 1997"
165:
160:
1698:Evolutionary game theory
1431:Antoine Augustin Cournot
1317:Guess 2/3 of the average
1114:Strictly determined game
908:Satisfaction equilibrium
726:Escalation of commitment
131:Outcome (disambiguation)
1703:Glossary of game theory
1302:Stackelberg competition
928:Strong Nash equilibrium
248:Choosing among outcomes
166:Strategies of Player B
162:Strategies of Player A
1728:Tragedy of the commons
1708:List of game theorists
1688:Confrontation analysis
1398:Sprague–Grundy theorem
918:Sequential equilibrium
838:Correlated equilibrium
156:Payoff Matrix Example
1501:Jean-François Mertens
545:. Cham, Switzerland.
439:10.1257/jel.37.3.1067
310:implementation theory
1630:Search optimizations
1506:Jennifer Tour Chayes
1393:Revelation principle
1388:Purification theorem
1327:Nash bargaining game
1292:Bertrand competition
1277:El Farol Bar problem
1242:Electronic mail game
1207:Lewis signaling game
751:Hierarchy of beliefs
604:Prisner, E. (2014).
262:economic equilibrium
51:improve this article
1678:Bounded rationality
1297:Cournot competition
1247:Rock paper scissors
1222:Battle of the sexes
1212:Volunteer's dilemma
1084:Perfect information
1011:Dominant strategies
848:Epsilon-equilibrium
731:Extensive-form game
302:corporate behaviour
157:
1657:Paranoid algorithm
1637:Alpha–beta pruning
1516:John Maynard Smith
1347:Rendezvous problem
1187:Traveler's dilemma
1177:Gift-exchange game
1172:Prisoner's dilemma
1089:Large Poisson game
1056:Bargaining problem
961:Backward induction
933:Subgame perfection
888:Proper equilibrium
398:"Nash Equilibrium"
242:Prisoner’s Dilemma
155:
1736:
1735:
1642:Aspiration window
1611:Suzanne Scotchmer
1566:Oskar Morgenstern
1461:Donald B. Gillies
1403:Zermelo's theorem
1332:Induction puzzles
1287:Fair cake-cutting
1262:Public goods game
1192:Coordination game
1066:Intransitive game
996:Forward induction
878:Pareto efficiency
858:Gibbs equilibrium
828:Berge equilibrium
776:Simultaneous game
615:978-1-61444-115-1
590:978-0-470-86080-9
552:978-3-319-69896-0
278:dominant strategy
228:
227:
127:
126:
119:
101:
16:(Redirected from
1756:
1723:Topological game
1718:No-win situation
1616:Thomas Schelling
1596:Robert B. Wilson
1556:Merrill M. Flood
1526:John von Neumann
1436:Ariel Rubinstein
1421:Albert W. Tucker
1272:War of attrition
1232:Matching pennies
873:Nash equilibrium
796:Mechanism design
761:Normal-form game
716:Cooperative game
689:
682:
675:
666:
665:
659:
658:
656:
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619:
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570:
564:
556:
538:
532:
531:
529:
528:
514:
508:
507:
489:
465:
459:
458:
433:(3): 1067–1082.
