1530:. This can be captured by the fact that computing a correlated equilibrium only requires solving a linear program whereas solving a Nash equilibrium requires finding its fixed point completely. Another way of seeing this is that it is possible for two players to respond to each other's historical plays of a game and end up converging to a correlated equilibrium.
1258:
99:
in 1974. The idea is that each player chooses their action according to their private observation of the value of the same public signal. A strategy assigns an action to every possible observation a player can make. If no player would want to deviate from their strategy (assuming the others also
1037:
1389:. If one is going to dare, it is better for the other to chicken out. But if one is going to chicken out, it is better for the other to dare. This leads to an interesting situation where each wants to dare, but only if the other might chicken out.
1474:
Since neither player has an incentive to deviate, this is a correlated equilibrium. The expected payoff for this equilibrium is 7(1/3) + 2(1/3) + 6(1/3) = 5 which is higher than the expected payoff of the mixed strategy Nash equilibrium.
192:
846:
463:
543:
930:
1253:{\displaystyle \sum _{\omega \in \Omega }q_{i}(\omega )u_{i}(s_{i}(\omega ),s_{-i}(\omega ))\geq \sum _{\omega \in \Omega }q_{i}(\omega )u_{i}(\phi _{i}(s_{i}(\omega )),s_{-i}(\omega ))}
1518:. In this correlated equilibrium, both players get 5.25 in expectation. It can be shown that this is the correlated equilibrium with maximal sum of expected payoffs to the two players.
1312:
1447:), with the same probability, i.e. probability 1/3 for each card. After drawing the card the third party informs the players of the strategy assigned to them on the card (but
633:
1455:, they would not want to deviate supposing the other player played their assigned strategy since they will get 7 (the highest payoff possible). Suppose a player is assigned
982:
695:
326:
1029:
570:
382:
776:
749:
660:
246:
219:
352:
1002:
866:
796:
722:
590:
490:
402:
286:
266:
126:
2923:
1471:
of Daring is 7(1/2) + 0(1/2) = 3.5 and the expected utility of chickening out is 2(1/2) + 6(1/2) = 4. So, the player would prefer chickening out.
1861:
1794:
1739:
2760:
2577:
2112:
1910:
2396:
2215:
1772:
1722:
1549:
2017:
1749:
2486:
2027:
2356:
131:
2537:
1955:
1930:
1514:
with probability 2/3, and gets expected payoff 14/3, which is equal to (not less than) the expected payoff when they play
805:
2887:
2313:
2067:
2057:
1992:
407:
2107:
2087:
2572:
495:
2821:
2542:
2200:
2042:
2037:
1786:
871:
2857:
2780:
2516:
2072:
1997:
1854:
2872:
2605:
2491:
2288:
2082:
1900:
2675:
1641:
Papadimitriou, Christos H.; Roughgarden, Tim (2008). "Computing correlated equilibria in multi-player games".
1314:
is a correlated equilibrium if no player can improve his or her expected utility via a strategy modification.
2877:
2476:
2446:
2102:
1890:
1266:
2811:
2902:
2882:
2862:
2481:
2386:
2245:
2195:
2190:
2122:
2092:
1940:
1746:
1650:
1597:
1558:
1920:
799:
2361:
2346:
1381:
pictured. In this game two individuals are challenging each other to a contest where each can either
595:
100:
don't deviate), the distribution from which the signals are drawn is called a correlated equilibrium.
2695:
2680:
2567:
2562:
2466:
2451:
2416:
2381:
1980:
1925:
1847:
935:
1655:
1602:
1563:
1526:
One of the advantages of correlated equilibria is that they are computationally less expensive than
668:
291:
2852:
2471:
2421:
2258:
2185:
2165:
2022:
1905:
2831:
2690:
2521:
2501:
2351:
2230:
2135:
2062:
2007:
1668:
1623:
1615:
1007:
548:
2816:
2785:
2740:
2635:
2506:
2461:
2436:
2366:
2240:
2170:
2160:
2052:
2002:
1950:
1790:
1768:
1735:
1718:
701:
2897:
2892:
2826:
2790:
2770:
2730:
2700:
2655:
2610:
2595:
2552:
2406:
2047:
1984:
1970:
1935:
1820:
1760:
1686:
Foster, Dean P.; Vohra, Rakesh V. (1996). "Calibrated
Learning and Correlated Equilibrium".
1660:
1607:
1568:
1468:
357:
92:
88:
46:
27:
1815:
1478:
The following correlated equilibrium has an even higher payoff to both players: Recommend (
1423:
Now consider a third party (or some natural event) that draws one of three cards labeled: (
754:
727:
638:
224:
197:
2795:
2755:
2710:
2625:
2620:
2341:
2293:
2180:
1945:
1915:
1885:
1800:. A comprehensive reference from a computational perspective; see Sections 3.4.5 and 4.6.
