150:” (Fig.5), which represents the following scenario. Two hunters can choose to either hunt a stag together (which provides the most economically efficient outcome) or they can individually hunt a Rabbit. Hunting Stags is challenging and requires cooperation. If the two hunters do not cooperate the chances of success is minimal. Thus, the scenario where both hunters choose to coordinate will provide the most beneficial output for society. A common problem associated with the stag hunt is the amount of trust required to achieve this output. Fig. 5 shows a situation in which both players (hunters) can benefit if they cooperate (hunting a stag). As you can see, cooperation might fail, because each hunter has an alternative which is safer because it does not require cooperation to succeed (hunting a hare). This example of the potential conflict between safety and social cooperation is originally due to
483:, where one player's incentive is to coordinate while the other player tries to avoid this. Discoordination games have no pure Nash equilibria. In Figure 1, choosing payoffs so that A > B, C < D, while a < b, c > d, creates a discoordination game. In each of the four possible states either player 1 or player 2 are better off by switching their strategy, so the only Nash equilibrium is mixed. The canonical example of a discoordination game is the
221:(or conflicting interest coordination), as seen in Fig. 4. In this game both players prefer engaging in the same activity over going alone, but their preferences differ over which activity they should engage in. Assume that a couple argues over what to do on the weekend. Both know that they will increase their utility by spending the weekend together, however the man prefers to watch a football game and the woman prefers to go shopping.
108:
player 1 thinks their payoff would fall from 2 to 1 if they deviated to Up, and player 2 thinks their payoff would fall from 4 to 3 if they chose Left. A player's optimal move depends on what they expect the other player to do, and they both do better if they coordinate than if they played an off-equilibrium combination of actions. This setup can be extended to more than two strategies or two players.
460:. While 101 is shorter, 280 is considered more scenic, so drivers might have different preferences between the two independent of the traffic flow. But each additional car on either route will slightly increase the drive time on that route, so additional traffic creates negative network externalities, and even scenery-minded drivers might opt to take 101 if 280 becomes too crowded. A
271:. In the generic coordination game above, a mixed Nash equilibrium is given by probabilities p = (d-b)/(a+d-b-c) to play Up and 1-p to play Down for player 1, and q = (D-C)/(A+D-B-C) to play Left and 1-q to play Right for player 2. Since d > b and d-b < a+d-b-c, p is always between zero and one, so existence is assured (similarly for q).
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number of errors accumulated by their worst performing team member. Players also had the option to purchase more time, the cost of doing so was subtracted from their payoff. While groups initially failed to coordinate, researchers observed about 80% of the groups in the experiment coordinated successfully when the game was repeated.
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rather than payoff dominance. Even when payoffs are better when players coordinate on one equilibrium, many times people will choose the less risky option where they are guaranteed some payoff and end up at an equilibrium that has sub-optimal payoff. Players are more likely to fail to coordinate on a
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analogues b > d and c > a for column-player 2). {Down, Left} and {Up, Right} are the two pure Nash equilibria. Chicken also requires that A > C, so a change from {Up, Left} to {Up, Right} improves player 2's payoff but reduces player 1's payoff, introducing conflict. This counters
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Games like the driving example above have illustrated the need for solution to coordination problems. Often we are confronted with circumstances where we must solve coordination problems without the ability to communicate with our partner. Many authors have suggested that particular equilibria are
145:
An assurance game describes the situation where neither player can offer a sufficient amount if they contribute alone, thus player 1 should defect from playing if player 2 defects. However, if Player 2 opts to contribute then player 1 should contribute also. An assurance game is commonly referred to
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was a weak-link experiment in which groups of individuals were asked to count and sort coins in an effort to measure the difference between individual and group incentives. Players in this experiment received a payoff based on their individual performance as well as a bonus that was weighted by the
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A typical case for a coordination game is choosing the sides of the road upon which to drive, a social standard which can save lives if it is widely adhered to. In a simplified example, assume that two drivers meet on a narrow dirt road. Both have to swerve in order to avoid a head-on collision. If
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Both (Up, Left) and (Down, Right) are Nash equilibria. If the players expect (Up, Left) to be played, then player 1 thinks their payoff would fall from 2 to 1 if they deviated to Down, and player 2 thinks their payoff would fall from 4 to 3 if they chose Right. If the players expect (Down, Right),
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Since the couple want to spend time together, they will derive no utility by doing an activity separately. If they go shopping, or to football game one person will derive some utility by being with the other person, but won’t derive utility from the activity itself. Unlike the other forms of
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in Fig. 2, successful passing is represented by a payoff of 8, and a collision by a payoff of 0. In this case there are two pure Nash equilibria: either both swerve to the left, or both swerve to the right. In this example, it doesn't matter
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244:) is a typical solution to a coordination problem. The choice of a voluntary standard tends to be stable in situations in which all parties can realize mutual gains, but only by making mutually consistent decisions.
