80:, this initial round of communication may enable the players to select among multiple equilibria, thereby achieving higher payoffs than in the uncoordinated case. The messages and strategies which yield this outcome are symmetric for each player. They are: 1) announce opera or football with even probability 2) if a person announces opera (or football), then upon hearing this message the other person will say opera (or football) as well (Farrell and
1487:
507:
545:
When interests are aligned, then information is fully disclosed. When conflict of interest is very large, all information is kept hidden. These are extreme cases. The model allowing for more subtle case when interests are close, but different and in these cases optimal behavior leads to some but not
204:
The form of the message does not matter, as long as there is mutual understanding, common interpretation. It could be a general statement from a central bank's chairman, a political speech in any language, etc. Whatever the form, it is eventually taken to mean "The state of the world is between
910:
1395:
1308:
91:, is a game whose only equilibrium is in dominant strategies. Any pre-play cheap talk will be ignored and players will play their dominant strategies (Defect, Defect) regardless of the messages sent.
1158:
72:
Cheap talk can, in general, be added to any game and has the potential to enhance the set of possible equilibrium outcomes. For example, one can add a round of cheap talk in the beginning of the
1020:
482:
must obtain the desired action by choosing what information to reveal. Each player's utility depends on the state of the world and on both players' decisions that eventually lead to action
84:, 1996). If they both announce different options, then no coordination is achieved. In the case of only one player messaging, this could also give that player a first-mover advantage.
357:
271:
to do. Utility is a way to quantify satisfaction or wishes. It can be financial profits, or non-financial satisfaction—for instance the extent to which the environment is protected.
1318:
426:
1421:
748:
1461:
1441:
1190:
27:
is communication between players that does not directly affect the payoffs of the game. Providing and receiving information is free. This is in contrast to
494:
We look for an equilibrium where each player decides optimally, assuming that the other player also decides optimally. Players are rational, although
1759:
187:
may disclose full information, but it may also give limited, blurred information: it will typically say "The state of the world is between
1641:, and a finer message, the blue area is more important. This implies higher utility. Disclosing more information benefits both parties.
957:
1634:. However, it remains quite coarse compared to full revelation, which would be the 45° line, but which is not a Nash equilibrium.
1998:
1059:
286:
76:. Each player announces whether they intend to go to the football game, or the opera. Because the Battle of the Sexes is a
2902:
361:
458:, meaning that the receiver wants to take action that matches the state of the world, which he does not know in general.
2719:
2249:
2047:
2538:
2357:
1967:
73:
2154:
1843:
498:
has only limited information. Expectations get realized, and there is no incentive to deviate from this situation.
3070:
2628:
1929:
59:
Therefore, an agent engaging in cheap talk could lie with impunity, but may choose in equilibrium not to do so.
2498:
2164:
1883:
2337:
2679:
2092:
2067:
1732:
546:
all information being disclosed, leading to various kinds of carefully worded sentences that we may observe.
430:
The theory applies to more general forms of utility, but quadratic preferences makes exposition easier. Thus
99:
It has been commonly argued that cheap talk will have no effect on the underlying structure of the game. In
87:
It is not guaranteed, however, that cheap talk will have an effect on equilibrium payoffs. Another game, the
3029:
2455:
2204:
2194:
2129:
905:{\displaystyle a_{i}={\bar {a}}(t_{i-1},t_{i})=\mathrm {arg} \max _{a}\int _{t_{i-1}}^{t_{i}}U^{R}(a,t)dt}
2244:
2224:
1626:
possible message, which does not give any information. So everything is red on the top left panel. With
2963:
2714:
2684:
2342:
2179:
2174:
1400:
31:, in which sending certain messages may be costly for the sender depending on the state of the world.
2999:
2922:
2658:
2209:
2134:
1991:
1808:
1699:
3014:
2747:
2633:
2430:
2219:
2037:
116:
2817:
1767:
1315:
must be small enough so that the numerator is positive. This determines the maximum allowed value
954:
as possible, we can show that quite intuitively the optimal action is the middle of the interval:
3019:
2618:
2588:
2239:
2027:
239:
updates his beliefs about the state of the world given new information that he might get, using
3044:
3024:
3004:
2953:
2623:
2528:
2387:
2332:
2259:
2229:
2149:
2077:
1803:
1694:
103:
authors have often argued that costly signalling best explains signalling between animals (see
28:
1921:
1390:{\displaystyle N^{*}=\langle -{\frac {1}{2}}+{\frac {1}{2}}{\sqrt {1+{\frac {2}{b}}}}\rangle }
2503:
2488:
2057:
684:
Since actions are functions of messages, actions are also constant over these intervals: for
88:
119:
indicate that cheap talk can have effects on the evolutionary dynamics of particular games.
