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the potential outcomes. If B cooperates, A should choose betrayal, as serving 3 months is better than serving 1 year. Moreover, if B chooses betrayal, then A should also choose betrayal as serving 2 years is better than serving 3. The choice to cooperate clearly provides a better outcome for the two prisoners however from a perspective of self interest this option would be deemed irrational. The aforementioned both cooperating option features the least total time spent in prison, serving 2 years total. This total is significantly less than the Nash
Equilibrium total, where both cooperate, of 4 years. However, given the constraints that Prisoners A and B are individually motivated, they will always choose betrayal. They do so by selecting the best option for themselves while considering each possible decisions of the other prisoner.
99:, a widely played hand game, is an example of a simultaneous game. Both players make a decision without knowledge of the opponent's decision, and reveal their hands at the same time. There are two players in this game and each of them has three different strategies to make their decision; the combination of strategy profiles (a complete set of each player's possible strategies) forms a 3Ă3 table. We will display Player 1's strategies as rows and Player 2's strategies as columns. In the table, the numbers in red represent the payoff to Player 1, the numbers in blue represent the payoff to Player 2. Hence, the pay off for a 2 player game in rock-paper-scissors will look like this:
821:
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charges. The prosecution therefore simultaneously offers both prisoners a deal where they can choose to cooperate with one another by remaining silent, or they can choose betrayal, meaning they testify against their partner and receive a reduced sentence. It should be mentioned that the prisoners cannot communicate with one another. Therefore, resulting in the following payoff matrix:
839:
the other hand, each player is perfectly capable of hunting a hare alone. The resulting dilemma is that neither player can be sure of what the other will choose to do. Thus, providing the potential for a player to receive no payoff should they be the only party to choose to hunt a Stag. Therefore, resulting in the following payoff matrix:
634:
Two members of a criminal gang have been apprehended by the police. Both individuals now sit in solitary confinement. The prosecutors have the evidence required to put both prisoners away on lesser charges. However, they do not possess the evidence required to convict the prisoners on their principle
256:
Even though simultaneous games are typically represented in normal form, they can be represented using extensive form too. While in extensive form one playerâs decision must be draw before that of the other, by definition such representation does not correspond to the real life timing of the playersâ
92:
The most common representation of a simultaneous game is normal form (matrix form). For a 2 player game; one player selects a row and the other player selects a column at the exact same time. Traditionally, within a cell, the first entry is the payoff of the row player, the second entry is the payoff
838:
is a simultaneous game in which there are two players. The decision to be made is whether or not each player wishes to hunt a Stag or a Hare. Naturally hunting a Stag will provide greater utility in comparison to hunting a Hare. However, in order to hunt a Stag both players need to work together. On
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and often implies a notion of ethical consideration. A simultaneous game, for example, is said to reach Pareto optimality if there is no alternative outcome that can make at least one player better off while leaving all other players at least as well off. Therefore, these outcomes are referred to as
587:
move (strategy), as it maximises the minimum possible payoff. Thus, the player can be assured a payoff of at least the maximin value, regardless of how the others are playing. The player doesnât have the know the payoffs of the other players in order to choose the maximin move, therefore players can
551:
For simultaneous games, players will typically select mixed strategies while very occasionally choosing pure strategies. The reason for this is that in a game where players donât know what the other one will choose it is best to pick the option that is likely to give the you the greatest benefit for
292:
A town has two companies, A and B, who currently make $ 8,000,000 each and need to determine whether they should advertise. The table below shows the payoff patterns; the rows are options of A and the columns are options of B. The entries are payoffs for A and B, respectively, separated by a comma.