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riskier option when the difference between taking the risk or the safe option is smaller. The laboratory results suggest that coordination failure is a common phenomenon in the setting of order-statistic games and
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as other agents. Conversely, game theorists have modeled behavior under negative externalities where choosing the same action creates a cost rather than a benefit. The generic term for this class of game is
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coordination games described previously, knowing your opponent’s strategy won’t help you decide on your course of action. Due to this there is a possibility that an equilibrium will not be reached.
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The pure Nash equilibria are the points in the bottom left and top right corners of the strategy space, while the mixed Nash equilibrium lies in the middle, at the intersection of the dashed lines.
38:. It describes the situation where a player will earn a higher payoff when they select the same course of action as another player. The game is not one of pure conflict, which results in multiple
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333:(ESS). The mixed Nash equilibrium is also Pareto dominated by the two pure Nash equilibria (since the players will fail to coordinate with non-zero probability), a quandary that led
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749:
Devetag, Giovanna; Ortmann, Andreas (2006-08-15). "When and Why? A Critical Survey on
Coordination Failure in the Laboratory". Rochester, NY: Social Science Research Network.
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Devetag, Giovanna; Ortmann, Andreas (2006-08-15). "When and Why? A Critical Survey on
Coordination Failure in the Laboratory". Rochester, NY: Social Science Research Network.
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over the number of other players choosing the same strategy (i.e., a game with negative network externalities). For instance, a driver could take
428:). Using the payoff matrix in Figure 1, a game is an anti-coordination game if B > A and C > D for row-player 1 (with
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both execute the same swerving maneuver they will manage to pass each other, but if they choose differing maneuvers they will collide. In the
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is a game where the only objective for all players is to be part of smaller of two groups. A well-known example of the minority game is the
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to play A and 1-q to play B for player 2. If we look at Fig 1. and apply the same probability equations we obtain the following results:
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366:. Sometimes these refinements conflict, which makes certain coordination games especially complicated and interesting (e.g. the
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the standard coordination game setup, where all unilateral changes in a strategy lead to either mutual gain or mutual loss.
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Coordination games have been studied in laboratory experiments. One such experiment by
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for 2x2 coordination games. Nash equilibria are at points where the two players' correspondences cross.
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In the generic coordination game in Fig. 6, a mixed Nash equilibrium is given by the probabilities:
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The concept of anti-coordination games has been extended to multi-player situation. A
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Thinking
Strategically: The Competitive Edge in Business, Politics, and Everyday Life
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When academics talk about coordination failure, most cases are that subjects achieve
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in which players choose matching strategies. Figure 1 shows a 2-player example.
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side both players pick, as long as they both pick the same. Both solutions are
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420:. The best-known example of a 2-player anti-coordination game is the game of
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focal for one reason or another. For instance, some equilibria may give
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Bortolotti, Stefania; Devetag, Giovanna; Ortmann, Andreas (2016-01-01).
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Bortolotti, Stefania; Devetag, Giovanna; Ortmann, Andreas (2016-01-01).
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This is different in another type of coordination game commonly called
370:, in which {Stag,Stag} has higher payoffs, but {Hare,Hare} is safer).