3065:
2837:
2822:
2709:
2704:
2608:
2593:
2558:
2523:
2117:
2062:
1984:
1892:
111:). This general belief has been receiving some challenges (see work by Carl Bergstrom and
8:
2994:
2613:
2563:
2400:
2327:
2302:
2159:
2042:
1685:
Crawford, Vincent P.; Sobel, Joel (November 1982). "Strategic
Information Transmission".
568:
there exists at least an equilibrium in which the set of induced actions has cardinality
2653:
1896:
2973:
2832:
2663:
2643:
2493:
2372:
2272:
2199:
2144:
1946:
1862:
1821:
1741:
1712:
1655:
1446:
1426:
104:
1904:
2958:
2927:
2882:
2777:
2648:
2603:
2578:
2508:
2382:
2307:
2297:
2189:
2139:
2087:
1963:
1908:
108:
77:
1950:
3039:
3034:
2968:
2932:
2912:
2872:
2842:
2797:
2752:
2737:
2694:
2548:
2322:
2184:
2121:
2107:
2072:
1938:
1900:
1852:
1813:
1704:
35:
2937:
2897:
2852:
2767:
2762:
2483:
2435:
2317:
2082:
2052:
2022:
518:
2802:
710:
The action function is now indirectly characterized by the fact that each value
2877:
2867:
2857:
2792:
2782:
2772:
2757:
2553:
2533:
2518:
2513:
2473:
2440:
2425:
2420:
2410:
2214:
1875:
1665:
1660:
240:
132:
In the basic form of the game, there are two players communicating, one sender
3059:
2917:
2907:
2862:
2847:
2827:
2598:
2573:
2445:
2415:
2405:
2392:
2292:
2234:
2169:
2102:
1834:
81:
2892:
2887:
2742:
2312:
1794:
541:, which means no information transmitted, is always an equilibrium outcome.
164: ; he has only ex-ante beliefs about it, and relies on a message from
112:
1912:
1876:"Efficiency in Evolutionary Games: Darwin, Nash, and the Secret Handshake"
588:
While messages could ex-ante assume an infinite number of possible values
3009:
2812:
2807:
2787:
2583:
2568:
2377:
2347:
2277:
2267:
2097:
2032:
2008:
1857:
1838:
1792:
Crawford, V. P.; Sobel, J. (1982). "Strategic
Information Transmission".
1650:
1303:{\displaystyle t_{i}=t_{1}i+2bi(i-1)\qquad t_{1}={\frac {1-2bN(N-1)}{N}}}
20:
1976:
2638:
1922:"Signals, Evolution and the Explanatory Power of Transient Information"
1866:
1825:
1745:
1716:
39:
2543:
2463:
2282:
535:, which means full information revelation, is not a Nash equilibrium.
251:. This action impacts both his own utility and the sender's utility.
1817:
1708:
55:
unverifiable (i.e. cannot be verified by a third party like a court)
2978:
2478:
1942:
661:
s are the bounds of intervals where the messages are constant: for
52:
non-binding (i.e. does not limit strategic choices by either party)
1038:, The sender has to be indifferent between sending either message
45:
To give a formal definition, cheap talk is communication that is:
2699:
2689:
2367:
1486:
100:
647:. This partition is shown on the top right segment of Figure 1.
1730:
Farrell, Joseph (1987). "Cheap Talk, Coordination, and Entry".
2468:
506:
267:
is based on maximizing his utility, given what he expects
152:
gets knowledge of the state of the world or of his "type"
1443:, i.e. the smallest positive integer greater or equal to
615:
Thus an equilibrium may be characterized by a partition
596:, actually they may take only a finite number of values
592:
for the infinite number of possible states of the world
1153:{\displaystyle U^{S}(a_{i},t_{i})=U^{S}(a_{i+1},t_{i})}
1449:
1429:
1403:
1321:
1193:
1062:
960:
751:
364:
289:
1960:
The Stag Hunt and the
Evolution of Social Structure
1455:
1435:
1415:
1389:
1302:
1152:
1014:
942:, and in the special case quadratic utility where
904:
450:between the two players, or alternatively as bias.
420:
351:
122:
115:2002, 2004). In particular, several models using
168:to possibly improve the accuracy of his beliefs.
3057:
1015:{\displaystyle a_{i}={\frac {t_{i-1}+t_{i}}{2}}}
827:
1493:Message and utilities for conflict of interest
575:there is no equilibrium that induces more than
470:wants a slightly higher action to be taken, if
1992:
1791:
1684:
1832:
1410:
1404:
1384:
1335:
1999:
1985:
94:
2006:
1856:
1807:
1698:
1471:. We now describe all the equilibria for
1024:
517:Crawford and Sobel characterize possible
42:has given rise to a variety of variants.
1962:. New York: Cambridge University Press.
