43:
275:
straightforward example of maximizing payoff is that of monetary gain, but for the purpose of a game theory analysis, this payoff can take any desired outcome—cash reward, minimization of exertion or discomfort, or promoting justice can all be modeled as amassing an overall “utility” for the player. The assumption of rationality states that players will always act in the way that best satisfies their ordering from best to worst of various possible outcomes.
333:. If both players have a strictly dominant strategy, the game has only one unique Nash equilibrium, referred to as a "dominant strategy equilibrium". However, that Nash equilibrium is not necessarily "efficient", meaning that there may be non-equilibrium outcomes of the game that would be better for both players. The classic game used to illustrate this is the
194:(≤) A: choosing B always gives at least as good an outcome as choosing A, no matter what the other players do, and there is at least one set of opponents' action for which B gives a better outcome than A. (Notice that if B strictly dominates A, then B weakly dominates A. Therefore, we can say "B dominates A" as synonymous of "B weakly dominates A".)
284:
The assumption that each player has knowledge of the game, knows the rules and payoffs associated with each course of action, and realizes that every other player has this same level of understanding. This is the premise that allows a player to make a value judgment on the actions of another player,
451:
removing dominated strategies. In the first step, all dominated strategies are removed from the strategy space of each of the players, since no rational player would ever play these strategies. This results in a new, smaller game. Some strategies—that were not dominated before—may be
211:
Neither A nor B dominates the other: B and A are not equivalent, and B neither dominates, nor is dominated by, A. Choosing A is better in some cases, while choosing B is better in other cases, depending on exactly how the opponent chooses to play. For example, B is "throw rock" while A is "throw
274:
The assumption that each player acts in a way that is designed to bring about what he or she most prefers given probabilities of various outcomes; von
Neumann and Morgenstern showed that if these preferences satisfy certain conditions, this is mathematically equivalent to maximizing a payoff. A
267:
A complete contingent plan for a player in the game. A complete contingent plan is a full specification of a player's behavior, describing each action a player would take at every possible decision point. Because information sets represent points in a game where a player must make a decision, a
432:
they will still get 0. This satisfies the requirements of a Nash equilibrium. Suppose both players choose C. Neither player will do better by unilaterally deviating—if a player switches to playing D, they will get 0. This also satisfies the requirements of a Nash equilibrium.
340:
Strictly dominated strategies cannot be a part of a Nash equilibrium, and as such, it is irrational for any player to play them. On the other hand, weakly dominated strategies may be part of Nash equilibria. For instance, consider the
459:, that is, each player knows that the rest of the players are rational, and each player knows that the rest of the players know that he knows that the rest of the players are rational, and so on ad infinitum (see Aumann, 1976).
201:
by A: there is at least one set of opponents' actions for which B gives a worse outcome than A, while all other sets of opponents' actions give A the same payoff as B. (Strategy A weakly dominates B).
447:
The iterated elimination (or deletion, or removal) of dominated strategies (also denominated as IESDS, or IDSDS, or IRSDS) is one common technique for solving games that involves
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that is better than any other strategy for one player, no matter how that player's opponent will play. Some very simple games can be solved using dominance.
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by A: choosing B always gives a worse outcome than choosing A, no matter what the other player(s) do. (Strategy A strictly dominates B).
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If a strictly dominant strategy exists for one player in a game, that player will play that strategy in each of the game's
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704:
498:
Leyton-Brown, Kevin; Shoham, Yoav (January 2008). "Essentials of Game Theory: A Concise
Multidisciplinary Introduction".
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A player can compare two strategies, A and B, to determine which one is better. The result of the comparison is one of:
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dominated in the smaller game. The first step is repeated, creating a new even smaller game, and so on.
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187:(≥) A: choosing B always gives a better outcome than choosing A, no matter what the other players do.
428:. Neither player will do any better by unilaterally deviating—if a player switches to playing
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backed by the assumption of rationality, into consideration when selecting an action.
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A comprehensive reference from a computational perspective; see
Sections 3.4.3, 4.5.
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player's strategy describes what that player will do at each information set.
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This process is valid since it is assumed that rationality among players is
448:
372:
where one gets 0 regardless. Since in one case, one does better by playing
1729:
1229:
732:
677:
Multiagent
Systems: Algorithmic, Game-Theoretic, and Logical Foundations
220:
This notion can be generalized beyond the comparison of two strategies.