1753:
1586:
Aumann, Robert (1987). "Correlated
Equilibrium as an Expression of Bayesian Rationality".
1527:
1393:
1378:
2660:
331:
1834:
2735:
2725:
2715:
2650:
2640:
2630:
2615:
2411:
2391:
2376:
2371:
2331:
2298:
2283:
2278:
2268:
2077:
1417:
987:
851:
781:
707:
575:
475:
387:
271:
251:
111:
2917:
2775:
2765:
2720:
2705:
2685:
2511:
2456:
2431:
2303:
2273:
2263:
2250:
2155:
2097:
2032:
1965:
1807:
1572:
1397:
698:
96:
61:
1672:
1627:
2750:
2745:
2600:
2175:
1588:
71:
2867:
2670:
2665:
2645:
2441:
2426:
2235:
2205:
2140:
2130:
1960:
1895:
1871:
1706:
1547:
Aumann, Robert (1974). "Subjectivity and correlation in randomized strategies".
80:
31:
2496:
2150:
1826:
1801:
2401:
2321:
2145:
1714:
1664:
1321:
2836:
2336:
1823:
to plot the set of correlated equilibria in a two player normal form game
1839:
1782:
Multiagent
Systems: Algorithmic, Game-Theoretic, and Logical Foundations
1502:) with probability 1/4 each. Then when a player is recommended to play
1451:
the strategy assigned to their opponent). Suppose a player is assigned
2557:
2547:
2225:
1619:
328:
and the remaining players choose a strategy profile described by the
1731:
Essentials of Game Theory: A Concise, Multidisciplinary
Introduction
1611:
2326:
1420:
equilibrium where both players chicken out with probability 2/3.
1780:
1843:
1729:
1745:. An 88-page mathematical introduction; see Section 3.5.
848:, assigning the same value to states in the same cell of
1269:
1040:
1010:
990:
938:
874:
854:
808:
784:
757:
730:
710:
671:
641:
598:
578:
551:
498:
478:
411:
410:
390:
360:
334:
294:
274:
254:
227:
200:
187:{\displaystyle \displaystyle (N,\{A_{i}\},\{u_{i}\})}
135:
134:
114:
1734:, San Rafael, CA: Morgan & Claypool Publishers,
841:{\displaystyle s_{i}\colon \Omega \rightarrow A_{i}}
2845:
2804:
2586:
2530:
2312:
2214:
2121:
1979:
1878:
67:
57:
52:
42:
37:
21:
1306:
1252:
1023:
996:
976:
932:is a correlated equilibrium of the strategic game
924:
860:
840:
790:
770:
743:
716:
689:
654:
627:
584:
564:
537:
484:
457:
396:
376:
346:
320:
280:
260:
240:
213:
186:
120:
1831:Topics on the border of Economics and Computation
458:{\displaystyle \displaystyle u_{i}(a_{i},a_{-i})}
538:{\displaystyle \phi _{i}\colon A_{i}\to A_{i}}
1855:
1775:(a modern introduction at the graduate level)
8:
1506:, they know that the other player will play
925:{\displaystyle ((\Omega ,\pi ),P_{i},s_{i})}
177:
164:
158:
145:
95:. It was first discussed by mathematician
1862:
1848:
1840:
1779:Shoham, Yoav; Leyton-Brown, Kevin (2009),
1728:Leyton-Brown, Kevin; Shoham, Yoav (2008),
1654:
1601:
1562:
1295:
1268:
1229:
1204:
1191:
1178:
1159:
1143:
1115:
1093:
1080:
1061:
1045:
1039:
1015:
1009:
989:
965:
952:
937:
913:
900:
873:
853:
832:
813:
807:
783:
762:
756:
735:
729:
709:
670:
646:
640:
616:
603:
597:
592:to modify his behavior by playing action
577:
556:
550:
529:
516:
503:
497:
477:
442:
429:
416:
409:
389:
365:
359:
333:
312:
299:
293:
273:
253:
232:
226:
205:
199:
171:
152:
133:
113:
91:that is more general than the well known
1833:(lowercase u should be replaced by u_i)
1539:
1510:with (conditional) probability 1/3 and
1307:{\displaystyle ((\Omega ,\pi ),P_{i})}
18:
1829:(2005) Lecture notes from the course
7:
1004:and for every strategy modification
1459:. Then the other player will play
1911:First-player and second-player win
1276:
1150:
1052:
881:
822:
675:
194:is characterized by an action set
14:
1550:Journal of Mathematical Economics
2924:Game theory equilibrium concepts
2018:Coalition-proof Nash equilibrium
628:{\displaystyle \phi _{i}(a_{i})}
977:{\displaystyle (N,A_{i},u_{i})}
868:'s information partition. Then
2028:Evolutionarily stable strategy
1522:Learning correlated equilibria
1486:) with probability 1/2, and (
1392:In this game, there are three
1301:
1285:
1273:
1270:
1247:
1244:
1238:
1219:
1216:
1210:
1197:
1184:
1171:
1165:
1133:
1130:
1124:
1105:
1099:
1086:
1073:
1067:
971:
939:
919:
890:
878:
875:
825:
751:be his information partition,