1485:
505:
1729:
352:{\displaystyle U^{S}(a,t)=-(a-t-b)^{2}}
3058:
1957:
1919:
1873:
201:". It may give no information at all.
1980:
421:{\displaystyle U^{R}(a,t)=-(a-t)^{2}}
489:
283:can be specified by the following:
13:
2048:First-player and second-player win
1517:This is the babbling equilibrium.
822:
819:
816:
14:
3082:
1678:
1416:{\displaystyle \langle Z\rangle }
743:is uniformly distributed over ),
2155:Coalition-proof Nash equilibrium
1844:Journal of Economic Perspectives
1183:We consider a partition of size
739:. Mathematically (assuming that
513:Cheap talk communication setting
49:costless to transmit and receive
1247:
123:Crawford and Sobel's definition
62:
2165:Evolutionarily stable strategy
1884:Journal of Theoretical Biology
1752:
1723:
1291:
1279:
1244:
1232:
1147:
1115:
1099:
1073:
893:
881:
809:
777:
771:
409:
396:
387:
375:
340:
321:
312:
300:
67:
1:
2093:Simultaneous action selection
1905:10.1016/S0022-5193(05)80082-7
1785:
1733:The RAND Journal of Economics
1166:This gives information about
438:have different objectives if
3030:List of games in game theory
2205:Quantal response equilibrium
2195:Perfect Bayesian equilibrium
2130:Bayes correlated equilibrium
631:of the set of types , where
275:The respective utilities of
7:
2499:Optional prisoner's dilemma
2225:Self-confirming equilibrium
1644:
1463:. Example: We assume that
583:
10:
3087:
2964:Principal variation search
2680:Aumann's agreement theorem
2343:Strategy-stealing argument
2250:Trembling hand equilibrium
2180:Markov perfect equilibrium
2175:Mertens-stable equilibrium
1762:The Biology of Information
679:
501:
254:
171:
127:
34:This basic setting set by
3000:Combinatorial game theory
2987:
2946:
2728:
2672:
2659:Princess and monster game
2454:
2356:
2258:
2210:Quasi-perfect equilibrium
2135:Bayesian Nash equilibrium
2116:
2015:
717:optimizes return for the
529:, but in a finite number.
478:does not control action,
263:regarding the content of
222:
3015:Evolutionary game theory
2748:Antoine Augustin Cournot
2634:Guess 2/3 of the average
2431:Strictly determined game
2220:Satisfaction equilibrium
2038:Escalation of commitment
1671:
179:decides to send message
117:evolutionary game theory
3020:Glossary of game theory
2619:Stackelberg competition
2240:Strong Nash equilibrium
247:decides to take action
143:
95:Biological applications
3071:Asymmetric information
3045:Tragedy of the commons
3025:List of game theorists
3005:Confrontation analysis
2715:Sprague–Grundy theorem
2230:Sequential equilibrium
2150:Correlated equilibrium
1874:Robson, A. J. (1990).
1509:
1457:
1437:
1417:
1391:
1304:
1154:
1025:Indifference condition
1016:
906:
514:
422:
353:
273:→ Quadratic utilities:
16:Game-theoretic concept
2818:Jean-François Mertens
1930:Philosophy of Science
1489:
1458:
1438:
1418:
1392:
1305:
1160:
1155:
1017:
907:
641:(N) < . . . < t
509:
423:
354:
2947:Search optimizations
2823:Jennifer Tour Chayes
2710:Revelation principle
2705:Purification theorem
2644:Nash bargaining game
2609:Bertrand competition
2594:El Farol Bar problem
2559:Electronic mail game
2524:Lewis signaling game
2063:Hierarchy of beliefs
1858:10.1257/jep.10.3.103
1447:
1427:
1401:
1319:
1191:
1187:. One can show that
1060:
958:
916:Quadratic utilities:
749:
525:There are typically
448:conflict of interest
362:
287:
2995:Bounded rationality
2614:Cournot competition
2564:Rock paper scissors
2539:Battle of the sexes
2529:Volunteer's dilemma
2401:Perfect information
2328:Dominant strategies
2160:Epsilon-equilibrium
2043:Extensive-form game
1958:Skyrms, B. (2004).
1920:Skyrms, B. (2002).