418:
412:
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408:
394:
388:
387:
385:
384:
370:
364:
363:
361:
360:
346:
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326:
266:Nash equilibrium
255:Pareto efficient
233:Nash equilibrium
158:
154:
142:expected utility
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59:
35:
27:
21:
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1759:
1758:
1757:
1755:
1754:
1753:
1739:
1738:
1737:
1732:
1666:
1652:max^n algorithm
1625:
1621:William Vickrey
1581:Reinhard Selten
1536:Kenneth Binmore
1451:David K. Levine
1446:Daniel Kahneman
1413:
1407:
1383:Negamax theorem
1373:Minimax theorem
1351:
1312:Diner's dilemma
1167:All-pay auction
1133:
1119:Stochastic game
1071:Mean-field game
1042:
1035:
1006:Markov strategy
942:
808:
800:
771:Sequential game
756:Information set
741:Game complexity
711:Congestion game
699:
693:
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378:www.ics.uci.edu
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60:
58:
48:
36:
23:
22:
18:Upside outcomes
15:
12:
11:
5:
1762:
1752:
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1734:
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1731:
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1725:
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1710:
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1631:
1627:
1626:
1624:
1623:
1618:
1613:
1608:
1603:
1598:
1593:
1588:
1586:Robert Axelrod
1583:
1578:
1573:
1568:
1563:
1561:Olga Bondareva
1558:
1553:
1551:Melvin Dresher
1548:
1543:
1541:Leonid Hurwicz
1538:
1533:
1528:
1523:
1518:
1513:
1508:
1503:
1498:
1493:
1488:
1483:
1478:
1476:Harold W. Kuhn
1473:
1468:
1466:Drew Fudenberg
1463:
1458:
1456:David M. Kreps
1453:
1448:
1443:
1441:Claude Shannon
1438:
1433:
1428:
1423:
1417:
1415:
1409:
1408:
1406:
1405:
1400:
1395:
1390:
1385:
1380:
1378:Nash's theorem
1375:
1370:
1365:
1359:
1357:
1353:
1352:
1350:
1349:
1344:
1339:
1334:
1329:
1324:
1319:
1314:
1309:
1304:
1299:
1294:
1289:
1284:
1279:
1274:
1269:
1264:
1259:
1254:
1249:
1244:
1239:
1237:Ultimatum game
1234:
1229:
1224:
1219:
1217:Dollar auction
1214:
1209:
1204:
1202:Centipede game
1199:
1194:
1189:
1184:
1179:
1174:
1169:
1164:
1159:
1157:Infinite chess
1154:
1149:
1143:
1141:
1135:
1134:
1132:
1131:
1126:
1124:Symmetric game
1121:
1116:
1111:
1109:Signaling game
1106:
1104:Screening game
1101:
1096:
1094:Potential game
1091:
1086:
1081:
1073:
1068:
1063:
1058:
1053:
1047:
1045:
1037:
1036:
1034:
1033:
1028:
1023:
1021:Mixed strategy
1018:
1013:
1008:
1003:
998:
993:
988:
983:
978:
973:
968:
963:
958:
952:
950:
944:
943:
941:
940:
935:
930:
925:
920:
915:
910:
905:
903:Risk dominance
900:
895:
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880:
875:
870:
865:
860:
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850:
845:
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835:
830:
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802:
801:
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793:
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783:
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748:
746:Graphical game
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728:
723:
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713:
707:
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691:
684:
677:
669:
661:
660:
635:
614:
596:
589:
572:
551:
533:
509:
480:(1): 147–177.
460:
413:
389:
365:
341:
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314:
285:
282:
249:
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9:
6:
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2:
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1701:
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1696:
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1691:
1689:
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1684:
1681:
1679:
1676:
1675:
1673:
1671:Miscellaneous
1669:
1663:
1660:
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1655:
1653:
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1648:
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1643:
1640:
1638:
1635:
1634:
1632:
1628:
1622:
1619:
1617:
1614:
1612:
1609:
1607:
1606:Samuel Bowles
1604:
1602:
1601:Roger Myerson
1599:
1597:
1594:
1592:
1591:Robert Aumann
1589:
1587:
1584:
1582:
1579:
1577:
1574:
1572:
1569:
1567:
1564:
1562:
1559:
1557:
1554:
1552:
1549:
1547:
1546:Lloyd Shapley
1544:
1542:
1539:
1537:
1534:
1532:
1531:Kenneth Arrow
1529:
1527:
1524:
1522:
1519:
1517:
1514:
1512:
1511:John Harsanyi
1509:
1507:
1504:
1502:
1499:
1497:
1494:
1492:
1489:
1487:
1484:
1482:
1481:Herbert Simon
1479:
1477:
1474:
1472:
1469:
1467:
1464:
1462:
1459:
1457:
1454:
1452:
1449:
1447:
1444:
1442:
1439:
1437:
1434:
1432:
1429:
1427:
1424:
1422:
1419:
1418:
1416:
1410:
1404:
1401:
1399:
1396:
1394:
1391:
1389:
1386:
1384:
1381:
1379:
1376:
1374:
1371:
1369:
1366:
1364:
1361:
1360:
1358:
1354:
1348:
1345:
1343:
1340:
1338:
1335:
1333:
1330:
1328:
1325:
1323:
1320:
1318:
1315:
1313:
1310:
1308:
1305:
1303:
1300:
1298:
1295:
1293:
1290:
1288:
1285:
1283:
1282:Fair division
1280:
1278:
1275:
1273:
1270:
1268:
1265:
1263:
1260:
1258:
1257:Dictator game
1255:
1253:
1250:
1248:
1245:
1243:
1240:
1238:
1235:
1233:
1230:
1228:
1225:
1223:
1220:
1218:
1215:
1213:
1210:
1208:
1205:
1203:
1200:
1198:
1195:
1193:
1190:
1188:
1185:
1183:
1180:
1178:
1175:
1173:
1170:
1168:
1165:
1163:
1160:
1158:
1155:
1153:
1150:
1148:
1145:
1144:
1142:
1140:
1136:
1130:
1129:Zero-sum game
1127:
1125:
1122:
1120:
1117:
1115:
1112:
1110:
1107:
1105:
1102:
1100:
1099:Repeated game
1097:
1095:
1092:
1090:
1087:
1085:
1082:
1080:
1078:
1074:
1072:
1069:
1067:
1064:
1062:
1059:
1057:
1054:
1052:
1049:
1048:
1046:
1044:
1038:
1032:
1029:
1027:
1024:
1022:
1019:
1017:
1016:Pure strategy
1014:
1012:
1009:
1007:
1004:
1002:
999:
997:
994:
992:
989:
987:
984:
982:
981:De-escalation
979:
977:
974:
972:
969:
967:
964:
962:
959:
957:
954:
953:
951:
949:
945:
939:
936:
934:
931:
929:
926:
924:
923:Shapley value
921:
919:
916:
914:
911:
909:
906:
904:
901:
899:
896:
894:
891:
889:
886:
884:
881:
879:
876:
874:
871:
869:
866:
864:
861:
859:
856:
854:
851:
849:
846:
844:
841:
839:
836:
834:
831:
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62:Find sources:
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40:This article
38:
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29:
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19:
1576:Peyton Young
1571:Paul Milgrom
1486:Hervé Moulin
1426:Amos Tversky
1368:Folk theorem
1079:-player game
1076:
1001:Grim trigger
652:. Retrieved
650:. 2019-10-31
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525:. Retrieved
522:Investopedia
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405:. Retrieved
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381:. Retrieved
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357:. Retrieved
354:Investopedia
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284:Applications
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49:Please help
44:verification
41:
1749:Game theory
1693:Coopetition
1496:Jean Tirole
1491:John Conway
1471:Eric Maskin
1267:Blotto game
1252:Pirate game
1061:Global game
1031:Tit for tat
966:Bid shading
956:Appeasement
806:Equilibrium
786:Solved game
721:Determinacy
704:Definitions
697:game theory
294:investments
138:game theory
1337:Trust game
1322:Kuhn poker
991:Escalation
986:Deterrence
976:Cheap talk
948:Strategies
766:Preference
695:Topics of
654:2023-04-24
527:2023-04-23
407:2023-04-23
383:2023-04-24
359:2023-04-23
316:References
77:newspapers
1521:John Nash
1227:Stag hunt
971:Collusion
624:cite book
561:cite book
504:254235057
496:1572-9338
447:0022-0515
150:game tree
1743:Category
1662:Lazy SMP
1356:Theorems
1307:Deadlock
1162:Checkers
1043:of games
810:concepts
238:rational
107:May 2008
1414:figures
1197:Chicken
1051:Auction
1041:Classes
455:2564872
244:game.
91:scholar
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1152:Chess
1139:Games
500:S2CID
451:JSTOR
336:(PDF)
98:JSTOR
84:books
833:Core
630:link
610:ISBN
608:. .
585:ISBN
567:link
547:ISBN
492:ISSN
443:ISSN
292:and
70:news
1412:Key
482:doi
478:243
435:doi
312:.
136:In
53:by
1745::
1147:Go
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