1450:
1440:
1118:
630:
Essentials of Game Theory: A Concise, Multidisciplinary
Introduction
1219:
500:
Synthesis
Lectures on Artificial Intelligence and Machine Learning
675:
736:
628:
36:
720:
This article incorporates material from
Dominant strategy on
703:"Strict Dominance in Mixed Strategies – Game Theory 101".
645:. An 88-page mathematical introduction; see Section 3.3.
253:
if some other strategy exists that strictly dominates B.
292:
260:
if some other strategy exists that weakly dominates B.
669:
Jim
Ratliff's Game Theory Course: Strategic Dominance
437:
Iterated elimination of strictly dominated strategies
396:
633:. San Rafael, CA: Morgan & Claypool Publishers.
1738:
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424:is a Nash equilibrium. Suppose both players choose
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101:
657:
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726:Creative Commons Attribution/Share-Alike License
712:Strategy : An Introduction to Game Theory
748:
8:
714:. Third ed. W.W. Norton & Company 2013.
660:Two-Person Game Theory: The Essential Ideas
755:
741:
733:
674:Shoham, Yoav; Leyton-Brown, Kevin (2009).
627:Leyton-Brown, Kevin; Shoham, Yoav (2008).
562:: CS1 maint: location missing publisher (
395:
87:Learn how and when to remove this message
532:Strategy: An Introduction to Game Theory
50:This article includes a list of general
490:
555:
98:
7:
525:
523:
521:
364:one gets 1; if one's opponent plays
27:Quality of a strategy in game theory
804:First-player and second-player win
591:Game Theory for Applied Economists
56:it lacks sufficient corresponding
25:
512:10.2200/S00108ED1V01Y200802AIM003
911:Coalition-proof Nash equilibrium
41:
664:. University of Michigan Press.
30:For the business strategy, see
921:Evolutionarily stable strategy
724:, which is licensed under the
612:. Princeton University Press.
593:. Princeton University Press.
409:
397:
246:every other possible strategy.
232:every other possible strategy.
1:
849:Simultaneous action selection
289:Dominance and Nash equilibria
1781:List of games in game theory
961:Quantal response equilibrium
951:Perfect Bayesian equilibrium
886:Bayes correlated equilibrium
534:(Third ed.). New York.
368:one gets 0. Compare this to
1250:Optional prisoner's dilemma
981:Self-confirming equilibrium
530:Joel, Watson (2013-05-09).
1833:
1715:Principal variation search
1431:Aumann's agreement theorem
1094:Strategy-stealing argument
1006:Trembling hand equilibrium
936:Markov perfect equilibrium
931:Mertens-stable equilibrium
682:Cambridge University Press
440:
360:: If one's opponent plays
352:weakly dominates strategy
29:
1751:Combinatorial game theory
1410:Princess and monster game
966:Quasi-perfect equilibrium
891:Bayesian Nash equilibrium
106:
1766:Evolutionary game theory
1499:Antoine Augustin Cournot
1385:Guess 2/3 of the average
1182:Strictly determined game
976:Satisfaction equilibrium
794:Escalation of commitment
698:Downloadable free online
608:Gintis, Herbert (2000).
589:Gibbons, Robert (1992).
1771:Glossary of game theory
1370:Stackelberg competition
996:Strong Nash equilibrium
707:. Retrieved 2021-12-17.
345:pictured at the right.
137:Rationalizable strategy
71:more precise citations.
18:Dominance (game theory)
1796:Tragedy of the commons
1776:List of game theorists
1756:Confrontation analysis
1466:Sprague–Grundy theorem
986:Sequential equilibrium
906:Correlated equilibrium
469:Max-dominated strategy
416:
380:and never does worse,
127:Strategy (game theory)
1569:Jean-François Mertens
649:at many universities.