1897:1990JThBi.144..379R
870:
527:multiple equilibria
74:Battle of the Sexes
2974:Paranoid algorithm
2954:Alpha–beta pruning
2833:John Maynard Smith
2664:Rendezvous problem
2504:Traveler's dilemma
2494:Gift-exchange game
2489:Prisoner's dilemma
2406:Large Poisson game
2373:Bargaining problem
2273:Backward induction
2245:Subgame perfection
2200:Proper equilibrium
1656:Handicap principle
1510:
1453:
1433:
1423:is the ceiling of
1413:
1387:
1300:
1150:
1012:
950:to be as close to
902:
836:
835:
557:such that for all
515:
462:is maximized when
454:is maximized when
446:is interpreted as
418:
349:
105:Handicap principle
89:Prisoner's Dilemma
3053:
3052:
2959:Aspiration window
2928:Suzanne Scotchmer
2883:Oskar Morgenstern
2778:Donald B. Gillies
2720:Zermelo's theorem
2649:Induction puzzles
2604:Fair cake-cutting
2579:Public goods game
2509:Coordination game
2383:Intransitive game
2308:Forward induction
2190:Pareto efficiency
2170:Gibbs equilibrium
2140:Berge equilibrium
2088:Simultaneous game
1630:, the message is
1456:{\displaystyle Z}
1436:{\displaystyle Z}
1382:
1380:
1362:
1349:
1298:
1010:
826:
774:
690:(N) < t < t
667:(N) < t < t
231:receives message
136:and one receiver
109:Signalling theory
78:coordination game
3078:
3040:Topological game
3035:No-win situation
2933:Thomas Schelling
2913:Robert B. Wilson
2873:Merrill M. Flood
2843:John von Neumann
2753:Ariel Rubinstein
2738:Albert W. Tucker
2589:War of attrition
2549:Matching pennies
2323:Pairing strategy
2185:Nash equilibrium
2108:Mechanism design
2073:Normal-form game
2028:Cooperative game
2001:
1994:
1987:
1978:
1977:
1973:
1954:
1926:
1916:
1880:
1870:
1860:
1829:
1811:
1802:(6): 1431–1451.
1779:
1778:
1776:
1775:
1766:. Archived from
1756:
1750:
1749:
1727:
1721:
1720:
1702:
1693:(6): 1431–1451.
1682:
1483:(see Figure 2).
1462:
1460:
1459:
1454:
1442:
1440:
1439:
1434:
1422:
1420:
1419:
1414:
1396:
1394:
1393:
1388:
1383:
1381:
1373:
1365:
1363:
1355:
1350:
1342:
1331:
1330:
1309:
1307:
1306:
1301:
1299:
1294:
1262:
1257:
1256:
1216:
1215:
1203:
1202:
1159:
1157:
1156:
1151:
1146:
1145:
1133:
1132:
1114:
1113:
1098:
1097:
1085:
1084:
1072:
1071:
1055:
1046:
1037:
1021:
1019:
1018:
1013:
1011:
1006:
1005:
1004:
992:
991:
975:
970:
969:
911:
909:
908:
903:
880:
879:
869:
868:
867:
857:
856:
855:
834:
825:
808:
807:
795:
794:
776:
775:
767:
761:
760:
660:
549:More generally:
490:Nash equilibrium
427:
425:
424:
419:
417:
416:
374:
373:
358:
356:
355:
350:
348:
347:
299:
298:
259:The decision of
36:Vincent Crawford
3086:
3085:
3081:
3080:
3079:
3077:
3076:
3075:
3056:
3055:
3054:
3049:
2983:
2969:max^n algorithm
2942:
2938:William Vickrey
2898:Reinhard Selten
2853:Kenneth Binmore
2768:David K. Levine
2763:Daniel Kahneman
2730:
2724:
2700:Negamax theorem
2690:Minimax theorem
2668:
2629:Diner's dilemma
2484:All-pay auction
2450:
2436:Stochastic game
2388:Mean-field game
2359:
2352:
2318:Markov strategy
2254:
2120:
2112:
2083:Sequential game
2068:Information set
2053:Game complexity
2023:Congestion game
2011:
2005:
1970:
1924:
1878:
1818:10.2307/1913390
1809:10.1.1.461.9770
1788:
1783:
1782:
1773:
1771:
1758:
1757:
1753:
1728:
1724:
1709:10.2307/1913390
1700:10.1.1.295.3462
1683:
1679:
1674:
1647:
1612:
1609:= 3/10 = 0.3, a
1608:
1604:
1596:
1592:
1588:
1584:
1569:
1565:
1557:
1553:
1549:
1534:
1526:
1522:
1448:
1445:
1444:
1428:
1425:
1424:
1402:
1399:
1398:
1372:
1364:
1354:
1341:
1326:
1322:
1320:
1317:
1316:
1263:
1261:
1252:
1248:
1211:
1207:
1198:
1194:
1192:
1189:
1188:
1175:
1141:
1137:
1122:
1118:
1109:
1105:
1093:
1089:
1080:
1076:
1067:
1063:
1061:
1058:
1057:
1053:
1048:
1044:
1039:
1035:
1030:
1027:
1000:
996:
981:
977:
976:
974:
965:
961:
959:
956:
955:
940:
933:
875:
871:
863:
859:
858:
845:
841:
840:
830:
815:
803:
799:
784:
780:
766:
765:
756:
752:
750:
747:
746:
737:
730:
721:, knowing that
715:
705:
701:
693:
689:
682:
674:
670:
666:
658:
655:
644:
640:
636:
628:
624:
620:
609:
605:
601:
586:
519:Nash equilibria
504:
492:
466:, meaning that
412:
408:
369:
365:
363:
360:
359:
343:
339:
294:
290:
288:
285:
284:
257:
225:
217:
210:
199:
192:
174:
146:
130:
125:
97:
70:
65:
17:
12:
11:
5:
3084:
3074:
3073:
3068:
3051:
3050:
3048:
3047:
3042:
3037:
3032:
3027:
3022:
3017:
3012:
3007:
3002:
2997:
2991:
2989:
2985:
2984:
2982:
2981:
2976:
2971:
2966:
2961:
2956:
2950:
2948:
2944:
2943:
2941:
2940:
2935:
2930:
2925:
2920:
2915:
2910:
2905:
2903:Robert Axelrod
2900:
2895:
2890:
2885:
2880:
2878:Olga Bondareva
2875:
2870:
2868:Melvin Dresher
2865:
2860:
2858:Leonid Hurwicz
2855:
2850:
2845:
2840:
2835:
2830:
2825:
2820:
2815:
2810:
2805:
2800:
2795:
2793:Harold W. Kuhn
2790:
2785:
2783:Drew Fudenberg
2780:
2775:
2773:David M. Kreps
2770:
2765:
2760:
2758:Claude Shannon
2755:
2750:
2745:
2740:
2734:
2732:
2726:
2725:
2723:
2722:
2717:
2712:
2707:
2702:
2697:
2695:Nash's theorem
2692:
2687:
2682:
2676:
2674:
2670:
2669:
2667:
2666:
2661:
2656:
2651:
2646:
2641:
2636:
2631:
2626:
2621:
2616:
2611:
2606:
2601:
2596:
2591:
2586:
2581:
2576:
2571:
2566:
2561:
2556:
2554:Ultimatum game
2551:
2546:
2541:
2536:
2534:Dollar auction
2531:
2526:
2521:
2519:Centipede game
2516:
2511:
2506:
2501:
2496:
2491:
2486:
2481:
2476:
2474:Infinite chess
2471:
2466:
2460:
2458:
2452:
2451:
2449:
2448:
2443:
2441:Symmetric game
2438:
2433:
2428:
2426:Signaling game
2423:
2421:Screening game
2418:
2413:
2411:Potential game
2408:
2403:
2398:
2390:
2385:
2380:
2375:
2370:
2364:
2362:
2354:
2353:
2351:
2350:
2345:
2340:
2338:Mixed strategy
2335:
2330:
2325:
2320:
2315:
2310:
2305:
2300:
2295:
2290:
2285:
2280:
2275:
2270:
2264:
2262:
2256:
2255:
2253:
2252:
2247:
2242:
2237:
2232:
2227:
2222:
2217:
2215:Risk dominance
2212:
2207:
2202:
2197:
2192:
2187:
2182:
2177:
2172:
2167:
2162:
2157:
2152:
2147:
2142:
2137:
2132:
2126:
2124:
2114:
2113:
2111:
2110:
2105:
2100:
2095:
2090:
2085:
2080:
2075:
2070:
2065:
2060:
2058:Graphical game
2055:
2050:
2045:
2040:
2035:
2030:
2025:
2019:
2017:
2013:
2012:
2004:
2003:
1996:
1989:
1981:
1975:
1974:
1968:
1955:
1943:10.1086/342451
1937:(3): 407–428.
1917:
1891:(3): 379–396.
1871:
1851:(3): 103–118.