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99: Figure 1: Payoffs for a Coordination Game (Player 1, Player 2)
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Coordination games are closely linked to the economic concept of
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Unlike the pure Nash equilibria, the mixed equilibrium is not an
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891:, Cambridge, Massachusetts: Harvard University Press, 1960 (
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to play Option A and 1-p to play Option B for player 1, and
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836:, Princeton, New Jersey: Princeton University Press, 1992 (
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A hybrid form of coordination and anti-coordination is the
615:"Definition of Coordination Game | Higher Rock Education"
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In contrast, an obligation standard (enforced by law as "
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136:. This is not true for all coordination games, as the
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659:"Game theory II: Battle of the sexes | Policonomics"
639:"Game theory II: Battle of the sexes | Policonomics"
440:is defined as a game where each player's payoff is
237:, a voluntary standard (when characterized also as
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311:for 2Ă—2 coordination games are shown in Fig. 7.
797:, Cambridge: Cambridge University Press, 1998 (
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34:is a type of simultaneous game found in
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345:Coordination and equilibrium selection
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27:Simultaneous game found in game theory
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464:is a crowding game in networks. The
591:"Assurance game - Game Theory .net"
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1026:First-player and second-player win
922:review of 'The Emergence of Norms'
834:Game Theory for Applied Economists
25:
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852:Convention: A Philosophical Study
567:"Assurance Game - P2P Foundation"
301:p = (4-3) / (4+4-3-3) = ½ and,
1133:Coalition-proof Nash equilibrium
512:Coordination failure (economics)
252:standard") is a solution to the
337:to propose the refinement of a
260:Mixed strategy Nash equilibrium
1143:Evolutionarily stable strategy
936:Journal of Economic Psychology
907:Micromotives and Macrobehavior
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716:Journal of Economic Psychology
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681:Edna Ullmann-Margalit (1977).
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409:positive network externalities
399:Other games with externalities
331:evolutionarily stable strategy
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1071:Simultaneous action selection
854:, Oxford: Blackwell, 1969 (
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264:Coordination games also have
2003:List of games in game theory
1183:Quantal response equilibrium
1173:Perfect Bayesian equilibrium
1108:Bayes correlated equilibrium
786:Other suggested literature:
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1472:Optional prisoner's dilemma
1203:Self-confirming equilibrium
689:. Oxford University Press.
619:www.higherrockeducation.org
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304:q = (2-1) / (2+2-1-1) = ½
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1937:Principal variation search
1653:Aumann's agreement theorem
1316:Strategy-stealing argument
1228:Trembling hand equilibrium
1158:Markov perfect equilibrium
1153:Mertens-stable equilibrium
909:, New York: Norton, 1978 (
821:, New York: Norton, 1991 (
728:10.1016/j.joep.2016.05.004
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1973:Combinatorial game theory
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1113:Bayesian Nash equilibrium
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1988:Evolutionary game theory
1721:Antoine Augustin Cournot
1607:Guess 2/3 of the average
1404:Strictly determined game
1198:Satisfaction equilibrium
1016:Escalation of commitment
889:The Strategy of Conflict
865:Martin J. Osborne &
527:Self-fulfilling prophecy
309:reaction correspondences
130:. This game is called a
1993:Glossary of game theory
1592:Stackelberg competition
1218:Strong Nash equilibrium
925:(subscription required)
871:A Course in Game Theory
320:Reaction correspondence
2018:Tragedy of the commons
1998:List of game theorists
1978:Confrontation analysis
1688:Sprague–Grundy theorem
1208:Sequential equilibrium
1128:Correlated equilibrium
770:Cite journal requires
685:The Emergence of Norms
571:wiki.p2pfoundation.net
418:anti-coordination game
356:naturally more salient
339:correlated equilibrium
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133:pure coordination game
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1791:Jean-François Mertens
532:Strategic complements
517:Equilibrium selection
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295:q = (D-C)/(A+D-B-C),
289:p = (d-b)/(a+d-b-c),
277:
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152:Jean-Jacques Rousseau
1920:Search optimizations
1796:Jennifer Tour Chayes
1683:Revelation principle
1678:Purification theorem
1617:Nash bargaining game
1582:Bertrand competition
1567:El Farol Bar problem
1532:Electronic mail game
1497:Lewis signaling game
1041:Hierarchy of beliefs
522:Non-cooperative game
481:discoordination game
470:El Farol Bar problem
407:, and in particular
374:Experimental results
18:Coordination problem
1968:Bounded rationality
1587:Cournot competition
1537:Rock paper scissors
1512:Battle of the sexes
1502:Volunteer's dilemma
1374:Perfect information
1301:Dominant strategies
1138:Epsilon-equilibrium
1021:Extensive-form game
848:David Kellogg Lewis
229:Voluntary standards
219:battle of the sexes
195:Battle of the Sexes
1947:Paranoid algorithm
1927:Alpha–beta pruning
1806:John Maynard Smith
1637:Rendezvous problem
1477:Traveler's dilemma
1467:Gift-exchange game
1462:Prisoner's dilemma
1379:Large Poisson game
1346:Bargaining problem
1251:Backward induction
1223:Subgame perfection
1178:Proper equilibrium
795:Coordination Games
595:www.gametheory.net
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254:prisoner's problem
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142:in Fig. 3 shows.