690:{\displaystyle (\Omega ,\pi )}
684:
672:
622:
609:
522:
451:
422:
321:{\displaystyle a_{i}\in A_{i}}
180:
136:
1:
1956:Simultaneous action selection
2888:List of games in game theory
2068:Quantal response equilibrium
2058:Perfect Bayesian equilibrium
1993:Bayes correlated equilibrium
1573:10.1016/0304-4068(74)90037-8
2357:Optional prisoner's dilemma
2088:Self-confirming equilibrium
1688:Games and Economic Behavior
1467:with probability 1/2. The
2940:
2822:Principal variation search
2538:Aumann's agreement theorem
2201:Strategy-stealing argument
2113:Trembling hand equilibrium
2043:Markov perfect equilibrium
2038:Mertens-stable equilibrium
1787:Cambridge University Press
2858:Combinatorial game theory
2517:Princess and monster game
2073:Quasi-perfect equilibrium
1998:Bayesian Nash equilibrium
1814:(note an important typo)
1810:(2004) Class notes from
1463:with probability 1/2 and
1368:
1024:{\displaystyle \phi _{i}}
565:{\displaystyle \phi _{i}}
26:
2873:Evolutionary game theory
2606:Antoine Augustin Cournot
2492:Guess 2/3 of the average
2289:Strictly determined game
2083:Satisfaction equilibrium
1901:Escalation of commitment
1802:Downloadable free online
635:when instructed to play
2878:Glossary of game theory
2477:Stackelberg competition
2103:Strong Nash equilibrium
1812:Algorithmic game theory
1765:A Course in Game Theory
1759:Osborne, Martin J. and
1665:10.1145/1379759.1379762
128:-player strategic game
2903:Tragedy of the commons
2883:List of game theorists
2863:Confrontation analysis
2573:Sprague–Grundy theorem
2093:Sequential equilibrium
2013:Correlated equilibrium
1819:Iskander Karibzhanov.
1308:
1254:
1025:
998:
978:
926:
862:
842:
792:
772:
745:
718:
691:
656:
629:
586:
566:
539:
486:
459:
398:
378:
377:{\displaystyle a_{-i}}
348:
322:
282:
262:
242:
215:
188:
122:
85:correlated equilibrium
22:Correlated equilibrium
2676:Jean-François Mertens
1756:at many universities.
1400:Nash equilibria are (
1309:
1255:
1026:
999:
979:
927:
863:
843:
793:
773:
771:{\displaystyle q_{i}}
746:
744:{\displaystyle P_{i}}
719:
692:
657:
655:{\displaystyle a_{i}}
630:
587:
567:
540:
487:
470:strategy modification
460:
399:
379:
349:
323:
283:
263:
243:
241:{\displaystyle u_{i}}
221:and utility function
216:
214:{\displaystyle A_{i}}
189:
123:
2805:Search optimizations
2681:Jennifer Tour Chayes
2568:Revelation principle
2563:Purification theorem
2502:Nash bargaining game
2467:Bertrand competition
2452:El Farol Bar problem
2417:Electronic mail game
2382:Lewis signaling game
1926:Hierarchy of beliefs
1705:Fudenberg, Drew and
1416:). There is also a
1267:
1038:
1008:
988:
984:if for every player
936:
872:
852:
806:
782:
755:
728:
708:
669:
639:
596:
576:
549:
496:
476:
408:
388:
358:
332:
292:
272:
252:
225:
198:
132:
112:
16:Game theory solution
2853:Bounded rationality
2472:Cournot competition
2422:Rock paper scissors
2397:Battle of the sexes
2387:Volunteer's dilemma
2259:Perfect information
2186:Dominant strategies
2023:Epsilon-equilibrium
1906:Extensive-form game
347:{\displaystyle N-1}
2832:Paranoid algorithm
2812:Alpha–beta pruning
2691:John Maynard Smith
2522:Rendezvous problem
2362:Traveler's dilemma
2352:Gift-exchange game
2347:Prisoner's dilemma
2264:Large Poisson game
2231:Bargaining problem
2136:Backward induction
2108:Subgame perfection
2063:Proper equilibrium
1752:2000-08-15 at the
1304:
1250:
1154:
1056:
1021:
994:
974:
922:
858:
838:
788:
768:
741:
714:
704:. For each player
687:
652:
625:
582:
562:
535:
482:
455:
454:
394:
374:
344:
318:
278:
258:
238:
211:
184:
183:
118:
2911:
2910:
2817:Aspiration window
2786:Suzanne Scotchmer
2741:Oskar Morgenstern
2636:Donald B. Gillies
2578:Zermelo's theorem
2507:Induction puzzles
2462:Fair cake-cutting
2437:Public goods game
2367:Coordination game
2241:Intransitive game
2171:Forward induction
2053:Pareto efficiency
2033:Gibbs equilibrium
2003:Berge equilibrium
1951:Simultaneous game
1796:978-0-521-89943-7
1741:978-1-59829-593-1
1649:(3): 14:1–14:29.