1830:
1787:
1784:
1781:
1780:
1751:
1722:
1676:
1675:
1673:
1670:
1669:
1668:
1666:Signaling game
1663:
1661:Screening game
1658:
1653:
1646:
1643:
1637:With a higher
1610:
1606:
1602:
1594:
1590:
1586:
1582:
1567:
1566:= 1/5 = 0.2, a
1563:
1555:
1554:= 2/5 = 0.4, t
1551:
1547:
1532:
1524:
1520:
1452:
1432:
1412:
1409:
1406:
1386:
1379:
1376:
1371:
1368:
1361:
1358:
1353:
1348:
1345:
1340:
1337:
1334:
1329:
1325:
1297:
1293:
1290:
1287:
1284:
1281:
1278:
1275:
1272:
1269:
1266:
1260:
1255:
1251:
1246:
1243:
1240:
1237:
1234:
1231:
1228:
1225:
1222:
1219:
1214:
1210:
1206:
1201:
1197:
1181:→ Practically:
1173:
1149:
1144:
1140:
1136:
1131:
1128:
1125:
1121:
1117:
1112:
1108:
1104:
1101:
1096:
1092:
1088:
1083:
1079:
1075:
1070:
1066:
1051:
1042:
1033:
1026:
1023:
1009:
1003:
999:
995:
990:
987:
984:
980:
973:
968:
964:
938:
931:
901:
898:
895:
892:
889:
886:
883:
878:
874:
866:
862:
854:
851:
848:
844:
839:
833:
829:
824:
821:
818:
814:
811:
806:
802:
798:
793:
790:
787:
783:
779:
773:
770:
764:
759:
755:
735:
728:
713:
703:
699:
691:
687:
681:
678:
672:
668:
664:
653:
642:
638:
634:
626:
622:
618:
607:
603:
599:
585:
582:
581:
580:
573:
572:; and moreover
566:
543:
542:
536:
530:
503:
500:
491:
488:
415:
411:
407:
404:
401:
398:
395:
392:
389:
386:
383:
380:
377:
372:
368:
346:
342:
338:
335:
332:
329:
326:
323:
320:
317:
314:
311:
308:
305:
302:
297:
293:
256:
253:
224:
221:
215:
208:
197:
190:
173:
170:
160:does not know
145:
142:
129:
126:
124:
121:
96:
93:
69:
66:
64:
61:
57:
56:
53:
50:
15:
9:
6:
4:
3:
2:
3083:
3072:
3069:
3067:
3064:
3063:
3061:
3046:
3043:
3041:
3038:
3036:
3033:
3031:
3028:
3026:
3023:
3021:
3018:
3016:
3013:
3011:
3008:
3006:
3003:
3001:
2998:
2996:
2993:
2992:
2990:
2988:Miscellaneous
2986:
2980:
2977:
2975:
2972:
2970:
2967:
2965:
2962:
2960:
2957:
2955:
2952:
2951:
2949:
2945:
2939:
2936:
2934:
2931:
2929:
2926:
2924:
2923:Samuel Bowles
2921:
2919:
2918:Roger Myerson
2916:
2914:
2911:
2909:
2908:Robert Aumann
2906:
2904:
2901:
2899:
2896:
2894:
2891:
2889:
2886:
2884:
2881:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2863:Lloyd Shapley
2861:
2859:
2856:
2854:
2851:
2849:
2848:Kenneth Arrow
2846:
2844:
2841:
2839:
2836:
2834:
2831:
2829:
2828:John Harsanyi
2826:
2824:
2821:
2819:
2816:
2814:
2811:
2809:
2806:
2804:
2801:
2799:
2798:Herbert Simon
2796:
2794:
2791:
2789:
2786:
2784:
2781:
2779:
2776:
2774:
2771:
2769:
2766:
2764:
2761:
2759:
2756:
2754:
2751:
2749:
2746:
2744:
2741:
2739:
2736:
2735:
2733:
2727:
2721:
2718:
2716:
2713:
2711:
2708:
2706:
2703:
2701:
2698:
2696:
2693:
2691:
2688:
2686:
2683:
2681:
2678:
2677:
2675:
2671:
2665:
2662:
2660:
2657:
2655:
2652:
2650:
2647:
2645:
2642:
2640:
2637:
2635:
2632:
2630:
2627:
2625:
2622:
2620:
2617:
2615:
2612:
2610:
2607:
2605:
2602:
2600:
2599:Fair division
2597:
2595:
2592:
2590:
2587:
2585:
2582:
2580:
2577:
2575:
2574:Dictator game
2572:
2570:
2567:
2565:
2562:
2560:
2557:
2555:
2552:
2550:
2547:
2545:
2542:
2540:
2537:
2535:
2532:
2530:
2527:
2525:
2522:
2520:
2517:
2515:
2512:
2510:
2507:
2505:
2502:
2500:
2497:
2495:
2492:
2490:
2487:
2485:
2482:
2480:
2477:
2475:
2472:
2470:
2467:
2465:
2462:
2461:
2459:
2457:
2453:
2447:
2446:Zero-sum game
2444:
2442:
2439:
2437:
2434:
2432:
2429:
2427:
2424:
2422:
2419:
2417:
2416:Repeated game
2414:
2412:
2409:
2407:
2404:
2402:
2399:
2397:
2395:
2391:
2389:
2386:
2384:
2381:
2379:
2376:
2374:
2371:
2369:
2366:
2365:
2363:
2361:
2355:
2349:
2346:
2344:
2341:
2339:
2336:
2334:
2333:Pure strategy
2331:
2329:
2326:
2324:
2321:
2319:
2316:
2314:
2311:
2309:
2306:
2304:
2301:
2299:
2296:
2294:
2293:De-escalation
2291:
2289:
2286:
2284:
2281:
2279:
2276:
2274:
2271:
2269:
2266:
2265:
2263:
2261:
2257:
2251:
2248:
2246:
2243:
2241:
2238:
2236:
2235:Shapley value
2233:
2231:
2228:
2226:
2223:
2221:
2218:
2216:
2213:
2211:
2208:
2206:
2203:
2201:
2198:
2196:
2193:
2191:
2188:
2186:
2183:
2181:
2178:
2176:
2173:
2171:
2168:
2166:
2163:
2161:
2158:
2156:
2153:
2151:
2148:
2146:
2143:
2141:
2138:
2136:
2133:
2131:
2128:
2127:
2125:
2123:
2119:
2115:
2109:
2106:
2104:
2103:Succinct game
2101:
2099:
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:
2020:
2018:
2014:
2010:
2002:
1997:
1995:
1990:
1988:
1983:
1982:
1979:
1971:
1969:0-521-82651-9
1965:
1961:
1956:
1952:
1948:
1944:
1940:
1936:
1932:
1931:
1923:
1918:
1914:
1910:
1906:
1902:
1898:
1894:
1890:
1886:
1885:
1877:
1872:
1868:
1864:
1859:
1854:
1850:
1846:
1845:
1840:
1836:
1833:Farrell, J.;
1831:
1827:
1823:
1819:
1815:
1810:
1805:
1801:
1797:
1796:
1790:
1789:
1770:on 2005-03-04
1769:
1765:
1763:
1755:
1747:
1743:
1739:
1735:
1734:
1726:
1718:
1714:
1710:
1706:
1701:
1696:
1692:
1688:
1681:
1677:
1667:
1664:
1662:
1659:
1657:
1654:
1652:
1649:
1648:
1642:
1640:
1635:
1633:
1629:
1625:
1622:, we get the
1621:
1616:
1614:
1598:
1579:
1578:
1573:
1571:
1559:
1544:
1543:
1538:
1536:
1528:
1516:
1515:
1508:
1504:
1500:
1496:
1492:
1488:
1484:
1482:
1478:
1474:
1470:
1466:
1450:
1430:
1407:
1377:
1374:
1369:
1366:
1359:
1356:
1351:
1346:
1343:
1338:
1332:
1327:
1323:
1314:
1310:
1295:
1288:
1285:
1282:
1276:
1273:
1270:
1267:
1264:
1258:
1253:
1249:
1241:
1238:
1235:
1229:
1226:
1223:
1220:
1217:
1212:
1208:
1204:
1199:
1195:
1186:
1182:
1178:
1176:
1169:
1164:
1163:
1142:
1138:
1134:
1129:
1126:
1123:
1119:
1110:
1106:
1102:
1094:
1090:
1086:
1081:
1077:
1068:
1064:
1054:
1045:
1036:
1022:
1007:
1001:
997:
993:
988:
985:
982:
978:
971:
966:
962:
953:
949:
946:wants action
945:
941:
934:
927:
923:
918:
917:
912:
899:
896:
890:
887:
884:
876:
872:
864:
860:
852:
849:
846:
842:
837:
831:
812:
804:
800:
796:
791:
788:
785:
781:
768:
762:
757:
753:
744:
742:
738:
731:
724:
720:
716:
708:
706:
695:
677:
675:
671:(N), ÎĽ(t) = m
657:
648:
646:
630:
613:
611:
595:
591:
578:
574:
571:
567:
564:
560:
556:
553:There exists
552:
551:
550:
547:
540:
537:
534:
531:
528:
524:
523:
522:
520:
512:
508:
499:
497:
487:
485:
481:
477:
473:
469:
465:
461:
457:
453:
449:
445:
441:
437:
433:
428:
413:
405:
402:
399:
393:
390:
384:
381:
378:
370:
366:
344:
336:
333:
330:
327:
324:
318:
315:
309:
306:
303:
295:
291:
282:
278:
274:
270:
266:
262:
252:
250:
246:
242:
238:
234:
230:
220:
218:
211:
202:
200:
193:
186:
182:
178:
169:
167:
163:
159:
155:
151:
141:
139:
135:
120:
118:
114:
110:
106:
102:
92:
90:
85:
83:
79:
75:
60:
54:
51:
48:
47:
46:
43:
41:
37:
32:
30:
26:
22:
2893:Peyton Young
2888:Paul Milgrom
2803:Hervé Moulin
2743:Amos Tversky
2685:Folk theorem
2396:-player game
2393:
2313:Grim trigger
2287:
1959:
1934:
1928:
1888:
1882:
1848:
1842:
1839:"Cheap Talk"
1799:
1795:Econometrica
1793:
1772:. Retrieved
1768:the original
1761:
1754:
1740:(1): 34–39.
