717:
three-person game. A particular move of a player in a zero-sum three-person game would be assumed to be clearly beneficial to him and may disbenefits to both other players, or benefits to one and disbenefits to the other opponent. Particularly, parallelism of interests between two players makes a cooperation desirable; it may happen that a player has a choice among various policies: Get into a parallelism interest with another player by adjusting his conduct, or the opposite; that he can choose with which of other two players he prefers to build such parallelism, and to what extent. The picture on the left shows that a typical example of a zero-sum three-person game. If Player 1 chooses to defence, but Player 2 & 3 chooses to offence, both of them will gain one point. At the same time, Player 1 will lose two-point because points are taken away by other players, and it is evident that Player 2 & 3 has parallelism of interests.
709:
780:
772:– whereby a buyer purchases a derivative contract to buy an underlying asset from the seller for a specified price on a specified date – is also an example of a zero-sum game. This is because the fundamental principle of these contracts is that they are agreements between two parties, and any gain made by one party must be matched by a loss sustained by the other.
682:
there is no Nash equilibrium strategy other than avoiding the play. Even if there is a credible zero-zero draw after a zero-sum game is started, it is not better than the avoiding strategy. In this sense, it's interesting to find reward-as-you-go in optimal choice computation shall prevail over all two players zero-sum games concerning starting the game or not.
745:
contribution to the host city may be a zero-sum game. Because for Hong Kong, the consumption of overseas tourists in Hong Kong is income, while the consumption of Hong Kong residents in opposite cities is outflow. In addition, the introduction of new airlines can also have a negative impact on existing airlines.
418:
similar reasoning, Blue would choose action C. If both players take these actions, Red will win 20 points. If Blue anticipates Red's reasoning and choice of action 1, Blue may choose action B, so as to win 10 points. If Red, in turn, anticipates this trick and goes for action 2, this wins Red 20 points.
775:
If the price of the underlying asset increases before the expiration date the buyer may exercise/ close the options/ futures contract. The buyers gain and corresponding sellers loss will be the difference between the strike price and value of the underlying asset at that time. Hence, the net transfer
417:
In this example game, both players know the payoff matrix and attempt to maximize the number of their points. Red could reason as follows: "With action 2, I could lose up to 20 points and can win only 20, and with action 1 I can lose only 10 but can win up to 30, so action 1 looks a lot better." With
817:
For instance, if
Company C announces a deal to acquire Company D, and investors believe that the acquisition will result in synergies and hence increased profitability for Company C, there will be an increased demand for Company C stock. In this scenario, all existing holders of Company C stock will
813:
The primary goal of the stock market is to match buyers and sellers, but the prevailing price is the one which equilibrates supply and demand. Stock prices generally move according to changes in future expectations, such as acquisition announcements, upside earnings surprises, or improved guidance.
432:
provides a way out of this conundrum. Instead of deciding on a definite action to take, the two players assign probabilities to their respective actions, and then use a random device which, according to these probabilities, chooses an action for them. Each player computes the probabilities so as to
681:
If avoiding a zero-sum game is an action choice with some probability for players, avoiding is always an equilibrium strategy for at least one player at a zero-sum game. For any two players zero-sum game where a zero-zero draw is impossible or non-credible after the play is started, such as poker,
793:
whereby Firm A pays a fixed rate and receives a floating rate; correspondingly Firm B pays a floating rate and receives a fixed rate. If rates increase, then Firm A will gain, and Firm B will lose by the rate differential (floating rate – fixed rate). If rates decrease, then Firm A will lose, and
672:
If all the solutions to the linear program are found, they will constitute all the Nash equilibria for the game. Conversely, any linear program can be converted into a two-player, zero-sum game by using a change of variables that puts it in the form of the above equations and thus such games are
227:
The idea of Pareto optimal payoff in a zero-sum game gives rise to a generalized relative selfish rationality standard, the punishing-the-opponent standard, where both players always seek to minimize the opponent's payoff at a favourable cost to themselves rather than prefer more over less. The
716:
It is clear that there are manifold relationships between players in a zero-sum three-person game, in a zero-sum two-person game, anything one player wins is necessarily lost by the other and vice versa; therefore, there is always an absolute antagonism of interests, and that is similar in the
744:
Therefore, the replacement effect should be considered when introducing a new model, which will lead to economic leakage and injection. Thus introducing new models requires caution. For example, if the number of new airlines departing from and arriving at the airport is the same, the economic
408:
The order of play proceeds as follows: The first player (red) chooses in secret one of the two actions 1 or 2; the second player (blue), unaware of the first player's choice, chooses in secret one of the three actions A, B or C. Then, the choices are revealed and each player's points total is
223:
In situation where one decision maker's gain (or loss) does not necessarily result in the other decision makers' loss (or gain), they are referred to as non-zero-sum. Thus, a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the
801:
are complex and multifaceted, with a range of participants engaging in a variety of activities. While some trades may result in a simple transfer of wealth from one party to another, the market as a whole is not purely competitive, and many transactions serve important economic functions.
