32:
game, where players have the option to "reject the deal", that is, to abstain from playing the game. This type of game can be used as a model for a number of real world situations in which agents are afforded the third option of abstaining from a game interaction such as an election.
41:
The structure of the optional prisoner's dilemma can be generalized from the standard prisoner's dilemma game setting. In this way, suppose that the two players are represented by the colors, red and blue, and that each player chooses to "Cooperate", "Defect" or "Abstain".
287:
Cardinot, Marcos; Gibbons, Maud; O'Riordan, Colm; Griffith, Josephine (2016). "Simulation of an
Optional Strategy in the Prisoner's Dilemma in Spatial and Non-spatial Environments".
375:
Cardinot, Marcos; O'Riordan, Colm; Griffith, Josephine (2016). "The
Optional Prisoner's Dilemma in a Spatial Environment: Coevolving Game Strategy and Link Weights".
325:
426:
392:
308:
1325:
1142:
677:
475:
961:
780:
292:
582:
1051:
1488:
592:
333:
1102:
520:
495:
1452:
878:
632:
622:
557:
672:
652:
1137:
379:. Proceedings of the 8th International Joint Conference on Computational Intelligence. Vol. 1. pp. 86–93.
1386:
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419:
358:
1437:
1170:
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853:
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1240:
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1011:
667:
455:
1376:
1467:
1447:
1427:
1046:
951:
810:
760:
755:
687:
657:
577:
505:
485:
926:
911:
29:
1260:
1245:
1132:
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1016:
981:
946:
545:
490:
412:
1417:
1036:
986:
823:
750:
730:
587:
470:
1396:
1255:
1086:
1066:
916:
795:
700:
627:
572:
350:
1493:
1381:
1350:
1305:
1200:
1071:
1026:
1001:
931:
805:
735:
725:
617:
567:
515:
388:
304:
1462:
1457:
1391:
1355:
1335:
1295:
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1220:
1175:
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1117:
971:
612:
549:
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500:
380:
342:
296:
1360:
1320:
1275:
1190:
1185:
906:
858:
745:
510:
480:
450:
1225:
230:
Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff
1300:
1290:
1280:
1215:
1205:
1195:
1180:
976:
956:
941:
936:
896:
863:
848:
843:
833:
642:
1482:
1340:
1330:
1285:
1270:
1250:
1076:
1021:
996:
868:
838:
828:
815:
720:
662:
597:
530:
46:
354:
1315:
1310:
1165:
740:
300:
1432:
1235:
1230:
1210:
1006:
991:
800:
770:
705:
695:
525:
460:
436:
25:
219:
If Blue defects while Red cooperates, then Blue receives the temptation payoff
1061:
715:
384:
966:
886:
710:
346:
1401:
901:
404:
1122:
1112:
790:
891:
241:
If one or both players abstain, both receive the loner's payoff
212:
If both players defect, they both receive the punishment payoff
408:
24:) game models a situation of conflict involving two players in
326:"Evolution of altriusm in optional and compulsory games"
205:
If both players cooperate, they both receive the reward
1410:
1369:
1151:
1095:
877:
779:
686:
544:
443:
249:The following condition must hold for the payoffs:
28:. It can be seen as an extension of the standard
420:
8:
223:, while Red receives the "sucker's" payoff,
234:, while Red receives the temptation payoff
427:
413:
405:
51:
279:
324:Batali, John; Kitcher, Philip (1995).
7:
295:. Vol. 9825. pp. 145–156.
476:First-player and second-player win
14:
293:Lecture Notes in Computer Science
583:Coalition-proof Nash equilibrium
593:Evolutionarily stable strategy
334:Journal of Theoretical Biology
1:
521:Simultaneous action selection
49:for the game is shown below:
1453:List of games in game theory
633:Quantal response equilibrium
623:Perfect Bayesian equilibrium
558:Bayes correlated equilibrium
301:10.1007/978-3-319-43488-9_14
53:Canonical OPD payoff matrix
922:Optional prisoner's dilemma
653:Self-confirming equilibrium
18:optional prisoner's dilemma
1510:
1387:Principal variation search
1103:Aumann's agreement theorem
766:Strategy-stealing argument
678:Trembling hand equilibrium
608:Markov perfect equilibrium
603:Mertens-stable equilibrium
289:From Animals to Animats 14
1423:Combinatorial game theory
1082:Princess and monster game
638:Quasi-perfect equilibrium
563:Bayesian Nash equilibrium
158:
114:
70:
65:
62:
59:
1438:Evolutionary game theory
1171:Antoine Augustin Cournot
1057:Guess 2/3 of the average
854:Strictly determined game
648:Satisfaction equilibrium
466:Escalation of commitment
385:10.5220/0006053900860093
1443:Glossary of game theory
1042:Stackelberg competition
668:Strong Nash equilibrium
209:for mutual cooperation.