1737:
1731:
1725:
1690:
1687:Econometrica
1686:
1680:
1638:
1636:
1631:
1627:
1623:
1619:
1617:
1600:
1580:
1576:
1575:
1574:
1570:= 7/10 = 0.7
1561:
1545:
1541:
1540:
1539:
1530:
1518:
1513:
1512:
1511:
1506:
1502:
1498:
1494:
1490:
1480:
1476:
1472:
1468:
1464:
1312:
1311:
1184:
1180:
1179:
1171:
1167:
1165:
1161:
1049:
1040:
1031:
1028:
951:
947:
943:
936:
929:
925:
921:
919:
915:
913:
745:
740:
733:
726:
722:
718:
711:
709:
697:
685:
683:
662:
651:
649:
632:
616:
614:
597:
593:
589:
587:
576:
569:
562:
558:
554:
548:
544:
538:
532:
526:
516:
510:
495:
493:
483:
479:
475:
471:
467:
463:
459:
455:
451:
447:
443:
442:. Parameter
439:
435:
431:
429:
280:
276:
272:
268:
264:
260:
258:
248:
244:
241:Bayes's rule
236:
232:
228:
226:
213:
206:
203:
195:
188:
184:
180:
176:
175:
165:
161:
157:
153:
149:
147:
137:
133:
131:
113:Brian Skyrms
98:
86:
71:
63:Applications
58:
44:
33:
24:
18:
3066:Game theory
3010:Coopetition
2813:Jean Tirole
2808:John Conway
2788:Eric Maskin
2584:Blotto game
2569:Pirate game
2378:Global game
2348:Tit for tat
2278:Bid shading
2268:Appeasement
2118:Equilibrium
2098:Solved game
2033:Determinacy
2016:Definitions
2009:game theory
1651:Game theory
1535:= 1/2 = 0.5
928:is between
924:knows that
920:Given that
725:is between
606:, . . . , m
156:. Receiver
68:Game theory
21:game theory
3060:Categories
2654:Trust game
2639:Kuhn poker
2303:Escalation
2298:Deterrence
2288:Cheap talk
2260:Strategies
2078:Preference
2007:Topics of
1786:References
1774:2005-03-17
1577:N = N = 3:
1162:1 ≤ i≤ N-1
698:α(t) = α(m
637:(N) < t
625:(N). . . t
533:Separating
183:. Message
40:Joel Sobel
29:signalling
25:cheap talk
2838:John Nash
2544:Stag hunt
2283:Collusion
1835:Rabin, M.
1804:CiteSeerX
1695:CiteSeerX
1605:= 1/15, a
1593:= 7/15, t
1589:= 2/15, t
1491:Figure 2:
1411:⟩
1405:⟨
1385:⟩
1339:−
1336:⟨
1328:∗
1286:−
1268:−
1239:−
986:−
850:−
838:∫
789:−
772:¯
563:1 ≤ N ≤ N
511:Figure 1:
464:a = t + b
403:−
394:−
334:−
328:−
319:−
227:Receiver
2979:Lazy SMP
2673:Theorems
2624:Deadlock
2479:Checkers
2360:of games
2122:concepts
1951:15843361
1837:(1996).
1645:See also
1624:coarsest
1495:b = 1/20
1465:b = 1/20
1170:and the
584:Messages
579:actions.
555:N > 0
539:Babbling
474:. Since
472:b > 0
2731:figures
2514:Chicken
2368:Auction
2358:Classes
1913:2395377
1893:Bibcode
1867:2138522
1826:1913390
1746:2555533
1717:1913390
1613:= 11/15
1467:. Then
680:Actions
645:(N) = 1
502:Theorem
255:Utility
172:Message
148:Sender
128:Setting
101:biology
1966:
1949:
1911:
1865:
1824:
1806:
1744:
1715:
1697:
1585:= 0, t
1550:= 0, t
1542:N = 2:
1523:= 0, t
1514:N = 1:
1505:, and
1497:, for
1397:where
621:(N), t
223:Action
2469:Chess
2456:Games
1947:S2CID
1925:(PDF)
1879:(PDF)
1863:JSTOR
1822:JSTOR
1742:JSTOR
1713:JSTOR
1672:Notes
1632:finer
1628:N = 3
1620:N = 1
1618:With
1479:, or
1469:N = 3
1032:t = t
702:) = a
659:'
633:0 = t
561:with
456:a = t
440:b ≠0
82:Rabin
2145:Core
1964:ISBN
1909:PMID
935:and
732:and
650:The
629:(N))
590:ÎĽ(t)
434:and
279:and
212:and
194:and
144:Type
38:and
2729:Key
1939:doi
1901:doi
1889:144
1853:doi
1814:doi
1705:doi
1597:= 1
1572:.
1558:= 1
1527:= 1
1499:N=1
1473:N=1
1047:or
1043:i-1
1029:At
932:i-1
828:max
694:(N)
688:i-1
665:i-1
656:(N)
602:, m
219:".
19:In
3062::
2464:Go
1945:.
1935:69
1933:.
1927:.
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