417:
415:{\displaystyle (D,D)}
214:Rock, Paper, Scissors
1698:Search optimizations
1574:Jennifer Tour Chayes
1461:Revelation principle
1456:Purification theorem
1395:Nash bargaining game
1360:Bertrand competition
1345:El Farol Bar problem
1310:Electronic mail game
1275:Lewis signaling game
819:Hierarchy of beliefs
610:Game Theory Evolving
394:
1746:Bounded rationality
1365:Cournot competition
1315:Rock paper scissors
1290:Battle of the sexes
1280:Volunteer's dilemma
1152:Perfect information
1079:Dominant strategies
916:Epsilon-equilibrium
799:Extensive-form game
1725:Paranoid algorithm
1705:Alpha–beta pruning
1584:John Maynard Smith
1415:Rendezvous problem
1255:Traveler's dilemma
1245:Gift-exchange game
1240:Prisoner's dilemma
1157:Large Poisson game
1124:Bargaining problem
1029:Backward induction
1001:Subgame perfection
956:Proper equilibrium
412:
335:Prisoner's Dilemma
251:strictly dominated
230:strictly dominates
206:strictly dominated
185:strictly dominates
152:Prisoner's dilemma
1804:
1803:
1710:Aspiration window
1679:Suzanne Scotchmer
1634:Oskar Morgenstern
1529:Donald B. Gillies
1471:Zermelo's theorem
1400:Induction puzzles
1355:Fair cake-cutting
1330:Public goods game
1260:Coordination game
1134:Intransitive game
1064:Forward induction
946:Pareto efficiency
926:Gibbs equilibrium
896:Berge equilibrium
844:Simultaneous game
705:gametheory101.com
691:978-0-521-89943-7
640:978-1-59829-593-1
576:Fudenberg, Drew;
443:Rationalizability
384:weakly dominates
356:Consider playing
327:
326:
226:strictly dominant
165:dominant strategy
157:
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102:Dominant strategy
97:
96:
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32:Market domination
16:(Redirected from
1824:
1791:Topological game
1786:No-win situation
1684:Thomas Schelling
1664:Robert B. Wilson
1624:Merrill M. Flood
1594:John von Neumann
1504:Ariel Rubinstein
1489:Albert W. Tucker
1340:War of attrition
1300:Matching pennies
941:Nash equilibrium
864:Mechanism design
829:Normal-form game
784:Cooperative game
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479:Winning strategy
457:common knowledge
423:
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388:. Despite this,
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280:Common Knowledge
258:weakly dominated
199:weakly dominated
192:weakly dominates
108:Solution concept
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67:this article by
58:inline citations
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1720:max^n algorithm
1693:
1689:William Vickrey
1649:Reinhard Selten
1604:Kenneth Binmore
1519:David K. Levine
1514:Daniel Kahneman
1481:
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1451:Negamax theorem
1441:Minimax theorem
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1380:Diner's dilemma
1235:All-pay auction
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1187:Stochastic game
1139:Mean-field game
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1074:Markov strategy
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839:Sequential game
824:Information set
809:Game complexity
779:Congestion game
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1674:Samuel Bowles
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1669:Roger Myerson
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1659:Robert Aumann
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1350:Fair division
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1325:Dictator game
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1197:Zero-sum game
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1170:
1168:
1167:Repeated game
1165:
1163:
1160:
1158:
1155:
1153:
1150:
1148:
1146:
1142:
1140:
1137:
1135:
1132:
1130:
1127:
1125:
1122:
1120:
1117:
1116:
1114:
1112:
1106:
1100:
1097:
1095:
1092:
1090:
1087:
1085:
1084:Pure strategy
1082:
1080:
1077:
1075:
1072:
1070:
1067:
1065:
1062:
1060:
1057:
1055:
1052:
1050:
1049:De-escalation
1047:
1045:
1042:
1040:
1037:
1035:
1032:
1030:
1027:
1025:
1022:
1021:
1019:
1017:
1013:
1007:
1004:
1002:
999:
997:
994:
992:
991:Shapley value
989:
987:
984:
982:
979:
977:
974:
972:
969:
967:
964:
962:
959:
957:
954:
952:
949:
947:
944:
942:
939:
937:
934:
932:
929:
927:
924:
922:
919:
917:
914:
912:
909:
907:
904:
902:
899:
897:
894:
892:
889:
887:
884:
883:
881:
879:
875:
871:
865:
862:
860:
859:Succinct game
857:
855:
852:
850:
847:
845:
842:
840:
837:
835:
832:
830:
827:
825:
822:
820:
817:
815:
812:
810:
807:
805:
802:
800:
797:
795:
792:
790:
787:
785:
782:
780:
777:
776:
774:
770:
766:
758:
753:
751:
746:
744:
739:
738:
735:
729:
727:
723:
718:
717:
713:
710:Watson Joel.