63:
of a situation that involves two competing entities, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero.
228:
punishing-the-opponent standard can be used in both zero-sum games (e.g. warfare game, chess) and non-zero-sum games (e.g. pooling selection games). The player in the game has a simple enough desire to maximise the profit for them, and the opponent wishes to minimise it.
660:
If the game matrix does not have all positive elements, add a constant to every element that is large enough to make them all positive. That will increase the value of the game by that constant, and will not affect the equilibrium mixed strategies for the equilibrium.
809:
is an excellent example of a positive-sum game, often erroneously labelled as a zero-sum game. This is a zero-sum fallacy: the perception that one trader in the stock market may only increase the value of their holdings if another trader decreases their holdings.
664:
The equilibrium mixed strategy for the minimizing player can be found by solving the dual of the given linear program. Alternatively, it can be found by using the above procedure to solve a modified payoff matrix which is the transpose and negation of
821:
Furthermore, in the long run, the stock market is a positive-sum game. As economic growth occurs, demand increases, output increases, companies grow, and company valuations increase, leading to value creation and wealth addition in the market.
767:
contract - whereby a buyer purchases a derivative contract which provides them with the right to buy an underlying asset from a seller at a specified strike price before a specified expiration date – is an example of a zero-sum game. A
693:". In some cases pursuing individual personal interest can enhance the collective well-being of the group, but in other situations, all parties pursuing personal interest results in mutually destructive behaviour.
748:
Consequently, when a new aviation model is introduced, feasibility tests need to be carried out in all aspects, taking into account the economic inflow and outflow and displacement effects caused by the model.
91:
where one person gains and another person loses, which results in a zero-net benefit for every player. In the markets and financial instruments, futures contracts and options are zero-sum games as well.
220:
Zero-sum games are a specific example of constant sum games where the sum of each outcome is always zero. Such games are distributive, not integrative; the pie cannot be enlarged by good negotiation.
224:
transaction, is in a non-zero-sum situation. Other non-zero-sum games are games in which the sum of gains and losses by the players is sometimes more or less than what they began with.
575:
is positive. The game will have at least one Nash equilibrium. The Nash equilibrium can be found (Raghavan 1994, p. 740) by solving the following linear program to find a vector
618:
1651:
760:
trading may be considered a zero-sum game, as each dollar gained by one party in a transaction must be lost by the other, hence yielding a net transfer of wealth of zero.
71:, where taking a more significant piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if
884:
of the players, as well as to the interpretation of utility functions. Furthermore, the word "game" does not imply the model is valid only for recreational
741:
Studies show that the entry of low-cost airlines into the Hong Kong market brought in $ 671 million in revenue and resulted in an outflow of $ 294 million.
571:(i.e. the player trying to minimize the payoff chooses the row and the player trying to maximize the payoff chooses the column). Assume every element of
99:
describes a situation in which the interacting parties' aggregate gains and losses can be less than or more than zero. A zero-sum game is also called a
1419:
Pratt, Stephen; Schucker, Markus (March 2018). "Economic impact of low-cost carrier in a saturated transport market: Net benefits or zero-sum game?".
696:
Copeland's review notes that an n-player non-zero-sum game can be converted into an (n+1)-player zero-sum game, where the n+1st player, denoted the
2885:
789:, which involve the exchange of cash flows from two different financial instruments, are also considered a zero-sum game. Consider a standard
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by that value gives a probability vector, giving the probability that the maximizing player will choose each possible pure strategy.
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refers to the perception that a given situation is like a zero-sum game, where one person's gain is equal to another person's loss.
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Example: Red chooses action 2 and Blue chooses action B. When the payoff is allocated, Red gains 20 points and Blue loses 20 points.
1357:
891:
Politics is sometimes called zero sum because in common usage the idea of a stalemate is perceived to be "zero sum"; politics and
797:
Whilst derivatives trading may be considered a zero-sum game, it is important to remember that this is not an absolute truth. The
405:
is a convenient representation. Consider these situations as an example, the two-player zero-sum game pictured at right or above.
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game, while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the
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If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Thus,
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1229:. International Series in Operations Research & Management Science. Vol. 201. Boston, MA: Springer US.
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840:, that society becomes increasingly non-zero-sum as it becomes more complex, specialized, and interdependent.
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Misstating the
Concept of Zero-Sum Games within the Context of Professional Sports Trading Strategies
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The zero-sum property (if one gains, another loses) means that any result of a zero-sum situation is
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700:, receives the negative of the sum of the gains of the other n-players (the global gain / loss).
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Economic benefits of low-cost airlines in saturated markets - net benefits or a zero-sum game
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1782:– comprehensive text on psychology and game theory. (Contents and Preface to Second Edition.)