1375:
1374:
1370:A game of Chicken
1139:
1041:
997:{\displaystyle i}
861:{\displaystyle i}
791:{\displaystyle i}
717:{\displaystyle i}
702:probability space
585:{\displaystyle i}
485:{\displaystyle i}
397:{\displaystyle i}
288:chooses strategy
281:{\displaystyle i}
261:{\displaystyle i}
121:{\displaystyle N}
104:Formal definition
77:
76:
2931:
2898:Topological game
2893:No-win situation
2791:Thomas Schelling
2771:Robert B. Wilson
2731:Merrill M. Flood
2701:John von Neumann
2611:Ariel Rubinstein
2596:Albert W. Tucker
2447:War of attrition
2407:Matching pennies
2048:Nash equilibrium
1971:Mechanism design
1936:Normal-form game
1891:Cooperative game
1864:
1857:
1850:
1841:
1799:
1761:Ariel Rubinstein
1744:
1692:
1691:
1683:
1677:
1676:
1658:
1638:
1632:
1631:
1605:
1583:
1577:
1576:
1566:
1544:
1469:expected utility
1322:
1313:
1311:
1310:
1305:
1300:
1299:
1263:In other words,
1259:
1257:
1256:
1251:
1237:
1236:
1209:
1208:
1196:
1195:
1183:
1182:
1164:
1163:
1153:
1123:
1122:
1098:
1097:
1085:
1084:
1066:
1065:
1055:
1030:
1028:
1027:
1022:
1020:
1019:
1003:
1001:
1000:
995:
983:
981:
980:
975:
970:
969:
957:
956:
931:
929:
928:
923:
918:
917:
905:
904:
867:
865:
864:
859:
847:
845:
844:
839:
837:
836:
818:
817:
797:
795:
794:
789:
777:
775:
774:
769:
767:
766:
750:
748:
747:
742:
740:
739:
723:
721:
720:
715:
696:
694:
693:
688:
661:
659:
658:
653:
651:
650:
634:
632:
631:
626:
621:
620:
608:
607:
591:
589:
588:
583:
571:
569:
568:
563:
561:
560:
544:
542:
541:
536:
534:
533:
521:
520:
508:
507:
491:
489:
488:
483:
464:
462:
461:
456:
450:
449:
434:
433:
421:
420:
403:
401:
400:
395:
383:
381:
380:
375:
373:
372:
353:
351:
350:
345:
327:
325:
324:
319:
317:
316:
304:
303:
287:
285:
284:
279:
267:
265:
264:
259:
248:for each player
247:
245:
244:
239:
237:
236:
220:
218:
217:
212:
210:
209:
193:
191:
190:
185:
176:
175:
157:
156:
127:
125:
124:
119:
93:Nash equilibrium
89:solution concept
47:Nash equilibrium
28:Solution concept
19:
2939:
2938:
2934:
2933:
2932:
2930:
2929:
2928:
2914:
2913:
2912:
2907:
2841:
2827:max^n algorithm
2800:
2796:William Vickrey
2756:Reinhard Selten
2711:Kenneth Binmore
2626:David K. Levine
2621:Daniel Kahneman
2588:
2582:
2558:Negamax theorem
2548:Minimax theorem
2526:
2487:Diner's dilemma
2342:All-pay auction
2308:
2294:Stochastic game
2246:Mean-field game
2217:
2210:
2181:Markov strategy
2117:
1983:
1975:
1946:Sequential game
1931:Information set
1916:Game complexity
1886:Congestion game
1874:
1868:
1838:
1797:
1778:
1754:Wayback Machine
1742:
1727:
1701:
1696:
1695:
1685:
1684:
1680:
1656:10.1.1.335.2634
1640:
1639:
1635:
1612:10.2307/1911154
1603:10.1.1.295.4243
1585:
1584:
1580:
1564:10.1.1.120.1740
1546:
1545:
1541:
1536:
1528:Nash equilibria
1524:
1394:Nash equilibria
1379:game of chicken
1320:
1291:
1265:
1264:
1225:
1200:
1187:
1174:
1155:
1111:
1089:
1076:
1057:
1036:
1035:
1011:
1006:
1005:
986:
985:
961:
948:
934:
933:
909:
896:
870:
869:
850:
849:
828:
809:
804:
803:
780:
779:
758:
753:
752:
731:
726:
725:
706:
705:
667:
666:
642:
637:
636:
612:
599:
594:
593:
574:
573:
552:
547:
546:
525:
512:
499:
494:
493:
474:
473:
438:
425:
412:
406:
405:
386:
385:
361:
356:
355:
330:
329:
308:
295:
290:
289:
270:
269:
250:
249:
228:
223:
222:
201:
196:
195:
167:
148:
130:
129:
110:
109:
106:
17:
12:
11:
5:
2937:
2935:
2927:
2926:
2916:
2915:
2909:
2908:
2906:
2905:
2900:
2895:
2890:
2885:
2880:
2875:
2870:
2865:
2860:
2855:
2849:
2847:
2843:
2842:
2840:
2839:
2834:
2829:
2824:
2819:
2814:
2808:
2806:
2802:
2801:
2799:
2798:
2793:
2788:
2783:
2778:
2773:
2768:
2763:
2761:Robert Axelrod
2758:
2753:
2748:
2743:
2738:
2736:Olga Bondareva
2733:
2728:
2726:Melvin Dresher
2723:
2718:
2716:Leonid Hurwicz
2713:
2708:
2703:
2698:
2693:
2688:
2683:
2678:
2673:
2668:
2663:
2658:
2653:
2651:Harold W. Kuhn
2648:
2643:
2641:Drew Fudenberg
2638:
2633:
2631:David M. Kreps
2628:
2623:
2618:
2616:Claude Shannon
2613:
2608:
2603:
2598:
2592:
2590:
2584:
2583:
2581:
2580:
2575:
2570:
2565:
2560:
2555:
2553:Nash's theorem
2550:
2545:
2540:
2534:
2532:
2528:
2527:
2525:
2524:
2519:
2514:
2509:
2504:
2499:
2494:
2489:
2484:
2479:
2474:
2469:
2464:
2459:
2454:
2449:
2444:
2439:
2434:
2429:
2424:
2419:
2414:
2412:Ultimatum game
2409:
2404:
2399:
2394:
2392:Dollar auction
2389:
2384:
2379:
2377:Centipede game
2374:
2369:
2364:
2359:
2354:
2349:
2344:
2339:
2334:
2332:Infinite chess
2329:
2324:
2318:
2316:
2310:
2309:
2307:
2306:
2301:
2299:Symmetric game
2296:
2291:
2286:
2284:Signaling game
2281:
2279:Screening game
2276:
2271:
2269:Potential game
2266:
2261:
2256:
2248:
2243:
2238:
2233:
2228:
2222:
2220:
2212:
2211:
2209:
2208:
2203:
2198:
2196:Mixed strategy
2193:
2188:
2183:
2178:
2173:
2168:
2163:
2158:
2153:
2148:
2143:
2138:
2133:
2127:
2125:
2119:
2118:
2116:
2115:
2110:
2105:
2100:
2095:
2090:
2085:
2080:
2078:Risk dominance
2075:
2070:
2065:
2060:
2055:
2050:
2045:
2040:
2035:
2030:
2025:
2020:
2015:
2010:
2005:
2000:
1995:
1989:
1987:
1977:
1976:
1974:
1973:
1968:
1963:
1958:
1953:
1948:
1943:
1938:
1933:
1928:
1923:
1921:Graphical game
1918:
1913:
1908:
1903:
1898:
1893:
1888:
1882:
1880:
1876:
1875:
1869:
1867:
1866:
1859:
1852:
1844:
1837:
1836:
1824:
1817:
1805:
1795:
1776:
1757:
1740:
1725:
1702:
1700:
1697:
1694:
1693:
1678:
1633:
1578:
1538:
1537:
1535:
1532:
1523:
1520:
1418:mixed strategy
1373:
1372:
1366:
1365:
1362:
1359:
1352:
1351:
1348:
1345:
1338:
1337:
1331:
1325:
1319:
1316:
1303:
1298:
1294:
1290:
1287:
1284:
1281:
1278:
1275:
1272:
1261:
1260:
1249:
1246:
1243:
1240:
1235:
1232:
1228:
1224:
1221:
1218:
1215:
1212:
1207:
1203:
1199:
1194:
1190:
1186:
1181:
1177:
1173:
1170:
1167:
1162:
1158:
1152:
1149:
1146:
1142:
1138:
1135:
1132:
1129:
1126:
1121:
1118:
1114:
1110:
1107:
1104:
1101:
1096:
1092:
1088:
1083:
1079:
1075:
1072:
1069:
1064:
1060:
1054:
1051:
1048:
1044:
1018:
1014:
993:
973:
968:
964:
960:
955:
951:
947:
944:
941:
921:
916:
912:
908:
903:
899:
895:
892:
889:
886:
883:
880:
877:
857:
835:
831:
827:
824:
821:
816:
812:
787:
765:
761:
738:
734:
713:
686:
683:
680:
677:
674:
649:
645:
624:
619:
615:
611:
606:
602:
581:
559:
555:
532:
528:
524:
519:
515:
511:
506:
502:
492:is a function
481:
453:
448:
445:
441:
437:
432:
428:
424:
419:
415:
404:'s utility is
393:
384:, then player
371:
368:
364:
343:
340:
337:
315:
311:
307:
302:
298:
277:
268:. When player
257:
235:
231:
208:
204:
182:
179:
174:
170:
166:
163:
160:
155:
151:
147:
144:
141:
138:
117:
105:
102:
75:
74:
69:
65:
64:
59:
55:
54:
50:
49:
44:
40:
39:
35:
34:
24:
23:
15:
13:
10:
9:
6:
4:
3:
2:
2936:
2925:
2922:
2921:
2919:
2904:
2901:
2899:
2896:
2894:
2891:
2889:
2886:
2884:
2881:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2861:
2859:
2856:
2854:
2851:
2850:
2848:
2846:Miscellaneous
2844:
2838:
2835:
2833:
2830:
2828:
2825:
2823:
2820:
2818:
2815:
2813:
2810:
2809:
2807:
2803:
2797:
2794:
2792:
2789:
2787:
2784:
2782:
2781:Samuel Bowles
2779:
2777:
2776:Roger Myerson
2774:
2772:
2769:
2767:
2766:Robert Aumann
2764:
2762:
2759:
2757:
2754:
2752:
2749:
2747:
2744:
2742:
2739:
2737:
2734:
2732:
2729:
2727:
2724:
2722:
2721:Lloyd Shapley
2719:
2717:
2714:
2712:
2709:
2707:
2706:Kenneth Arrow
2704:
2702:
2699:
2697:
2694:
2692:
2689:
2687:
2686:John Harsanyi
2684:
2682:
2679:
2677:
2674:
2672:
2669:
2667:
2664:
2662:
2659:
2657:
2656:Herbert Simon
2654:
2652:
2649:
2647:
2644:
2642:
2639:
2637:
2634:
2632:
2629:
2627:
2624:
2622:
2619:
2617:
2614:
2612:
2609:
2607:
2604:
2602:
2599:
2597:
2594:
2593:
2591:
2585:
2579:
2576:
2574:
2571:
2569:
2566:
2564:
2561:
2559:
2556:
2554:
2551:
2549:
2546:
2544:
2541:
2539:
2536:
2535:
2533:
2529:
2523:
2520:
2518:
2515:
2513:
2510:
2508:
2505:
2503:
2500:
2498:
2495:
2493:
2490:
2488:
2485:
2483:
2480:
2478:
2475:
2473:
2470:
2468:
2465:
2463:
2460:
2458:
2457:Fair division
2455:
2453:
2450:
2448:
2445:
2443:
2440:
2438:
2435:
2433:
2432:Dictator game
2430:
2428:
2425:
2423:
2420:
2418:
2415:
2413:
2410:
2408:
2405:
2403:
2400:
2398:
2395:
2393:
2390:
2388:
2385:
2383:
2380:
2378:
2375:
2373:
2370:
2368:
2365:
2363:
2360:
2358:
2355:
2353:
2350:
2348:
2345:
2343:
2340:
2338:
2335:
2333:
2330:
2328:
2325:
2323:
2320:
2319:
2317:
2315:
2311:
2305:
2304:Zero-sum game
2302:
2300:
2297:
2295:
2292:
2290:
2287:
2285:
2282:
2280:
2277:
2275:
2274:Repeated game
2272:
2270:
2267:
2265:
2262:
2260:
2257:
2255:
2253:
2249:
2247:
2244:
2242:
2239:
2237:
2234:
2232:
2229:
2227:
2224:
2223:
2221:
2219:
2213:
2207:
2204:
2202:
2199:
2197:
2194:
2192:
2191:Pure strategy
2189:
2187:
2184:
2182:
2179:
2177:
2174:
2172:
2169:
2167:
2164:
2162:
2159:
2157:
2156:De-escalation
2154:
2152:
2149:
2147:
2144:
2142:
2139:
2137:
2134:
2132:
2129:
2128:
2126:
2124:
2120:
2114:
2111:
2109:
2106:
2104:
2101:
2099:
2098:Shapley value
2096:
2094:
2091:
2089:
2086:
2084:
2081:
2079:
2076:
2074:
2071:
2069:
2066:
2064:
2061:
2059:
2056:
2054:
2051:
2049:
2046:
2044:
2041:
2039:
2036:
2034:
2031:
2029:
2026:
2024:
2021:
2019:
2016:
2014:
2011:
2009:
2006:
2004:
2001:
1999:
1996:
1994:
1991:
1990:
1988:
1986:
1982:
1978:
1972:
1969:
1967:
1966:Succinct game
1964:
1962:
1959:
1957:
1954:
1952:
1949:
1947:
1944:
1942:
1939:
1937:
1934:
1932:
1929:
1927:
1924:
1922:
1919:
1917:
1914:
1912:
1909:
1907:
1904:
1902:
1899:
1897:
1894:
1892:
1889:
1887:
1884:
1883:
1881:
1877:
1873:
1865:
1860:
1858:
1853:
1851:
1846:
1845:
1842:
1835:
1832:
1828:
1825:
1822:
1818:
1816:
1813:
1809:
1806:
1803:
1798:
1792:
1788:
1784:
1783:
1777:
1774:
1773:0-262-65040-1
1770:
1767:, MIT Press.