709:
706:
702:
699:
693:
687:
683:
679:
678:
672:
670:
667:
662:
661:
655:
651:
648:
642:
636:
632:
631:
625:
621:
619:0-691-00943-0
615:
611:
606:
602:
600:0-691-00395-5
596:
592:
587:
583:
579:
574:
573:
565:
559:
551:
547:
543:
541:9780393918380
537:
533:
526:
524:
522:
518:
513:
509:
505:
501:
494:
491:
484:
480:
477:
475:
472:
470:
467:
466:
462:
460:
458:
453:
450:
444:
436:
434:
431:
427:
406:
403:
400:
387:
383:
379:
375:
371:
367:
363:
359:
355:
351:
346:
344:
343:payoff matrix
338:
336:
332:
322:
319:
316:
315:
311:
308:
305:
304:
300:
297:
295:
294:
288:
286:
283:
281:
276:
273:
269:
266:
259:
255:
252:
248:
245:
242:
238:
234:
231:
227:
223:
222:
221:
215:
212:scissors" in
210:
207:
203:
200:
196:
193:
189:
186:
182:
181:
180:
174:
172:
170:
166:
162:
153:
150:
146:
141:
138:
135:
131:
128:
125:
121:
116:
113:
109:
105:
100:
91:
88:
80:
70:
66:
60:
59:
53:
48:
39:
38:
33:
19:
1644:Peyton Young
1639:Paul Milgrom
1554:Hervé Moulin
1494:Amos Tversky
1436:Folk theorem
1147:-player game
1144:
1078:
1069:Grim trigger
719:
711:
680:. New York:
676:
659:
654:Rapoport, A.
629:
609:
590:
584:. MIT Press.
581:
578:Tirole, Jean
531:
503:
499:
493:
454:
446:
429:
425:
385:
381:
377:
373:
369:
365:
361:
357:
353:
349:
347:
339:
328:
278:
277:
272:Rationality:
271:
270:
264:
263:
257:
250:
243:
240:
236:
229:
225:
219:
205:
198:
191:
184:
178:
164:
158:
143:Significance
118:Relationship
83:
77:January 2016
74:
55:
1817:Game theory
1761:Coopetition
1564:Jean Tirole
1559:John Conway
1539:Eric Maskin
1335:Blotto game
1320:Pirate game
1129:Global game
1099:Tit for tat
1034:Bid shading
1024:Appeasement
874:Equilibrium
854:Solved game
789:Determinacy
772:Definitions
765:game theory
647:Free online
582:Game Theory
449:iteratively
376:instead of
175:Terminology
161:game theory
133:Superset of
112:game theory
69:introducing
1405:Trust game
1390:Kuhn poker
1059:Escalation
1054:Deterrence
1044:Cheap talk
1016:Strategies
834:Preference
763:Topics of
722:PlanetMath
485:References
52:references
1589:John Nash
1295:Stag hunt
1039:Collusion
558:cite book
550:842323069
506:(1): 36.
348:Strategy
265:Strategy:
244:dominates
123:Subset of
1811:Category
1730:Lazy SMP
1424:Theorems
1375:Deadlock
1230:Checkers
1111:of games
878:concepts
656:(1966).
580:(1993).
463:See also
169:strategy
148:Used for
1482:figures
1265:Chicken
1119:Auction
1109:Classes
422:
390:
65:improve
688:
637:
616:
597:
548:
538:
241:weakly
54:, but
1220:Chess
1207:Games
323:0, 0
320:0, 0
312:0, 0
309:1, 1
204:B is
197:B is
167:is a
901:Core
686:ISBN
635:ISBN
614:ISBN
595:ISBN
564:link
546:OCLC
536:ISBN
163:, a
1480:Key
508:doi
159:In
110:in
1813::
1215:Go
684:.
560:}}
556:{{
544:.
520:^
502:.
430:C,
370:D,
366:D,
362:C,
354:D.
337:.
317:D
306:C
301:D
298:C
190:B
183:B
1145:n
756:e
749:t
742:v
728:.
700:.
694:.
643:.
622:.
603:.
566:)
552:.
514:.
510::
504:2
426:D
410:)
407:D
404:,
401:D
398:(
386:D
382:C
378:D
374:C
358:C
350:C
282::
216:.
90:)
84:(
79:)
75:(
61:.
34:.
20:)
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