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For the example given above, it turns out that Red should choose action 1 with probability
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Zero-sum games and particularly their solutions are commonly misunderstood by critics of
217:. Generally, any game where all strategies are Pareto optimal is called a conflict game.
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1390:(60th anniversary ed.). Princeton: Princeton University Press. pp. 220–223.
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vector, the inverse of the sum of its elements is the value of the game. Multiplying
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enjoy gains without incurring any corresponding measurable losses to other players.
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method can compute probably optimal strategies for all two-player zero-sum games.
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Ilan Adler (2012) The equivalence of linear programs and zero-sum games. Springer
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Amsterdam, by
Raghavan, T. E. S., Edited by Aumann and Hart, pp. 735–759,
1303:(60th anniversary ed.). Princeton: Princeton University Press. p. 98.
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vector must be nonnegative, and the second constraint says each element of the
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17:
1440:"Why are Gambling Markets Organized so Differently from Financial Markets?"
1550:"The Stock Market as a Game: An Agent Based Approach to Trading in Stocks"
169:
126:
2793:
2293:
1736:
1796:
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Firm B will gain by the rate differential (fixed rate – floating rate).
669:(adding a constant so it is positive), then solving the resulting game.
563:
is the payoff obtained when the minimizing player chooses pure strategy
2514:
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1534:
1502:
442:
248:
1421:
Tourism
Economics: The Business and Finance of Tourism and Recreation
1518:
1034:(60th anniversary ed.). Princeton: Princeton University Press.
75:. Other examples of zero-sum games in daily life include games like
1570:
Zero-Sum Game: The Rise of the World's
Largest Derivatives Exchange
1340:
Wenliang Wang (2015). Pooling Game Theory and Public
Pension Plan.
1281:
Wenliang Wang (2015). Pooling Game Theory and Public
Pension Plan.
1124:"Learning game strategy design through iterated Prisoner's Dilemma"
437:
point-loss independent of the opponent's strategy. This leads to a
2283:
84:
80:
76:
868: + 1)th player representing the global profit or loss.
255:
all give the same solution. If the players are allowed to play a
1711:
895:
are not zero sum games, however, because they do not constitute
885:
1800:
1128:
International
Journal of Computer Applications in Technology
707:
540:
for a two-player, zero-sum game can be found by solving a
441:
problem with the optimal strategies for each player. This
685:
The most common or simple example from the subfield of
544:
problem. Suppose a zero-sum game has a payoff matrix
1165:
Microeconomics: Behavior, Institutions, and
Evolution
589:
1599:. Princeton University Press (1953). June 25, 2005.
512:
to the three actions A, B, and C. Red will then win
409:
affected according to the payoff for those choices.
236:
For two-player finite zero-sum games, the different
2802:
2761:
2543:
2487:
2269:
2171:
2078:
1936:
1835:
1362:. By John von Neumann and Oskar Morgenstern (1944).
1006:"Zero-Sum Game Meaning: Examples of Zero-Sum Games"
612:
567:and the maximizing player chooses pure strategy
73:all participants value each unit of cake equally
975:. Cambridge: Cambridge University Press. 2011.
880:, usually with respect to the independence and
1677:"Zero-sum game | Define Zero-sum game at"
860:players is equivalent to a zero-sum game with
649:vector must be at least 1. For the resulting
641:The first constraint says each element of the
480:, and Blue should assign the probabilities 0,
27:Situation where total gains match total losses
1812:
1478:"Options vs. Futures: What's the Difference?"
1386:Von Neumann, John; Oskar Morgenstern (2007).
1366:Bulletin of the American Mathematical Society
1299:Von Neumann, John; Oskar Morgenstern (2007).
1086:
1084:
1030:Von Neumann, John; Oskar Morgenstern (2007).
8:
1358:Arthur H. Copeland (July 1945) Book review,
206:Another example of the classic zero-sum game
1199:"Two-Person Zero-Sum Games: Basic Concepts"
673:equivalent to linear programs, in general.
1819:
1805:
1797:
604:
594:
588:
1788:and its mixed strategy Nash equilibrium.
1122:Chiong, Raymond; Jankovic, Lubo (2008).
778:
266:
1097:Playing for real: a text on game theory
964:
856:proved that any non-zero-sum game for
259:, the game always has an equilibrium.
1596:Theory of Games and Economic Behavior
1388:Theory of games and economic behavior
1381:
1379:
1377:
1360:Theory of games and economic behavior
1301:Theory of games and economic behavior
1032:Theory of games and economic behavior
973:Cambridge business English dictionary
7:
1438:Levitt, Steven D. (February 2004).