1766:
1762:
1758:
1755:
1751:
1748:
1743:
1737:
1733:
1732:
1726:
1724:
1723:0-262-06141-4
1720:
1716:
1712:
1708:
1704:
1703:
1698:
1689:
1682:
1679:
1674:
1670:
1666:
1662:
1657:
1652:
1648:
1644:
1637:
1634:
1629:
1625:
1621:
1617:
1613:
1609:
1604:
1599:
1595:
1591:
1590:
1582:
1579:
1574:
1570:
1565:
1560:
1556:
1552:
1551:
1543:
1540:
1533:
1531:
1529:
1521:
1519:
1517:
1513:
1509:
1505:
1501:
1497:
1493:
1489:
1485:
1481:
1476:
1472:
1470:
1466:
1462:
1458:
1454:
1450:
1446:
1442:
1438:
1434:
1430:
1426:
1421:
1419:
1415:
1411:
1407:
1403:
1399:
1398:pure strategy
1395:
1390:
1388:
1384:
1380:
1377:Consider the
1371:
1367:
1363:
1360:
1357:
1354:
1353:
1349:
1346:
1343:
1340:
1339:
1335:
1332:
1329:
1326:
1324:
1323:
1317:
1315:
1296:
1292:
1288:
1282:
1279:
1241:
1233:
1230:
1226:
1222:
1213:
1205:
1201:
1192:
1188:
1179:
1175:
1168:
1160:
1156:
1147:
1144:
1140:
1136:
1127:
1119:
1116:
1112:
1108:
1102:
1094:
1090:
1081:
1077:
1070:
1062:
1058:
1049:
1046:
1042:
1034:
1033:
1032:
1016:
1012:
991:
966:
962:
958:
953:
949:
945:
942:
914:
910:
906:
901:
897:
893:
887:
884:
855:
833:
829:
819:
814:
810:
801:
785:
763:
759:
736:
732:
711:
703:
700:
681:
678:
663:
647:
643:
617:
613:
604:
600:
579:
572:tells player
557:
553:
530:
526:
517:
513:
509:
504:
500:
479:
471:
466:
446:
443:
439:
435:
430:
426:
417:
413:
391:
369:
366:
362:
341:
338:
335:
313:
309:
305:
300:
296:
275:
255:
233:
229:
206:
202:
172:
168:
161:
153:
149:
142:
139:
115:
103:
101:
98:
97:Robert Aumann
94:
90:
86:
82:
73:
70:
66:
63:
62:Robert Aumann
60:
56:
51:
48:
45:
41:
36:
33:
29:
25:
20:
2751:Peyton Young
2746:Paul Milgrom
2661:Hervé Moulin
2601:Amos Tversky
2543:Folk theorem
2254:-player game
2251:
2176:Grim trigger
2012:
1830:
1811:
1785:, New York:
1781:
1764:
1730:
1710:
1687:
1681:
1646:
1642:
1636:
1593:
1589:Econometrica
1587:
1581:
1557:(1): 67–96.
1554:
1548:
1542:
1525:
1515:
1511:
1507:
1503:
1499:
1495:
1491:
1487:
1483:
1479:
1477:
1473:
1464:
1460:
1456:
1452:
1448:
1444:
1440:
1436:
1432:
1428:
1424:
1422:
1413:
1409:
1405:
1401:
1391:
1386:
1382:
1376:
1369:
1355:
1341:
1333:
1327:
1262:
664:
469:
467:
107:
84:
78:
53:Significance
38:Relationship
2868:Coopetition
2671:Jean Tirole
2666:John Conway
2646:Eric Maskin
2442:Blotto game
2427:Pirate game
2236:Global game
2206:Tit for tat
2141:Bid shading
2131:Appeasement
1981:Equilibrium
1961:Solved game
1896:Determinacy
1879:Definitions
1872:game theory
1821:MATLAB code
1747:Free online
1711:Game Theory
1707:Jean Tirole
1596:(1): 1–18.