1468:Tragedy of the commons
1448:List of game theorists
1428:Confrontation analysis
1138:Sprague–Grundy theorem
658:Sequential equilibrium
578:Correlated equilibrium
347:10.1006/jtbi.1995.0128
1489:Non-cooperative games
1241:Jean-François Mertens
1370:Search optimizations
1246:Jennifer Tour Chayes
1133:Revelation principle
1128:Purification theorem
1067:Nash bargaining game
1032:Bertrand competition
1017:El Farol Bar problem
982:Electronic mail game
947:Lewis signaling game
491:Hierarchy of beliefs
1418:Bounded rationality
1037:Cournot competition
987:Rock paper scissors
962:Battle of the sexes
952:Volunteer's dilemma
824:Perfect information
751:Dominant strategies
588:Epsilon-equilibrium
471:Extensive-form game
54:
1397:Paranoid algorithm
1377:Alpha–beta pruning
1256:John Maynard Smith
1087:Rendezvous problem
927:Traveler's dilemma
917:Gift-exchange game
912:Prisoner's dilemma
829:Large Poisson game
796:Bargaining problem
701:Backward induction
673:Subgame perfection
628:Proper equilibrium
52:
30:prisoner's dilemma
1476:
1475:
1382:Aspiration window
1351:Suzanne Scotchmer
1306:Oskar Morgenstern
1201:Donald B. Gillies
1143:Zermelo's theorem
1072:Induction puzzles
1027:Fair cake-cutting
1002:Public goods game
932:Coordination game
806:Intransitive game
736:Forward induction
618:Pareto efficiency
598:Gibbs equilibrium
568:Berge equilibrium
516:Simultaneous game
394:978-989-758-201-1
310:978-3-319-43487-2
202:
201:
1501:
1463:Topological game
1458:No-win situation
1356:Thomas Schelling
1336:Robert B. Wilson
1296:Merrill M. Flood
1266:John von Neumann
1176:Ariel Rubinstein
1161:Albert W. Tucker
1012:War of attrition
972:Matching pennies
613:Nash equilibrium
536:Mechanism design
501:Normal-form game
456:Cooperative game
429:
422:
415:
406:
399:
398:
372:
366:
365:
363:
357:. Archived from
330:
321:
315:
314:
284:
198:
192:
185:
179:
172:
166:
154:
148:
141:
135:
128:
122:
110:
104:
97:
91:
84:
78:
55:
1509:
1508:
1504:
1503:
1502:
1500:
1499:
1498:
1479:
1478:
1477:
1472:
1406:
1392:max^n algorithm
1365:
1361:William Vickrey
1321:Reinhard Selten
1276:Kenneth Binmore
1191:David K. Levine
1186:Daniel Kahneman
1153:
1147:
1123:Negamax theorem
1113:Minimax theorem
1091:
1052:Diner's dilemma
907:All-pay auction
873:
859:Stochastic game
811:Mean-field game
782:
775:
746:Markov strategy
682:
548:
540:
511:Sequential game
496:Information set
481:Game complexity
451:Congestion game
439:
433:
403:
402:
395:
374:
373:
369:
361:
328:
323:
322:
318:
311:
286:
285:
281:
276:
194:
188:
181:
175:
168:
162:
150:
144:
137:
131:
124:
118:
106:
100:
93:
87:
80:
74:
39:
12:
11:
5:
1507:
1505:
1497:
1496:
1491:
1481:
1480:
1474:
1473:
1471:
1470:
1465:
1460:
1455:
1450:
1445:
1440:
1435:
1430:
1425:
1420:
1414:
1412:
1408:
1407:
1405:
1404:
1399:
1394:
1389:
1384:
1379:
1373:
1371:
1367:
1366:
1364:
1363:
1358:
1353:
1348:
1343:
1338:
1333:
1328:
1326:Robert Axelrod
1323:
1318:
1313:
1308:
1303:
1301:Olga Bondareva
1298:
1293:
1291:Melvin Dresher
1288:
1283:
1281:Leonid Hurwicz
1278:
1273:
1268:
1263:
1258:
1253:
1248:
1243:
1238:
1233:
1228:
1223:
1218:
1216:Harold W. Kuhn
1213:
1208:
1206:Drew Fudenberg
1203:
1198:
1196:David M. Kreps
1193:
1188:
1183:
1181:Claude Shannon
1178:
1173:
1168:
1163:
1157:
1155:
1149:
1148:
1146:
1145:
1140:
1135:
1130:
1125:
1120:
1118:Nash's theorem
1115:
1110:
1105:
1099:
1097:
1093:
1092:
1090:
1089:
1084:
1079:
1074:
1069:
1064:
1059:
1054:
1049:
1044:
1039:
1034:
1029:
1024:
1019:
1014:
1009:
1004:
999:
994:
989:
984:
979:
977:Ultimatum game
974:
969:
964:
959:
957:Dollar auction
954:
949:
944:
942:Centipede game
939:
934:
929:
924:
919:
914:
909:
904:
899:
897:Infinite chess
894:
889:
883:
881:
875:
874:
872:
871:
866:
864:Symmetric game
861:
856:
851:
849:Signaling game
846:
844:Screening game
841:
836:
834:Potential game
831:
826:
821:
813:
808:
803:
798:
793:
787:
785:
777:
776:
774:
773:
768:
763:
761:Mixed strategy
758:
753:
748:
743:
738:
733:
728:
723:
718:
713:
708:
703:
698:
692:
690:
684:
683:
681:
680:
675:
670:
665:
660:
655:
650:
645:
643:Risk dominance
640:
635:
630:
625:
620:
615:
610:
605:
600:
595:
590:
585:
580:
575:
570:
565:
560:
554:
552:
542:
541:
539:
538:
533:
528:
523:
518:
513:
508:
503:
498:
493:
488:
486:Graphical game
483:
478:
473:
468:
463:
458:
453:
447:
445:
441:
440:
434:
432:
431:
424:
417:
409:
401:
400:
393:
367:
364:on 2019-02-22.
341:(2): 161–171.
316:
309:
278:
277:
275:
272:
247:
246:
239:
228:
217:
210:
200:
199:
186:
173:
160:
156:
155:
142:
129:
116:
112:
111:
98:
85:
72:
68:
67:
64:
61:
58:
38:
35:
13:
10:
9:
6:
4:
3:
2:
1506:
1495:
1492:
1490:
1487:
1486:
1484:
1469:
1466:
1464:
1461:
1459:
1456:
1454:
1451:
1449:
1446:
1444:
1441:
1439:
1436:
1434:
1431:
1429:
1426:
1424:
1421:
1419:
1416:
1415:
1413:
1411:Miscellaneous
1409:
1403:
1400:
1398:
1395:
1393:
1390:
1388:
1385:
1383:
1380:
1378:
1375:
1374:
1372:
1368:
1362:
1359:
1357:
1354:
1352:
1349:
1347:
1346:Samuel Bowles
1344:
1342:
1341:Roger Myerson
1339:
1337:
1334:
1332:
1331:Robert Aumann
1329:
1327:
1324:
1322:
1319:
1317:
1314:
1312:
1309:
1307:
1304:
1302:
1299:
1297:
1294:
1292:
1289:
1287:
1286:Lloyd Shapley
1284:
1282:
1279:
1277:
1274:
1272:
1271:Kenneth Arrow
1269:
1267:
1264:
1262:
1259:
1257:
1254:
1252:
1251:John Harsanyi
1249:
1247:
1244:
1242:
1239:
1237:
1234:
1232:
1229:
1227:
1224:
1222:
1221:Herbert Simon
1219:
1217:
1214:
1212:
1209:
1207:
1204:
1202:
1199:
1197:
1194:
1192:
1189:
1187:
1184:
1182:
1179:
1177:
1174:
1172:
1169:
1167:
1164:
1162:
1159:
1158:
1156:
1150:
1144:
1141:
1139:
1136:
1134:
1131:
1129:
1126:
1124:
1121:
1119:
1116:
1114:
1111:
1109:
1106:
1104:
1101:
1100:
1098:
1094:
1088:
1085:
1083:
1080:
1078:
1075:
1073:
1070:
1068:
1065:
1063:
1060:
1058:
1055:
1053:
1050:
1048:
1045:
1043:
1040:
1038:
1035:
1033:
1030:
1028:
1025:
1023:
1022:Fair division
1020:
1018:
1015:
1013:
1010:
1008:
1005:
1003:
1000:
998:
997:Dictator game
995:
993:
990:
988:
985:
983:
980:
978:
975:
973:
970:
968:
965:
963:
960:
958:
955:
953:
950:
948:
945:
943:
940:
938:
935:
933:
930:
928:
925:
923:
920:
918:
915:
913:
910:
908:
905:
903:
900:
898:
895:
893:
890:
888:
885:
884:
882:
880:
876:
870:
869:Zero-sum game
867:
865:
862:
860:
857:
855:
852:
850:
847:
845:
842:
840:
839:Repeated game
837:
835:
832:
830:
827:
825:
822:
820:
818:
814:
812:
809:
807:
804:
802:
799:
797:
794:
792:
789:
788:
786:
784:
778:
772:
769:
767:
764:
762:
759:
757:
756:Pure strategy
754:
752:
749:
747:
744:
742:
739:
737:
734:
732:
729:
727:
724:
722:
721:De-escalation
719:
717:
714:
712:
709:
707:
704:
702:
699:
697:
694:
693:
691:
689:
685:
679:
676:
674:
671:
669:
666:
664:
663:Shapley value
661:
659:
656:
654:
651:
649:
646:
644:
641:
639:
636:
634:
631:
629:
626:
624:
621:
619:
616:
614:
611:
609:
606:
604:
601:
599:
596:
594:
591:
589:
586:
584:
581:
579:
576:
574:
571:
569:
566:
564:
561:
559:
556:
555:
553:
551:
547:
543:
537:
534:
532:
531:Succinct game
529:
527:
524:
522:
519:
517:
514:
512:
509:
507:
504:
502:
499:
497:
494:
492:
489:
487:
484:
482:
479:
477:
474:
472:
469:
467:
464:
462:
459:
457:
454:
452:
449:
448:
446:
442:
438:
430:
425:
423:
418:
416:
411:
410:
407:
396:
390:
386:
382:
378:
371:
368:
360:
356:
352:
348:
344:
340:
336:
335:
327:
320:
317:
312:
306:
302:
298:
294:
290:
283:
280:
273:
271:
270:
266:
262:
258:
254:
250:
244:
240:
237:
233:
229:
226:
222:
218:
215:
211:
208:
204:
203:
197:
191:
187:
184:
178:
174:
171:
165:
161:
157:
153:
147:
143:
140:
134:
130:
127:
121:
117:
113:
109:
103:
99:
96:
90:
86:
83:
77:
73:
69:
57:
56:
50:
48:
47:payoff matrix
43:
37:Payoff matrix
36:
34:
31:
27:
23:
19:
1316:Peyton Young
1311:Paul Milgrom
1226:Hervé Moulin
1166:Amos Tversky
1108:Folk theorem
921:
819:-player game
816:
741:Grim trigger
376:
370:
359:the original
338:
332:
319:
288:
282:
268:
264:
260:
256:
252:
251:
248:
242:
235:
231:
224:
220:
213:
206:
195:
189:
182:
176:
169:
163:
151:
145:
138:
132:
125:
119:
107:
101:
94:
88:
81:
75:
44:
40:
21:
17:
15:
1433:Coopetition
1236:Jean Tirole
1231:John Conway
1211:Eric Maskin
1007:Blotto game
992:Pirate game
801:Global game
771:Tit for tat
706:Bid shading
696:Appeasement
546:Equilibrium
526:Solved game
461:Determinacy
444:Definitions
437:game theory
26:game theory
1483:Categories
1077:Trust game
1062:Kuhn poker
731:Escalation
726:Deterrence
716:Cheap talk
688:Strategies
506:Preference
435:Topics of
274:References
71:Cooperate
60:Cooperate
1261:John Nash
967:Stag hunt
711:Collusion
1494:Dilemmas
1402:Lazy SMP
1096:Theorems
1047:Deadlock
902:Checkers
783:of games
550:concepts
355:35935283
159:Abstain
66:Abstain
1154:figures
937:Chicken
791:Auction
781:Classes
115:Defect
63:Defect
391:
353:
307:
892:Chess
879:Games
362:(PDF)
351:S2CID
329:(PDF)
267:>
263:>
259:>
255:>
573:Core
389:ISBN
377:ECTA
305:ISBN
45:The
16:The
1152:Key
381:doi
343:doi
339:175
297:doi
22:OPD
1485::
887:Go
387:.
349:.
337:.
331:.
303:.
291:.
193:,
180:,
167:,
149:,
136:,
123:,
105:,
92:,
79:,
817:n
428:e
421:t
414:v
397:.
383::
345::
313:.
299::
269:S
265:P
261:L
257:R
253:T
245:.
243:L
238:.
236:T
232:S
227:.
225:S
221:T
216:.
214:P
207:R
196:L
190:L
183:L
177:L
170:L
164:L
152:L
146:L
139:P
133:P
126:S
120:T
108:L
102:L
95:T
89:S
82:R
76:R
20:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.