837:Nonzero: The Logic of Human Destiny
753:Zero-sum games in financial markets
1868:First-player and second-player win
1780:Game Theory & its Applications
1752:(1997) Transaction Publishers, by
1729:Handbook of Game Theory – volume 2
25:
428:had the fundamental insight that
267:
1975:Coalition-proof Nash equilibrium
1750:Power: Its Forms, Bases and Uses
1456:10.1111/j.1468-0297.2004.00207.x
119:is a classic non-zero-sum game.
1628:"The flaw in zero sum politics"
2886:International relations theory
1985:Evolutionarily stable strategy
1652:"Lexington: Zero-sum politics"
1626:Rubin, Jennifer (2013-10-04).
1567:Olson, Erika S. (2010-10-26).
1548:Engle, Eric (September 2008).
1100:. Oxford University Press US.
613:{\displaystyle \sum _{i}u_{i}}
464:and action 2 with probability
1:
1913:Simultaneous action selection
864: + 1 players; the (
2845:List of games in game theory
2025:Quantal response equilibrium
2015:Perfect Bayesian equilibrium
1950:Bayes correlated equilibrium
1501:Turnbull, Stuart M. (1987).
620:Subject to the constraints:
528:points on average per game.
269:A zero-sum game (Two person)
107:which is closely related to
2314:Optional prisoner's dilemma
2045:Self-confirming equilibrium
1554:Quantitative Finance Papers
704:Zero-sum three-person games
53:mathematical representation
2907:
2779:Principal variation search
2495:Aumann's agreement theorem
2158:Strategy-stealing argument
2070:Trembling hand equilibrium
2000:Markov perfect equilibrium
1995:Mertens-stable equilibrium
1774:Play zero-sum games online
1371:(7) pp 498-504 (July 1945)
1289:. Chapter 1 and Chapter 4.
1171:Princeton University Press
712:Zero-sum three-person game
109:linear programming duality
40:
29:
2815:Combinatorial game theory
2474:Princess and monster game
2030:Quasi-perfect equilibrium
1955:Bayesian Nash equilibrium
1733:Zero-sum two-person games
1573:. John Wiley & Sons.
1503:"Swaps: A Zero Sum Game?"
1235:10.1007/978-1-4614-9050-0
1226:Two-Person Zero-Sum Games
1140:10.1504/ijcat.2008.020957
830:It has been theorized by
204:
161:
43:Zero sum (disambiguation)
2891:Game theory game classes
2830:Evolutionary game theory
2563:Antoine Augustin Cournot
2449:Guess 2/3 of the average
2246:Strictly determined game
2040:Satisfaction equilibrium
1858:Escalation of commitment
1786:A playable zero-sum game
1364:Review published in the
30:Not to be confused with
2835:Glossary of game theory
2434:Stackelberg competition
2060:Strong Nash equilibrium
1708:Pardon the Interruption
1223:Washburn, Alan (2014).
1161:Bowles, Samuel (2004).
2860:Tragedy of the commons
2840:List of game theorists
2820:Confrontation analysis
2530:Sprague–Grundy theorem
2050:Sequential equilibrium
1970:Correlated equilibrium
1263:Monash Business School
942:Lump of labour fallacy
783:
713:
614:
2881:Non-cooperative games
2633:Jean-François Mertens
927:Comparative advantage
782:
711:
615:
433:minimize the maximum
163:Generic zero-sum game
2762:Search optimizations
2638:Jennifer Tour Chayes
2525:Revelation principle
2520:Purification theorem
2459:Nash bargaining game
2424:Bertrand competition
2409:El Farol Bar problem
2374:Electronic mail game
2339:Lewis signaling game
1883:Hierarchy of beliefs
1507:Financial Management
1444:The Economic Journal
1112:, chapters 1 & 7
587:
101:strictly competitive
41:For other uses, see
2810:Bounded rationality
2429:Cournot competition
2379:Rock paper scissors
2354:Battle of the sexes
2344:Volunteer's dilemma
2216:Perfect information
2143:Dominant strategies
1980:Epsilon-equilibrium
1863:Extensive-form game
1632:The Washington Post
1259:"Non Zero Sum Game"
776:of wealth is zero.
689:is the concept of "
271:
2789:Paranoid algorithm
2769:Alpha–beta pruning
2648:John Maynard Smith
2479:Rendezvous problem
2319:Traveler's dilemma
2309:Gift-exchange game
2304:Prisoner's dilemma
2221:Large Poisson game
2188:Bargaining problem
2093:Backward induction
2065:Subgame perfection
2020:Proper equilibrium
1792:Positive Sum Games
1776:by Elmer G. Wiens.
1556:– via RePEc.
1466:– via RePEc.