62:
if the game is simultaneous than if it is sequential because they have less information to act on at each step in the game. For example, in a two player continuous game that is sequential, the second player can act in response to the action taken by the first player. However, this is not possible in
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game, a wife and husband decide independently whether to go to a football game or the ballet. Each person likes to do something together with the other, but the husband prefers football and the wife prefers ballet. The two Nash equilibria, and therefore the best responses for both husband and wife,
706:
This game results in a clear dominant strategy of betrayal where the only strong Nash
Equilibrium is for both prisoners to confess. This is because we assume both prisoners to be rational and possessing no loyalty towards one another. Therefore, betrayal provides a greater reward for a majority of
280:
In a simultaneous game, players only have one move and all players' moves are made simultaneously. The number of players in a game must be stipulated and all possible moves for each player must be listed. Each player may have different roles and options for moves. However, each player has a finite
80:
Given that decision makers are rational, then so is individual rationality. An outcome is individually rational if it yields each player at least his security level. The security level for Player i is the amount max min Hi (s) that the player can guarantee themselves unilaterally, that is, without
75:
A simple example is rock-paper-scissors in which all players make their choice at the exact same time. However moving at exactly the same time isnât always taken literally, instead players may move without being able to see the choices of other players. A simple example is an election in which not
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is when no one can gain a higher payoff by deviating from their move, provided others stick with their original choices. Nash equilibria are self-enforcing contracts, in which negotiation happens prior to the game being played in which each player best sticks with their negotiated move. In a Nash
881:
The game is designed to illustrate a clear Pareto optimality where both players cooperate to hunt a Stag. However, due to the inherent risk of the game, such an outcome does not always come to fruition. It is imperative to note that Pareto optimality is not a strategic solution for simultaneous
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Some people always expect the worst and believe that others want to bring them down when in fact others want to maximise their payoffs. Still, nonetheless, player A will concentrate on their smallest possible payoff, believing this is what player A will get, they will choose the option with the
50:, which are played by the players taking turns (moves alternate between players). In other words, both players normally act at the same time in a simultaneous game. Even if the players do not act at the same time, both players are uninformed of each other's move while making their decisions.
71:
In sequential games, players observe what rivals have done in the past and there is a specific order of play. However, in simultaneous games, all players select strategies without observing the choices of their rivals and players choose at the exact same time.
783:
Simultaneous games are designed to inform strategic choices in competitive and non cooperative environments. However, is important to note that Nash equilibria and many of the aforementioned strategies generally fail to result in socially desirable outcomes.
93:
of the column player. The âcellâ that is chosen is the outcome of the game. To determine which "cell" is chosen, the payoffs for both the row player and the column player must be compared respectively. Each player is best off where their payoff is higher.
337:
A zero-sum game is when the sum of payoffs equals zero for any outcome i.e. the losers pay for the winners gains. For a zero-sum 2-player game the payoff of player A doesnât have to be displayed since it is the negative of the payoff of player B.
524:
All of the above examples have been symmetric. All players have the same options so if players interchange their moves, they also interchange their payoffs. By design, symmetric games are fair in which every player is given the same chances.
344:
Rockâpaperâscissors is being played by two friends, A and B for $ 10. The first cell stands for a payoff of 0 for both players. The second cell is a payoff of 10 for A which has to be paid by B, therefore a payoff of -10 for B.
570:
Firstly, identify any dominant strategies for all players. If each player has a dominant strategy, then players will play that strategy however if there is more than one dominant strategy then any of them are possible.
257:
decisions in a simultaneous game. The key to modeling simultaneous games in the extensive form is to get the information sets right. A dashed line between nodes in extensive form representation of a game represents
433:
A classroom vote is held as to whether or not they should have an increased amount of free time. Player A selects the matrix, player B selects the row, and player C selects the column. The payoffs are:
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Secondly, if there arenât any dominant strategies, identify all strategies dominated by other strategies. Then eliminate the dominated strategies and the remaining are strategies players will play.
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provides a player with the highest possible payoff for any strategy of the other players. In simultaneous games, the best move a player can make is to follow their dominant strategy, if one exists.
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544:
are those in which players pick only one strategy from their best response. A Pure
Strategy determines all your possible moves in a game, it is a complete plan for a player in a given game.
265:
1281:
Munoz-Garcia, F. and Toro-Gonzalez, D., 2016. Pure
Strategy Nash Equilibrium and Simultaneous-Move Games with Complete Information. Strategy and Game Theory, pp.25-60. Available at: <
261:
and specifies that, during the game, a party cannot distinguish between the nodes, due to the party being unaware of the other party's decision (by definition of "simultaneous game").
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games. However, the ideal informs players about the potential for more efficient outcomes. Moreover, potentially providing insight into how players should learn to play over time.
1074:
1239:
Prisner, E., 2014. Game Theory
Through Examples. Mathematical Association of America Inc. Switzerland: The Mathematical Association of America, pp.25-30. Available at: <
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the lowest risk given the other player could choose anything i.e. if you pick your best option but the other player also picks their best option, someone will suffer.
253:). Information sets are used to emphasize the imperfect information. Although it is not simple, it is easier to use game trees for games with more than 2 players.
1073:
Sun, C., 2019. Simultaneous and
Sequential Choice in a Symmetric TwoâPlayer Game with CanyonâShaped Payoffs. Japanese Economic Review, Available at: <
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are for them to both pick the same leisure activity e.g. (ballet, ballet) or (football, football). The table below shows the payoff for each option:
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the concept refers to a state in which an economy has maximized efficiency in terms of resource allocation. Pareto
Efficiency is closely linked to
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1192:
1075:
https://www.researchgate.net/publication/332377544_Simultaneous_and_Sequential_Choice_in_a_Symmetric_Two-Player_Game_with_Canyon-Shaped_Payoffs
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are those in which players randomize strategies in their best responses set. These have associated probabilities with each set of strategies.