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1932:Aspiration window
1901:Suzanne Scotchmer
1856:Oskar Morgenstern
1751:Donald B. Gillies
1693:Zermelo's theorem
1622:Induction puzzles
1577:Fair cake-cutting
1552:Public goods game
1482:Coordination game
1356:Intransitive game
1286:Forward induction
1168:Pareto efficiency
1148:Gibbs equilibrium
1118:Berge equilibrium
1066:Simultaneous game
696:978-0-19-824411-0
497:Collective action
280:Coordination Game
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167:Pure Coordination
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32:coordination game
16:(Redirected from
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2013:Topological game
2008:No-win situation
1906:Thomas Schelling
1886:Robert B. Wilson
1846:Merrill M. Flood
1816:John von Neumann
1726:Ariel Rubinstein
1711:Albert W. Tucker
1562:War of attrition
1522:Matching pennies
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1086:Mechanism design
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1006:Cooperative game
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1028:
1023:
1018:
1013:
1008:
1003:
997:
995:
991:
990:
982:
981:
974:
967:
959:
953:
952:
949:
928:
920:Adrian Piper:
918:
900:
882:
863:
845:
830:
813:Barry Nalebuff
806:
791:Russell Cooper
782:
781:
772:|journal=
741:
702:
695:
670:
650:
630:
606:
582:
557:
556:
554:
551:
550:
549:
544:
539:
537:Social dilemma
534:
529:
524:
519:
514:
509:
504:
499:
492:
489:
450:Interstate 280
446:U.S. Route 101
442:non-increasing
426:Hawk-Dove game
400:
397:
388:risk dominance
375:
372:
352:higher payoffs
346:
343:
266:mixed strategy
261:
258:
230:
227:
213:
212:
199:
185:
184:
180:Assurance Game
171:
139:assurance game
113:
110:
103:
101:
100:
96:
95:
92:
91:
88:
87:
84:
81:
77:
76:
73:
70:
67:
63:
62:
59:
55:
54:
51:
26:
9:
6:
4:
3:
2:
2051:
2040:
2037:
2036:
2034:
2019:
2016:
2014:
2011:
2009:
2006:
2004:
2001:
1999:
1996:
1994:
1991:
1989:
1986:
1984:
1981:
1979:
1976:
1974:
1971:
1969:
1966:
1965:
1963:
1961:Miscellaneous
1959:
1953:
1950:
1948:
1945:
1943:
1940:
1938:
1935:
1933:
1930:
1928:
1925:
1924:
1922:
1918:
1912:
1909:
1907:
1904:
1902:
1899:
1897:
1896:Samuel Bowles
1894:
1892:
1891:Roger Myerson
1889:
1887:
1884:
1882:
1881:Robert Aumann
1879:
1877:
1874:
1872:
1869:
1867:
1864:
1862:
1859:
1857:
1854:
1852:
1849:
1847:
1844:
1842:
1839:
1837:
1836:Lloyd Shapley
1834:
1832:
1829:
1827:
1824:
1822:
1821:Kenneth Arrow
1819:
1817:
1814:
1812:
1809:
1807:
1804:
1802:
1801:John Harsanyi
1799:
1797:
1794:
1792:
1789:
1787:
1784:
1782:
1779:
1777:
1774:
1772:
1771:Herbert Simon
1769:
1767:
1764:
1762:
1759:
1757:
1754:
1752:
1749:
1747:
1744:
1742:
1739:
1737:
1734:
1732:
1729:
1727:
1724:
1722:
1719:
1717:
1714:
1712:
1709:
1708:
1706:
1700:
1694:
1691:
1689:
1686:
1684:
1681:
1679:
1676:
1674:
1671:
1669:
1666:
1664:
1661:
1659:
1656:
1654:
1651:
1650:
1648:
1644:
1638:
1635:
1633:
1630:
1628:
1625:
1623:
1620:
1618:
1615:
1613:
1610:
1608:
1605:
1603:
1600:
1598:
1595:
1593:
1590:
1588:
1585:
1583:
1580:
1578:
1575:
1573:
1572:Fair division
1570:
1568:
1565:
1563:
1560:
1558:
1555:
1553:
1550:
1548:
1547:Dictator game
1545:
1543:
1540:
1538:
1535:
1533:
1530:
1528:
1525:
1523:
1520:
1518:
1515:
1513:
1510:
1508:
1505:
1503:
1500:
1498:
1495:
1493:
1490:
1488:
1485:
1483:
1480:
1478:
1475:
1473:
1470:
1468:
1465:
1463:
1460:
1458:
1455:
1453:
1450:
1448:
1445:
1443:
1440:
1438:
1435:
1434:
1432:
1430:
1426:
1420:
1419:Zero-sum game
1417:
1415:
1412:
1410:
1407:
1405:
1402:
1400:
1397:
1395:
1392:
1390:
1389:Repeated game
1387:
1385:
1382:
1380:
1377:
1375:
1372:
1370:
1368:
1364:
1362:
1359:
1357:
1354:
1352:
1349:
1347:
1344:
1342:
1339:
1338:
1336:
1334:
1328:
1322:
1319:
1317:
1314:
1312:
1309:
1307:
1306:Pure strategy
1304:
1302:
1299:
1297:
1294:
1292:
1289:
1287:
1284:
1282:
1279:
1277:
1274:
1272:
1271:De-escalation
1269:
1267:
1264:
1262:
1259:
1257:
1254:
1252:
1249:
1247:
1244:
1243:
1241:
1239:
1235:
1229:
1226:
1224:
1221:
1219:
1216:
1214:
1213:Shapley value
1211:
1209:
1206:
1204:
1201:
1199:
1196:
1194:
1191:
1189:
1186:
1184:
1181:
1179:
1176:
1174:
1171:
1169:
1166:
1164:
1161:
1159:
1156:
1154:
1151:
1149:
1146:
1144:
1141:
1139:
1136:
1134:
1131:
1129:
1126:
1124:
1121:
1119:
1116:
1114:
1111:
1109:
1106:
1105:
1103:
1101:
1097:
1093:
1087:
1084:
1082:
1081:Succinct game
1079:
1077:
1074:
1072:
1069:
1067:
1064:
1062:
1059:
1057:
1054:
1052:
1049:
1047:
1044:
1042:
1039:
1037:
1034:
1032:
1029:
1027:
1024:
1022:
1019:
1017:
1014:
1012:
1009:
1007:
1004:
1002:
999:
998:
996:
992:
988:
980:
975:
973:
968:
966:
961:
960:
957:
950:
948:
945:
941:
937:
933:
929:
923:
919:
916:
915:0-393-32946-1
912:
908:
904:
901:
898:
897:0-674-84031-3
894:
890:
886:
883:
880:
879:0-262-65040-1
876:
872:
868:
864:
861:
860:0-631-23257-5
857:
853:
849:
846:
843:
842:0-691-00395-5
839:
835:
831:
828:
827:0-393-32946-1
824:
820:
819:
814:
810:
809:Avinash Dixit
807:
804:
803:0-521-57896-5
800:
796:
792:
789:
788:
787:
777:
764:
756:
752:
745:
737:
733:
729:
725:
721:
717:
713:
706:
698:
692:
687:
686:
677:
675:
660:
654:
640:
634:
620:
616:
610:
596:
592:
586:
572:
568:
562:
558:
548:
545:
543:
540:
538:
535:
533:
530:
528:
525:
523:
520:
518:
515:
513:
510:
508:
505:
503:
500:
498:
495:
494:
488:
486:
482:
477:
475:
471:
467:
466:minority game
463:
459:
455:
454:San Francisco
451:
447:
443:
439:
438:crowding game
434:
431:
427:
423:
419:
414:
410:
406:
405:externalities
396:
394:
389:
384:
381:
371:
369:
365:
361:
357:
353:
342:
340:
336:
335:Robert Aumann
332:
327:
321:
316:
312:
310:
305:
302:
299:
296:
293:
290:
287:
281:
276:
272:
270:
267:
257:
255:
251:
250:
243:
241:
236:
226:
222:
220:
209:
204:
200:
196:
191:
187:
186:
181:
176:
172:
168:
163:
159:
158:
155:
153:
149:
143:
141:
140:
135:
134:
129:
125:
120:
119:payoff matrix
109:
102:
97:
93:
89:
85:
82:
78:
74:
71:
64:
60:
57:
56:
53:Player 2
49:
46:
44:
41:
40:pure strategy
37:
33:
19:
1866:Peyton Young
1861:Paul Milgrom
1776:Hervé Moulin
1716:Amos Tversky
1658:Folk theorem
1481:
1369:-player game
1366:
1291:Grim trigger
942:(C): 60–73.