791:interest rate swap
784:
714:
677:Universal solution
610:
599:
542:linear programming
439:linear programming
117:Prisoner's Dilemma
2868:
2867:
2774:Aspiration window
2743:Suzanne Scotchmer
2698:Oskar Morgenstern
2593:Donald B. Gillies
2535:Zermelo's theorem
2464:Induction puzzles
2419:Fair cake-cutting
2394:Public goods game
2324:Coordination game
2198:Intransitive game
2128:Forward induction
2010:Pareto efficiency
1990:Gibbs equilibrium
1960:Berge equilibrium
1908:Simultaneous game
1762:978-1-56000-822-4
1722:, performance by
1580:978-0-470-62420-3
1397:978-1-4008-2946-0
1310:978-1-4008-2946-0
1244:978-1-4614-9049-4
1107:978-0-19-530057-4
1041:978-1-4008-2946-0
982:978-0-521-12250-4
947:Positive-sum game
909:zero-sum thinking
903:Zero-sum thinking
897:conserved systems
872:Misunderstandings
854:Oskar Morgenstern
799:financial markets
721:Real life example
698:fictitious player
687:social psychology
590:
399:
398:
241:solution concepts
211:
210:
168:
167:
16:(Redirected from
2898:
2855:Topological game
2850:No-win situation
2748:Thomas Schelling
2728:Robert B. Wilson
2688:Merrill M. Flood
2658:John von Neumann
2568:Ariel Rubinstein
2553:Albert W. Tucker
2404:War of attrition
2364:Matching pennies
2005:Nash equilibrium
1928:Mechanism design
1893:Normal-form game
1848:Cooperative game
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1474:
1468:
1467:
1435:
1429:
1428:
1416:
1410:
1409:
1383:
1372:
1355:
1349:
1338:
1332:
1329:
1323:
1322:
1296:
1290:
1279:
1273:
1272:
1270:
1269:
1255:
1249:
1248:
1220:
1214:
1213:
1211:
1210:
1195:
1189:
1188:
1168:
1158:
1152:
1151:
1119:
1113:
1111:
1088:
1079:
1078:
1076:
1075:
1060:
1054:
1053:
1027:
1021:
1020:
1018:
1017:
1001:
995:
994:
969:
952:No-win situation
937:Gains from trade
850:John von Neumann
770:futures contract
738:
737:
733:
668:
656:
652:
648:
644:
636:
628:
619:
617:
616:
611:
609:
608:
598:
578:
574:
570:
566:
562:
547:
538:Nash equilibrium
527:
525:
524:
521:
518:
511:
509:
508:
505:
502:
495:
493:
492:
489:
486:
479:
477:
476:
473:
470:
463:
461:
460:
457:
454:
426:John von Neumann
394:
389:
382:
377:
370:
365:
359:
349:
344:
337:
332:
325:
320:
314:
305:
298:
291:
283:
278:
272:
245:Nash equilibrium
170:
127:
113:Nash equilibrium
21:
2906:
2905:
2901:
2900:
2899:
2897:
2896:
2895:
2871:
2870:
2869:
2864:
2798:
2784:max^n algorithm
2757:
2753:William Vickrey
2713:Reinhard Selten
2668:Kenneth Binmore
2583:David K. Levine
2578:Daniel Kahneman
2545:
2539:
2515:Negamax theorem
2505:Minimax theorem
2483:
2444:Diner's dilemma
2299:All-pay auction
2265:
2251:Stochastic game
2203:Mean-field game
2174:
2167:
2138:Markov strategy
2074:
1940:
1932:
1903:Sequential game
1888:Information set
1873:Game complexity
1843:Congestion game
1831:
1825:
1770:
1716:Tony Kornheiser
1700:
1698:Further reading
1695:
1694:
1685:
1683:
1675:
1674:
1670:
1661:
1659:
1650:
1649:
1645:
1636:
1634:
1625:
1624:
1620:
1611:
1609:
1607:
1593:
1592:
1588:
1581:
1566:
1565:
1561:
1547:
1546:
1542:
1519:10.2307/3665544
1500:
1499:
1495:
1486:
1484:
1476:
1475:
1471:
1450:(10): 223–246.
1437:
1436:
1432:
1418:
1417:
1413:
1398:
1385:
1384:
1375:
1356:
1352:
1339:
1335:
1330:
1326:
1311:
1298:
1297:
1293:
1280:
1276:
1267:
1265:
1257:
1256:
1252:
1245:
1222:
1221:
1217:
1208:
1206:
1197:
1196:
1192:
1185:
1160:
1159:
1155:
1121:
1120:
1116:
1108:
1090:
1089:
1082:
1073:
1071:
1065:"Zero-Sum Game"
1062:
1061:
1057:
1042:
1029:
1028:
1024:
1015:
1013:
1004:Blakely, Sara.