1396:. The two
1387:chicken out
1358:hicken out
1336:hicken out
545:. That is,
472:for player
81:game theory
58:Proposed by
43:Superset of
32:game theory
2512:Trust game
2497:Kuhn poker
2166:Escalation
2161:Deterrence
2151:Cheap talk
2123:Strategies
1941:Preference
1870:Topics of
1827:Noam Nisan
1808:Éva Tardos
1534:References
1318:An example
2696:John Nash
2402:Stag hunt
2146:Collusion
1715:MIT Press
1651:CiteSeerX
1598:CiteSeerX
1559:CiteSeerX
1283:π
1277:Ω
1242:ω
1231:−
1214:ω
1189:ϕ
1169:ω
1151:Ω
1148:∈
1145:ω
1141:∑
1137:≥
1128:ω
1117:−
1103:ω
1071:ω
1053:Ω
1050:∈
1047:ω
1043:∑
1013:ϕ
888:π
882:Ω
826:→
823:Ω
820::
800:posterior
699:countable
682:π
676:Ω
601:ϕ
554:ϕ
523:→
510::
501:ϕ
444:−
367:−
339:−
306:∈
2918:Category
2837:Lazy SMP
2531:Theorems
2482:Deadlock
2337:Checkers
2218:of games
1985:concepts
1763:(1994).
1750:Archived
1717:, 1991,
1673:53224027
1628:18649722
1439:), and (
802:and let
2589:figures
2372:Chicken
2226:Auction
2216:Classes
1709:(1991)
1699:Sources
1620:1911154
1494:) and (
1408:) and (
354:-tuple
72:Chicken
68:Example
1793:
1771:
1738:
1721:
1671:
1653:
1643:J. ACM
1626:
1618:
1600:
1561:
724:, let
2327:Chess
2314:Games
1669:S2CID
1624:S2CID
1616:JSTOR
1364:6, 6
1361:2, 7
1350:7, 2
1347:0, 0
697:be a
87:is a
2008:Core
1791:ISBN
1769:ISBN
1736:ISBN
1719:ISBN
1431:), (
1383:dare
1344:are
1330:are
665:Let
83:, a
2587:Key
1661:doi
1608:doi
1569:doi
1449:not
1385:or
798:'s
778:be
108:An
79:In
30:in
2920::
2322:Go
1789:,
1713:,
1667:.
1659:.
1647:55
1645:.
1622:.
1614:.
1606:.
1594:55
1592:.
1567:.
1553:.
1498:,
1490:,
1482:,
1443:,
1435:,
1427:,
1412:,
1404:,
1031::
662:.
468:A
465:.
2252:n
1863:e
1856:t
1849:v
1804:.
1690:.
1675:.
1663::
1630:.
1610::
1575:.
1571::
1555:1
1516:D
1512:C
1508:D
1504:C
1500:D
1496:C
1492:C
1488:D
1484:C
1480:C
1465:D
1461:C
1457:C
1453:D
1445:D
1441:C
1437:C
1433:D
1429:C
1425:C
1414:D
1410:C
1406:C
1402:D
1356:C
1342:D
1334:C
1328:D
1302:)
1297:i
1293:P
1289:,
1286:)
1280:,
1274:(
1271:(
1248:)
1245:)
1239:(
1234:i
1227:s
1223:,
1220:)
1217:)
1211:(
1206:i
1202:s
1198:(
1193:i
1185:(
1180:i
1176:u
1172:)
1166:(
1161:i
1157:q
1134:)
1131:)
1125:(
1120:i
1113:s
1109:,
1106:)
1100:(
1095:i
1091:s
1087:(
1082:i
1078:u
1074:)
1068:(
1063:i
1059:q
1017:i
992:i
972:)
967:i
963:u
959:,
954:i
950:A
946:,
943:N
940:(
920:)
915:i
911:s
907:,
902:i
898:P
894:,
891:)
885:,
879:(
876:(
856:i
834:i
830:A
815:i
811:s
786:i
764:i
760:q
737:i
733:P
712:i
685:)
679:,
673:(
648:i
644:a
623:)
618:i
614:a
610:(
605:i
580:i
558:i
531:i
527:A
518:i
514:A
505:i
480:i
452:)
447:i
440:a
436:,
431:i
427:a
423:(
418:i
414:u
392:i
370:i
363:a
342:1
336:N
314:i
310:A
301:i
297:a
276:i
256:i
234:i
230:u
207:i
203:A
181:)
178:}
173:i
169:u
165:{
162:,
159:}
154:i
150:A
146:{
143:,
140:N
137:(
116:N
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.