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is a game where each player chooses their action without knowledge of the actions chosen by other players. Simultaneous games contrast with
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In a simultaneous game, players will make their moves simultaneously, determine the outcome of the game and receive their payoffs.
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Game theory should provide players with advice on how to find which move is best. These are known as âBest
Responseâ strategies.
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1349:"Pareto-Optimality or Pareto-Efficiency: Same Concept, Different Names? An Analysis Over a Century of Economic Literature"
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1391:"In a Weakly Dominated Strategy Is Strength: Evolution of Optimality in Stag Hunt Augmented with a Punishment Option"
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all voters will vote literally at the same time but each voter will vote not knowing what anyone else has chosen.
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Some variants of chess that belong to this class of games include synchronous chess and parity chess.
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The Path to
Equilibrium in Sequential and Simultaneous Games (Brocas, Carrillo, Sachdeva; 2016).
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and is one of the most famous games in Game theory. The game is usually presented as follows:
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choose the maximin strategy in a simultaneous game regardless of what the other players choose.
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1438:"Achieving Socially Optimal Outcomes in Multiagent Systems with Reinforcement Social Learning"
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Ross, D., 2019. Game Theory. Stanford
Encyclopedia of Philosophy, pp.7-80. Available at: <
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Equilibrium, each player is best responded to the choices of the other player.
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Vernengo, Matias; Caldentey, Esteban Perez; Rosser Jr, Barkley J, eds. (2020).
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920:. Richards, Daniel Jay., Norman, George, 1946- (Fifth ed.). Hoboken, NJ.
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Industrial organization : contemporary theory and empirical applications
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Another common representation of a simultaneous game is extensive form (
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Prisoners of reason : game theory and neoliberal political economy
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The simultaneous game of rockâpaperâscissors modeled in extensive form
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1995:
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2010:
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Mailath, George J.; Samuelson, Larry; Swinkels, Jeroen M. (1993).
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1241:
https://www.maa.org/sites/default/files/pdf/ebooks/GTE_sample.pdf
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representations are usually used for simultaneous games. Given a
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2000:
1283:
https://link.springer.com/chapter/10.1007/978-3-319-32963-5_2
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a simultaneous game where both players act at the same time.
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986:. McGraw Hill Education (India) Private Limited. 2018.
1355:, Emerald Group Publishing Limited, pp. 129â145,
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An example of a simultaneous zero-sum 2-player game:
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ACM Transactions on Autonomous and Adaptive Systems
795:is a notion rooted in the theoretical construct of
1347:Berthonnet, IrĂšne; Delclite, Thomas (2014-10-10),
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1246:
1069:
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1065:
1266:
555:
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1062:
1016:"Extensive Form Reasoning in Normal Form Games"
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1261:https://plato.stanford.edu/entries/game-theory
1161:Strategy : an introduction to game theory
767:
1524:
1492:The Classified Encyclopedia of Chess Variants
1388:
1158:
1332:: CS1 maint: multiple names: authors list (
430:An example of a simultaneous 3-player game:
289:An example of a simultaneous 2-player game:
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952:) CS1 maint: multiple names: authors list (
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81:considering the actions of other players.
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281:number of options available to choose.
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1512:
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799:. Originating with Italian economist
725:
614:
480:
439:
30:is an example of a simultaneous game.
1436:Hao, Jianye; Leung, Ho-Fung (2013).
1154:
1152:
787:
567:When analyzing a simultaneous game:
1205:
916:Pepall, Lynne, 1952- (2014-01-28).
779:, Italian sociologist and economist
591:
577:
13:
1580:First-player and second-player win
1297:
1288:
583:highest value. This option is the
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66:
14:
2614:
1149:
84:
1687:Coalition-proof Nash equilibrium
1361:10.1108/s0743-415420140000032005
815:
507:B votes against extra free time
491:C votes against extra free time
481:A votes against extra free time
466:B votes against extra free time
450:C votes against extra free time
275:
1429:
1382:
1340:
984:Managerial Economics: 3 edition
812:socially desirable outcomes.
1697:Evolutionarily stable strategy
1304:. Cambridge University Press.
1199:
1080:
976:
964:
909:
556:Dominant vs Dominated Strategy
284:
58:, players will have different
1:
1625:Simultaneous action selection
1490:(2007). Beasley, John (ed.).