1003:
1002:
998:
983:
971:
970:
966:
961:
956:
917:
907:In psychology,
905:
874:
846:
828:
755:
739:
735:
731:
729:
728:
723:
706:
679:
666:
654:
650:
646:
642:
639:
638:
631:
629:
623:
600:
585:
584:
576:
572:
568:
564:
561:
549:
545:
534:
522:
519:
516:
515:
513:
506:
503:
500:
499:
497:
490:
487:
484:
483:
481:
474:
471:
468:
467:
465:
458:
455:
452:
451:
449:
395:
392:
390:
387:
383:
380:
378:
375:
371:
368:
366:
363:
355:
350:
347:
345:
342:
338:
335:
333:
330:
326:
323:
321:
318:
310:
301:
294:
287:
284:
281:
279:
276:
265:
234:
125:
105:minimax theorem
61:economic theory
46:
39:
28:
23:
22:
15:
12:
11:
5:
2904:
2902:
2894:
2893:
2888:
2883:
2873:
2872:
2866:
2865:
2863:
2862:
2857:
2852:
2847:
2842:
2837:
2832:
2827:
2822:
2817:
2812:
2806:
2804:
2800:
2799:
2797:
2796:
2791:
2786:
2781:
2776:
2771:
2765:
2763:
2759:
2758:
2756:
2755:
2750:
2745:
2740:
2735:
2730:
2725:
2720:
2718:Robert Axelrod
2715:
2710:
2705:
2700:
2695:
2693:Olga Bondareva
2690:
2685:
2683:Melvin Dresher
2680:
2675:
2673:Leonid Hurwicz
2670:
2665:
2660:
2655:
2650:
2645:
2640:
2635:
2630:
2625:
2620:
2615:
2610:
2608:Harold W. Kuhn
2605:
2600:
2598:Drew Fudenberg
2595:
2590:
2588:David M. Kreps
2585:
2580:
2575:
2573:Claude Shannon
2570:
2565:
2560:
2555:
2549:
2547:
2541:
2540:
2538:
2537:
2532:
2527:
2522:
2517:
2512:
2510:Nash's theorem
2507:
2502:
2497:
2491:
2489:
2485:
2484:
2482:
2481:
2476:
2471:
2466:
2461:
2456:
2451:
2446:
2441:
2436:
2431:
2426:
2421:
2416:
2411:
2406:
2401:
2396:
2391:
2386:
2381:
2376:
2371:
2369:Ultimatum game
2366:
2361:
2356:
2351:
2349:Dollar auction
2346:
2341:
2336:
2334:Centipede game
2331:
2326:
2321:
2316:
2311:
2306:
2301:
2296:
2291:
2289:Infinite chess
2286:
2281:
2275:
2273:
2267:
2266:
2264:
2263:
2258:
2256:Symmetric game
2253:
2248:
2243:
2241:Signaling game
2238:
2236:Screening game
2233:
2228:
2226:Potential game
2223:
2218:
2213:
2205:
2200:
2195:
2190:
2185:
2179:
2177:
2169:
2168:
2166:
2165:
2160:
2155:
2153:Mixed strategy
2150:
2145:
2140:
2135:
2130:
2125:
2120:
2115:
2110:
2105:
2100:
2095:
2090:
2084:
2082:
2076:
2075:
2073:
2072:
2067:
2062:
2057:
2052:
2047:
2042:
2037:
2035:Risk dominance
2032:
2027:
2022:
2017:
2012:
2007:
2002:
1997:
1992:
1987:
1982:
1977:
1972:
1967:
1962:
1957:
1952:
1946:
1944:
1934:
1933:
1931:
1930:
1925:
1920:
1915:
1910:
1905:
1900:
1895:
1890:
1885:
1880:
1878:Graphical game
1875:
1870:
1865:
1860:
1855:
1850:
1845:
1839:
1837:
1833:
1832:
1826:
1824:
1823:
1816:
1809:
1801:
1795:
1794:
1789:
1783:
1777:
1769:
1768:External links
1766:
1765:
1764:
1747:
1726:
1720:Michael Wilbon
1699:
1696:
1693:
1692:
1681:Dictionary.com
1668:
1643:
1618:
1605:
1586:
1579:
1559:
1540:
1493:
1469:
1430:
1411:
1396:
1373:
1350:
1346:978-1507658246
1333:
1324:
1309:
1291:
1287:978-1507658246
1274:
1250:
1243:
1215:
1190:
1183:
1153:
1114:
1106:
1080:
1063:Kenton, Will.