939:
935:
906:
888:
870:
851:
833:
816:
794:
785:
763:cite journal
744:
722:(C): 60–73.
719:
715:
705:
684:
662:. Retrieved
653:
642:. Retrieved
633:
622:. Retrieved
618:
609:
598:. Retrieved
594:
585:
574:. Retrieved
570:
561:
542:Supermodular
480:
478:
472:proposed by
461:
437:
435:
417:
402:
385:
377:
362:, or may be
348:
328:
325:
306:
303:
300:
297:
294:
291:
288:
284:
279:
263:
247:
239:
232:
223:
216:
207:
194:
179:
166:
144:
137:
131:
123:
115:
106:
31:
29:
1983:Coopetition
1786:Jean Tirole
1781:John Conway
1761:Eric Maskin
1557:Blotto game
1542:Pirate game
1351:Global game
1321:Tit for tat
1256:Bid shading
1246:Appeasement
1096:Equilibrium
1076:Solved game
1011:Determinacy
994:Definitions
987:game theory
318:Figure 7 -
36:game theory
1627:Trust game
1612:Kuhn poker
1281:Escalation
1276:Deterrence
1266:Cheap talk
1238:Strategies
1056:Preference
985:Topics of
664:2021-04-23
644:2021-04-26
624:2021-04-23
600:2021-04-23
576:2021-04-23
553:References
1811:John Nash
1517:Stag hunt
1261:Collusion
947:0167-4870
736:0167-4870
430:lowercase
393:stag-hunt
368:Stag hunt
208:Stag Hunt
148:stag hunt
2033:Category
1952:Lazy SMP
1646:Theorems
1597:Deadlock
1452:Checkers
1333:of games
1100:concepts
491:See also
458:San Jose
242:standard
240:de facto
112:Examples
66:Player 1
1704:figures
1487:Chicken
1341:Auction
1331:Classes
422:Chicken
413:network
395:games.
278:Fig 6.
249:de jure
206:Fig. 5
193:Fig. 4
165:Fig. 2
913:
895:
877:
858:
840:
825:
811:&
801:
755:924186
753:
734:
693:
487:game.
178:Fig.3
146:as a “
1442:Chess
1429:Games
452:from
364:safer
354:, be
124:which
61:Right
1123:Core
944:ISSN
911:ISBN
893:ISBN
875:ISBN
856:ISBN
838:ISBN
823:ISBN
799:ISBN
776:help
751:SSRN
732:ISSN
691:ISBN
307:The
80:Down
58:Left
1702:Key
724:doi
456:to
448:or
233:In
86:2,4
83:1,3
75:1,3
72:2,4
2035::
1437:Go
940:56
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793::
767::
765:}}
761:{{
730:.
720:56
718:.
714:.
673:^
617:.
593:.
569:.
476:.
358:,
341:.
256:.
154:.
69:Up
30:A
1367:n
978:e
971:t
964:v
934:.
778:)
774:(
757:.
738:.
726::
699:.
667:.
647:.
627:.
603:.
579:.
20:)
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