1389:Vanderschraaf, Peter (2016).
902:
897:Simultaneous action selection
2562:List of games in game theory
1737:Quantal response equilibrium
1727:Perfect Bayesian equilibrium
1662:Bayes correlated equilibrium
1163:(Third ed.). New York.
1159:Watson, Joel. (2013-05-09).
529:Strategies - The Best Choice
496:B votes for extra free time
488:C votes for extra free time
455:B votes for extra free time
447:C votes for extra free time
440:A votes for extra free time
7:
2031:Optional prisoner's dilemma
1757:Self-confirming equilibrium
885:
768:Socially Desirable Outcomes
10:
2619:
2496:Principal variation search
2212:Aumann's agreement theorem
1875:Strategy-stealing argument
1782:Trembling hand equilibrium
1712:Markov perfect equilibrium
1707:Mertens-stable equilibrium
1206:A V, Murali (2014-10-07).
119:
116:
113:
104:
15:
2532:Combinatorial game theory
2519:
2478:
2260:
2204:
2191:Princess and monster game
1986:
1888:
1790:
1742:Quasi-perfect equilibrium
1667:Bayesian Nash equilibrium
1648:
1547:
1099:10.1057/978-1-349-95121-5
740:
727:
2598:Game theory game classes
2547:Evolutionary game theory
2280:Antoine Augustin Cournot
2166:Guess 2/3 of the average
1963:Strictly determined game
1752:Satisfaction equilibrium
1570:Escalation of commitment
667:Prisoner A stays silent
649:Prisoner B stays silent
16:Not to be confused with
2552:Glossary of game theory
2151:Stackelberg competition
1772:Strong Nash equilibrium
1298:M., Amadae, S. (2016).
18:simultaneous exhibition
2577:Tragedy of the commons
2557:List of game theorists
2537:Confrontation analysis
2247:SpragueâGrundy theorem
1762:Sequential equilibrium
1682:Correlated equilibrium
971:http://www-bcf.usc.edu
827:
780:
611:
537:Pure vs Mixed Strategy
333:Two Players (zero sum)
269:
31:
2350:Jean-François Mertens
1395:Philosophy of Science
836:Jean-Jacques Rousseau
823:
807:which is an ideal of
775:
694:Prisoner A: 3 Months
682:Prisoner B: 3 Months
607:
426:Three or more Players
267:
259:information asymmetry
26:
2479:Search optimizations
2355:Jennifer Tour Chayes
2242:Revelation principle
2237:Purification theorem
2176:Nash bargaining game
2141:Bertrand competition
2126:El Farol Bar problem
2091:Electronic mail game
2056:Lewis signaling game
1595:Hierarchy of beliefs
700:Each serves 2 Years
696:Prisoner B: 3 Years
680:Prisoner A: 3 Years
320:A doesnât advertise
304:B doesnât advertise
2527:Bounded rationality
2146:Cournot competition
2096:Rock paper scissors
2071:Battle of the sexes
2061:Volunteer's dilemma
1933:Perfect information
1860:Dominant strategies
1692:Epsilon-equilibrium
1575:Extensive-form game
844:
797:perfect competition
717:battle of the sexes
711:Battle of the Sexes
688:Prisoner A Confess
677:Each serves 1 Year
659:Prisoner B Confess
97:Rockâpaperâscissors
28:Rockâpaperâscissors
2506:Paranoid algorithm
2486:Alphaâbeta pruning
2365:John Maynard Smith
2196:Rendezvous problem
2036:Traveler's dilemma
2026:Gift-exchange game
2021:Prisoner's dilemma
1938:Large Poisson game
1905:Bargaining problem
1805:Backward induction
1777:Subgame perfection
1732:Proper equilibrium
842:
828:
781:
621:prisonerâs dilemma
615:Prisoner's Dilemma
612:
270:
32:
2585:
2584:
2491:Aspiration window
2460:Suzanne Scotchmer
2415:Oskar Morgenstern
2310:Donald B. Gillies
2252:Zermelo's theorem
2181:Induction puzzles
2136:Fair cake-cutting
2111:Public goods game
2041:Coordination game
1915:Intransitive game
1840:Forward induction
1722:Pareto efficiency
1702:Gibbs equilibrium
1672:Berge equilibrium
1620:Simultaneous game
1501:978-0-9555168-0-1
1370:978-1-78441-154-1
1353:A Research Annual
1311:978-1-107-67119-5
1170:978-0-393-91838-0
1108:978-1-349-95121-5
993:978-93-87067-63-9
927:978-1-118-25030-3
879:
878:
809:Welfare Economics
805:Pareto Optimality
793:Pareto efficiency
788:Pareto Optimality
765:
764:
704:
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609:Prisoners dilemma
562:dominant strategy
517:
516:
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330:
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247:
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40:simultaneous game
2610:
2572:Topological game
2567:No-win situation
2465:Thomas Schelling
2445:Robert B. Wilson
2405:Merrill M. Flood
2375:John von Neumann
2285:Ariel Rubinstein
2270:Albert W. Tucker
2121:War of attrition
2081:Matching pennies
1855:Pairing strategy
1717:Nash equilibrium
1640:Mechanism design
1605:Normal-form game
1560:Cooperative game
1533:
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1494:. John Beasley.