1055:
1040:
1022:
1012:. Master Class
996:
981:
963:
962:
960:
957:
955:
954:
949:
944:
939:
934:
929:
924:
918:
916:
913:
904:
901:
893:macroeconomics
873:
870:
845:
842:
827:
824:
754:
751:
727:
724:
722:
719:
705:
702:
678:
675:
630:
622:
607:
603:
597:
593:
581:
553:
548:where element
533:
530:
397:
396:
391:
386:
384:
379:
374:
372:
367:
362:
360:
352:
351:
346:
341:
339:
334:
329:
327:
322:
317:
315:
307:
306:
299:
292:
285:
280:
275:
264:
261:
257:mixed strategy
238:game theoretic
233:
230:
215:Pareto optimal
209:
208:
202:
201:
198:
195:
191:
190:
187:
184:
180:
179:
176:
173:
166:
165:
159:
158:
155:
152:
148:
147:
144:
141:
137:
136:
133:
130:
124:
121:
69:cutting a cake
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2903:
2892:
2889:
2887:
2884:
2882:
2879:
2878:
2876:
2861:
2858:
2856:
2853:
2851:
2848:
2846:
2843:
2841:
2838:
2836:
2833:
2831:
2828:
2826:
2823:
2821:
2818:
2816:
2813:
2811:
2808:
2807:
2805:
2803:Miscellaneous
2801:
2795:
2792:
2790:
2787:
2785:
2782:
2780:
2777:
2775:
2772:
2770:
2767:
2766:
2764:
2760:
2754:
2751:
2749:
2746:
2744:
2741:
2739:
2738:Samuel Bowles
2736:
2734:
2733:Roger Myerson
2731:
2729:
2726:
2724:
2723:Robert Aumann
2721:
2719:
2716:
2714:
2711:
2709:
2706:
2704:
2701:
2699:
2696:
2694:
2691:
2689:
2686:
2684:
2681:
2679:
2678:Lloyd Shapley
2676:
2674:
2671:
2669:
2666:
2664:
2663:Kenneth Arrow
2661:
2659:
2656:
2654:
2651:
2649:
2646:
2644:
2643:John Harsanyi
2641:
2639:
2636:
2634:
2631:
2629:
2626:
2624:
2621:
2619:
2616:
2614:
2613:Herbert Simon
2611:
2609:
2606:
2604:
2601:
2599:
2596:
2594:
2591:
2589:
2586:
2584:
2581:
2579:
2576:
2574:
2571:
2569:
2566:
2564:
2561:
2559:
2556:
2554:
2551:
2550:
2548:
2542:
2536:
2533:
2531:
2528:
2526:
2523:
2521:
2518:
2516:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2493:
2492:
2490:
2486:
2480:
2477:
2475:
2472:
2470:
2467:
2465:
2462:
2460:
2457:
2455:
2452:
2450:
2447:
2445:
2442:
2440:
2437:
2435:
2432:
2430:
2427:
2425:
2422:
2420:
2417:
2415:
2414:Fair division
2412:
2410:
2407:
2405:
2402:
2400:
2397:
2395:
2392:
2390:
2389:Dictator game
2387:
2385:
2382:
2380:
2377:
2375:
2372:
2370:
2367:
2365:
2362:
2360:
2357:
2355:
2352:
2350:
2347:
2345:
2342:
2340:
2337:
2335:
2332:
2330:
2327:
2325:
2322:
2320:
2317:
2315:
2312:
2310:
2307:
2305:
2302:
2300:
2297:
2295:
2292:
2290:
2287:
2285:
2282:
2280:
2277:
2276:
2274:
2272:
2268:
2262:
2261:Zero-sum game
2259:
2257:
2254:
2252:
2249:
2247:
2244:
2242:
2239:
2237:
2234:
2232:
2231:Repeated game
2229:
2227:
2224:
2222:
2219:
2217:
2214:
2212:
2210:
2206:
2204:
2201:
2199:
2196:
2194:
2191:
2189:
2186:
2184:
2181:
2180:
2178:
2176:
2170:
2164:
2161:
2159:
2156:
2154:
2151:
2149:
2148:Pure strategy
2146:
2144:
2141:
2139:
2136:
2134:
2131:
2129:
2126:
2124:
2121:
2119:
2116:
2114:
2113:De-escalation
2111:
2109:
2106:
2104:
2101:
2099:
2096:
2094:
2091:
2089:
2086:
2085:
2083:
2081:
2077:
2071:
2068:
2066:
2063:
2061:
2058:
2056:
2055:Shapley value
2053:
2051:
2048:
2046:
2043:
2041:
2038:
2036:
2033:
2031:
2028:
2026:
2023:
2021:
2018:
2016:
2013:
2011:
2008:
2006:
2003:
2001:
1998:
1996:
1993:
1991:
1988:
1986:
1983:
1981:
1978:
1976:
1973:
1971:
1968:
1966:
1963:
1961:
1958:
1956:
1953:
1951:
1948:
1947:
1945:
1943:
1939:
1935:
1929:
1926:
1924:
1923:Succinct game
1921:
1919:
1916:
1914:
1911:
1909:
1906:
1904:
1901:
1899:
1896:
1894:
1891:
1889:
1886:
1884:
1881:
1879:
1876:
1874:
1871:
1869:
1866:
1864:
1861:
1859:
1856:
1854:
1851:
1849:
1846:
1844:
1841:
1840:
1838:
1834:
1830:
1822:
1817:
1815:
1810:
1808:
1803:
1802:
1799:
1793:
1790:
1787:
1784:
1781:
1778:
1775:
1772:
1771:
1767:
1763:
1759:
1755:
1751:
1748:
1746:
1745:0-444-89427-6
1742:
1738:
1734:
1730:
1727:
1725:
1721:
1717:
1714:, created by
1713:
1710:(2010-09-23)
1709:
1705:
1702:
1701:
1697:
1682:
1678:
1672:
1669:
1657:
1656:The Economist
1653:
1647:
1644:
1633:
1629:
1622:
1619:
1608:
1606:9780691130613
1602:
1598:
1597:
1590:
1587:
1582:
1576:
1572:
1571:
1563:
1560:
1555:
1551:
1544:
1541:
1536:
1532:
1528:
1524:
1520:
1516:
1512:
1508:
1504:
1497:
1494:
1483:
1479:
1473:
1470:
1465:
1461:
1457:
1453:
1449:
1445:
1441:
1434:
1431:
1427:(2): 149–170.