1488:Pritchard, D. B.
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623:originated with
598:Nash Equilibrium
592:Nash Equilibrium
578:Maximin Strategy
546:Mixed strategies
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48:sequential games
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2608:
2607:
2588:
2587:
2586:
2581:
2515:
2501:max^n algorithm
2474:
2470:William Vickrey
2430:Reinhard Selten
2385:Kenneth Binmore
2300:David K. Levine
2295:Daniel Kahneman
2262:
2256:
2232:Negamax theorem
2222:Minimax theorem
2200:
2161:Diner's dilemma
2016:All-pay auction
1982:
1968:Stochastic game
1920:Mean-field game
1891:
1884:
1850:Markov strategy
1786:
1652:
1644:
1615:Sequential game
1600:Information set
1585:Game complexity
1555:Congestion game
1543:
1537:
1502:
1478:
1477:
1454:10.1145/2517329
1434:
1430:
1387:
1383:
1375:
1373:
1371:
1345:
1341:
1325:
1324:
1312:
1296:
1289:
1280:
1267:
1258:
1247:
1238:
1225:
1216:
1214:
1204:
1200:
1184:
1183:
1171:
1157:
1150:
1138:
1137:
1128:
1127:
1121:
1119:
1109:
1085:
1081:
1072:
1063:
1032:10.2307/2951552
1012:
1001:
994:
982:
981:
977:
969:
965:
941:
940:
928:
914:
910:
905:
892:Sequential game
888:
834:by philosopher
818:
801:Vilfredo Pareto
790:
777:Vilfredo Pareto
770:
713:
646:
643:
617:
594:
580:
558:
542:Pure strategies
539:
531:
522:
520:Symmetric Games
428:
417:
412:
407:
397:
392:
387:
377:
372:
367:
335:
287:
278:
243:
240:
238:
235:
231:
228:
226:
223:
219:
216:
214:
211:
202:
199:
197:
194:
190:
187:
185:
182:
178:
175:
173:
170:
161:
158:
156:
153:
149:
146:
144:
141:
137:
134:
132:
129:
111:
109:
107:
87:
79:
69:
67:Characteristics
56:continuous game
21:
12:
11:
5:
2616:
2606:
2605:
2600:
2583:
2582:
2580:
2579:
2574:
2569:
2564:
2559:
2554:
2549:
2544:
2539:
2534:
2529:
2523:
2521:
2517:
2516:
2514:
2513:
2508:
2503:
2498:
2493:
2488:
2482:
2480:
2476:
2475:
2473:
2472:
2467:
2462:
2457:
2452:
2447:
2442:
2437:
2435:Robert Axelrod
2432:
2427:
2422:
2417:
2412:
2410:Olga Bondareva
2407:
2402:
2400:Melvin Dresher
2397:
2392:
2390:Leonid Hurwicz
2387:
2382:
2377:
2372:
2367:
2362:
2357:
2352:
2347:
2342:
2337:
2332:
2327:
2325:Harold W. Kuhn
2322:
2317:
2315:Drew Fudenberg
2312:
2307:
2305:David M. Kreps
2302:
2297:
2292:
2290:Claude Shannon
2287:
2282:
2277:
2272:
2266:
2264:
2258:
2257:
2255:
2254:
2249:
2244:
2239:
2234:
2229:
2227:Nash's theorem
2224:
2219:
2214:
2208:
2206:
2202:
2201:
2199:
2198:
2193:
2188:
2183:
2178:
2173:
2168:
2163:
2158:
2153:
2148:
2143:
2138:
2133:
2128:
2123:
2118:
2113:
2108:
2103:
2098:
2093:
2088:
2086:Ultimatum game
2083:
2078:
2073:
2068:
2066:Dollar auction
2063:
2058:
2053:
2051:Centipede game
2048:
2043:
2038:
2033:
2028:
2023:
2018:
2013:
2008:
2006:Infinite chess
2003:
1998:
1992:
1990:
1984:
1983:
1981:
1980:
1975:
1973:Symmetric game
1970:
1965:
1960:
1958:Signaling game
1955:
1953:Screening game
1950:
1945:
1943:Potential game
1940:
1935:
1930:
1922:
1917:
1912:
1907:
1902:
1896:
1894:
1886:
1885:
1883:
1882:
1877:
1872:
1870:Mixed strategy
1867:
1862:
1857:
1852:
1847:
1842:
1837:
1832:
1827:
1822:
1817:
1812:
1807:
1802:
1796:
1794:
1788:
1787:
1785:
1784:
1779:
1774:
1769:
1764:
1759:
1754:
1749:
1747:Risk dominance
1744:
1739:
1734:
1729:
1724:
1719:
1714:
1709:
1704:
1699:
1694:
1689:
1684:
1679:
1674:
1669:
1664:
1658:
1656:
1646:
1645:
1643:
1642:
1637:
1632:
1627:
1622:
1617:
1612:
1607:
1602:
1597:
1592:
1590:Graphical game
1587:
1582:
1577:
1572:
1567:
1562:
1557:
1551:
1549:
1545:
1544:
1536:
1535:
1528:
1521:
1513:
1507:
1506:
1500:
1476:
1475:
1428:
1407:10.1086/684166
1381:
1369:
1339:
1310:
1287:
1265:
1245:
1223:
1208:"Parity Chess"
1198:
1169:
1148:
1139:|website=
1107:
1079:
1061:
1026:(2): 273â302.
999:
992:
975:
963:
926:
907:
906:
904:
901:
900:
899:
894:
887:
884:
877:
876:
873:
870:
866:
865:
862:
859:
855:
854:
851:
848:
817:
814:
789:
786:
769:
766:
763:
762:
759:
756:
752:
751:
748:
745:
742:
738:
737:
734:
730:
729:
726:
712:
709:
702:
701:
698:
692:
685:
684:
678:
675:
664:
663:
657:
647:
644:
641:
629:Melvin Dresher
616:
613:
593:
590:
579:
576:
557:
554:
538:
535:
530:
527:
521:
518:
515:
514:
511:
508:
504:
503:
500:
497:
493:
492:
489:
486:
483:
482:
474:
473:
470:
467:
463:
462:
459:
456:
452:
451:
448:
445:
442:
441:
427:
424:
421:
420:
415:
410:
405:
401:
400:
395:
390:
385:
381:
380:
375:
370:
365:
361:
360:
357:
354:
351:
334:
331:
328:
327:
324:
321:
317:
316:
313:
310:
306:
305:
302:
299:
286:
283:
277:
274:
245:
244:
239:
234:
232:
227:
222:
220:
215:
210:
208:
204:
203:
198:
193:
191:
186:
181:
179:
174:
169:
167:
163:
162:
157:
152:
150:
145:
140:
138:
133:
128:
126:
122:
121:
118:
115:
112:
108:
105:
86:
85:Representation
83:
68:
65:
9:
6:
4:
3:
2:
2615:
2604:
2601:
2599:
2596:
2595:
2593:
2578:
2575:
2573:
2570:
2568:
2565:
2563:
2560:
2558:
2555:
2553:
2550:
2548:
2545:
2543:
2540:
2538:
2535:
2533:
2530:
2528:
2525:
2524:
2522:
2520:Miscellaneous
2518:
2512:
2509:
2507:
2504:
2502:
2499:
2497:
2494:
2492:
2489:
2487:
2484:
2483:
2481:
2477:
2471:
2468:
2466:
2463:
2461:
2458:
2456:
2455:Samuel Bowles
2453:
2451:
2450:Roger Myerson
2448:
2446:
2443:
2441:
2440:Robert Aumann
2438:
2436:
2433:
2431:
2428:
2426:
2423:
2421:
2418:
2416:
2413:
2411:
2408:
2406:
2403:
2401:
2398:
2396:
2395:Lloyd Shapley
2393:
2391:
2388:
2386:
2383:
2381:
2380:Kenneth Arrow
2378:
2376:
2373:
2371:
2368:
2366:
2363:
2361:
2360:John Harsanyi
2358:
2356:
2353:
2351:
2348:
2346:
2343:
2341:
2338:
2336:
2333:
2331:
2330:Herbert Simon
2328:
2326:
2323:
2321:
2318:
2316:
2313:
2311:
2308:
2306:
2303:
2301:
2298:
2296:
2293:
2291:
2288:
2286:
2283:
2281:
2278:
2276:
2273:
2271:
2268:
2267:
2265:
2259:
2253:
2250:
2248:
2245:
2243:
2240:
2238:
2235:
2233:
2230:
2228:
2225:
2223:
2220:
2218:
2215:
2213:
2210:
2209:
2207:
2203:
2197:
2194:
2192:
2189:
2187:
2184:
2182:
2179:
2177:
2174:
2172:
2169:
2167:
2164:
2162:
2159:
2157:
2154:
2152:
2149:
2147:
2144:
2142:
2139:
2137:
2134:
2132:
2131:Fair division
2129:
2127:
2124:
2122:
2119:
2117:
2114:
2112:
2109:
2107:
2106:Dictator game
2104:
2102:
2099:
2097:
2094:
2092:
2089:
2087:
2084:
2082:
2079:
2077:
2074:
2072:
2069:
2067:
2064:
2062:
2059:
2057:
2054:
2052:
2049:
2047:
2044:
2042:
2039:
2037:
2034:
2032:
2029:
2027:
2024:
2022:
2019:
2017:
2014:
2012:
2009:
2007:
2004:
2002:
1999:
1997:
1994:
1993:
1991:
1989:
1985:
1979:
1978:Zero-sum game
1976:
1974:
1971:
1969:
1966:
1964:
1961:
1959:
1956:
1954:
1951:
1949:
1948:Repeated game
1946:
1944:
1941:
1939:
1936:
1934:
1931:
1929:
1927:
1923:
1921:
1918:
1916:
1913:
1911:
1908:
1906:
1903:
1901:
1898:
1897:
1895:
1893:
1887:
1881:
1878:
1876:
1873:
1871:
1868:
1866:
1865:Pure strategy
1863:
1861:
1858:
1856:
1853:
1851:
1848:
1846:
1843:
1841:
1838:
1836:
1833:
1831:
1828:
1826:
1825:De-escalation
1823:
1821:
1818:
1816:
1813:
1811:
1808:
1806:
1803:
1801:
1798:
1797:
1795:
1793:
1789:
1783:
1780:
1778:
1775:
1773:
1770:
1768:
1767:Shapley value
1765:
1763:
1760:
1758:
1755:
1753:
1750:
1748:
1745:
1743:
1740:
1738:
1735:
1733:
1730:
1728:
1725:
1723:
1720:
1718:
1715:
1713:
1710:
1708:
1705:
1703:
1700:
1698:
1695:
1693:
1690:
1688:
1685:
1683:
1680:
1678:
1675:
1673:
1670:
1668:
1665:
1663:
1660:
1659:
1657:
1655:
1651:
1647:
1641:
1638:
1636:
1635:Succinct game
1633:
1631:
1628:
1626:
1623:
1621:
1618:
1616:
1613:
1611:
1608:
1606:
1603:
1601:
1598:
1596:
1593:
1591:
1588:
1586:
1583:
1581:
1578:
1576:
1573:
1571:
1568:
1566:
1563:
1561:
1558:
1556:
1553:
1552:
1550:
1546:
1542:
1534:
1529:
1527:
1522:
1520:
1515:
1514:
1511:
1503:
1497:
1493:
1489:
1485:
1484:
1483:
1482:
1471:
1467:
1463:
1459:
1455:
1451:
1447:
1443:
1439:
1432:
1424:
1420:
1416:
1412:
1408:
1404:
1400:
1396:
1392:
1385:
1372:
1366:
1362:
1358:
1354:
1350:
1343:
1335:
1329:
1321:
1317:
1313:
1307:
1303:
1302:
1294:
1292:
1284:
1278:
1276:
1274:
1272:
1270:
1262:
1256:
1254:
1252:
1250:
1242:
1236:
1234:
1232:
1230:
1228:
1213:
1209:
1202:
1194:
1188:
1180:
1176:
1172:
1166:
1162:
1155:
1153:
1144:
1132:
1118:
1114:
1110:
1104:
1100:
1096:
1092:
1091:
1083:
1076:
1070:
1068:
1066:
1057:
1053:
1049:
1045:
1041:
1037:
1033:
1029:
1025:
1021:
1017:
1010:
1008:
1006:
1004:
995:
989:
985:
979:
972:
967:
959:
955:
951:
945:
937:
933:
929:
923:
919:
912:
908:
898:
895:
893:
890:
889:
883:
874:
871:
868:
867:
863:
860:
857:
856:
852:
849:
847:
846:
840:
837:
833:
826:
822:
816:The Stag Hunt
813:
810:
806:
802:
798:
794:
785:
778:
774:
760:
757:
754:
753:
749:
746:
743:
739:
735:
732:
731:
724:
721:
718:
708:
699:
697:
693:
691:
687:
686:
683:
679:
676:
674:
672:
666:
665:
662:
658:
656:
654:
648:
640:
639:
636:
632:
630:
626:
625:Merrill Flood
622:
610:
606:
602:
599:
589:
586:
575:
572:
568:
565:
563:
553:
549:
547:
543:
534:
526:
512:
510:0,0,−1
509:
506:
505:
502:0,−1,0
501:
498:
495:
494:
490:
487:
485:
484:
479:
472:−1,0,0
471:
468:
465:
464:
460:
457:
454:
453:
449:
446:
444:
443:
438:
435:
431:
416:
411:
406:
403:
402:
396:
391:
386:
383:
382:
376:
371:
366:
363:
362:
358:
355:
352:
350:
349:
346:
342:
339:
325:
322:
319:
318:
314:
311:
309:A advertises
308:
307:
303:
301:B advertises
300:
298:
297:
294:
290:
282:
276:Bimatrix Game
273:
266:
262:
260:
254:
252:
233:
221:
209:
206:
205:
192:
180:
168:
165:
164:
151:
139:
127:
124:
123:
103:
100:
98:
94:
90:
82:
77:
73:
64:
61:
57:
53:
49:
45:
41:
37:
29:
25:
19:
2425:Peyton Young
2420:Paul Milgrom
2335:Hervé Moulin
2275:Amos Tversky
2217:Folk theorem
1928:-player game
1925:
1845:Grim trigger
1619:
1491:
1481:Bibliography
1480:
1479:
1445:
1441:
1431:
1401:(1): 29â59.
1398:
1394:
1384:
1374:, retrieved
1352:
1342:
1300:
1215:. Retrieved
1201:
1160:
1120:. Retrieved
1090:U-M Weblogin
1089:
1082:
1023:
1020:Econometrica
1019:
983:
978:
966:
917:
911:
880:
829:
791:
782:
714:
705:
695:
689:
681:
670:
668:
660:
652:
650:
633:
618:
595:
581:
573:
569:
566:
559:
550:
540:
532:
523:
432:
429:
343:
340:
336:
291:
288:
279:
271:
255:
248:
95:
91:
88:
78:
74:
70:
43:
39:
33:
2603:Game theory
2542:Coopetition
2345:Jean Tirole
2340:John Conway
2320:Eric Maskin
2116:Blotto game
2101:Pirate game
1910:Global game
1880:Tit for tat
1810:Bid shading
1800:Appeasement
1650:Equilibrium
1630:Solved game
1565:Determinacy
1548:Definitions
1541:game theory
1448:(3): 1â23.
690:(Betrayal)
661:(Betrayal)
285:Two Players
52:Normal form
44:static game
36:game theory
2592:Categories
2186:Trust game
2171:Kuhn poker
1835:Escalation
1830:Deterrence
1820:Cheap talk
1792:Strategies
1610:Preference
1539:Topics of
1376:2021-04-25
1217:2017-01-15
1122:2021-11-20
903:References
843:Stag Hunt
671:ooperation
653:ooperation
645:Prisoner A
642:Prisoner B
2370:John Nash
2076:Stag hunt
1815:Collusion
1462:1556-4665
1423:124619436
1415:0031-8248
1328:cite book
1320:946968759
1187:cite book
1179:842323069
1141:ignored (
1131:cite book
1117:261084293
1040:0012-9682
944:cite book
936:788246625
832:Stag Hunt
825:Stag hunt
744:Football
733:Football
404:Scissors
359:Scissors
251:game tree
207:Scissors
120:Scissors
2511:Lazy SMP
2205:Theorems
2156:Deadlock
2011:Checkers
1892:of games
1654:concepts
886:See also
741:Husband
110:Player 1
106:Player 2
2263:figures
2046:Chicken
1900:Auction
1890:Classes
1470:7496856
1212:Blogger
1056:9876487
1048:2951552
755:Ballet
736:Ballet
715:In the
596:A pure
585:maximin
1498:
1468:
1460:
1421:
1413:
1367:
1318:
1308:
1285:> .
1263:> .
1243:> .
1177:
1167:
1115:
1105:
1077:> .
1054:
1046:
1038:
990:
934:
924:
513:0,0,0
499:2,1,1
469:1,2,1
461:1,1,2
458:1,1,1
384:Paper
356:Paper
166:Paper
117:Paper
2001:Chess
1988:Games
1466:S2CID
1419:S2CID
1113:S2CID
1052:S2CID
1044:JSTOR
869:Hare
858:Stag
853:Hare
850:Stag
728:Wife
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