1426:
1422:
1415:
1412:
1407:
1403:
1399:
1393:
1389:
1382:
1380:
1378:
1374:
1370:
1367:
1363:
1361:
1354:
1351:
1347:
1343:
1337:
1334:
1328:
1325:
1320:
1316:
1312:
1306:
1302:
1295:
1292:
1288:
1284:
1278:
1275:
1264:
1260:
1254:
1251:
1246:
1240:
1236:
1232:
1228:
1227:
1219:
1216:
1204:
1200:
1194:
1191:
1186:
1184:0-691-09163-3
1180:
1176:
1172:
1167:
1166:
1157:
1154:
1149:
1145:
1141:
1137:
1133:
1129:
1125:
1118:
1115:
1109:
1103:
1099:
1098:
1093:
1087:
1085:
1081:
1070:
1066:
1059:
1056:
1051:
1047:
1043:
1037:
1033:
1026:
1023:
1011:
1007:
1000:
997:
992:
988:
984:
978:
974:
968:
965:
958:
953:
950:
948:
945:
943:
940:
938:
935:
933:
932:Dutch disease
930:
928:
925:
923:
922:Bimatrix game
920:
919:
914:
912:
910:
902:
900:
898:
894:
889:
887:
883:
879:
871:
869:
867:
863:
859:
855:
851:
843:
841:
839:
838:
833:
832:Robert Wright
825:
823:
819:
815:
811:
808:
803:
800:
795:
792:
788:
781:
777:
773:
771:
766:
761:
759:
752:
750:
746:
742:
734:
725:
720:
718:
710:
703:
701:
699:
694:
692:
688:
683:
676:
674:
670:
662:
658:
634:
626:
621:
605:
601:
595:
591:
580:
560:
556:
552:
543:
539:
531:
529:
446:
444:
440:
436:
431:
427:
423:
419:
415:
414:
410:
406:
404:
403:payoff matrix
385:
373:
361:
358:
354:
353:
340:
328:
316:
313:
309:
308:
304:
300:
297:
293:
290:
286:
274:
273:
270:
262:
260:
258:
254:
250:
246:
242:
239:
231:
229:
225:
221:
218:
216:
207:
203:
199:
196:
193:
192:
188:
185:
182:
181:
177:
174:
172:
171:
164:
160:
156:
153:
150:
149:
145:
142:
139:
138:
134:
131:
129:
128:
122:
120:
118:
114:
110:
106:
102:
98:
95:In contrast,
93:
90:
86:
82:
78:
74:
70:
65:
62:
58:
54:
50:
49:Zero-sum game
44:
37:
33:
19:
2708:Peyton Young
2703:Paul Milgrom
2618:Hervé Moulin
2558:Amos Tversky
2500:Folk theorem
2260:
2211:-player game
2208:
2133:Grim trigger
1754:Dennis Wrong
1749:
1732:
1728:
1724:Bill Simmons
1707:
1703:
1684:. Retrieved
1680:
1671:
1660:. Retrieved
1658:. 2014-02-08
1655:
1646:
1635:. Retrieved
1631:
1621:
1610:. Retrieved
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1513:(1): 15–21.
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1496:
1485:. Retrieved
1482:Investopedia
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1348:. Chapter 4.
1336:
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1294:
1277:
1266:. Retrieved
1262:
1253:
1225:
1218:
1207:. Retrieved
1205:. Neos Guide
1202:
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1156:
1131:
1127:
1117:
1096:
1072:. Retrieved
1069:Investopedia
1068:
1058:
1031:
1025:
1014:. Retrieved
1010:Master Class
1009:
999:
972:
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906:
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875:
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834:in his book
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807:stock market
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691:social traps
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100:
97:non-zero-sum
96:
94:
66:
48:
47:
18:Non-zero sum
2825:Coopetition
2628:Jean Tirole
2623:John Conway
2603:Eric Maskin
2399:Blotto game
2384:Pirate game
2193:Global game
2163:Tit for tat
2098:Bid shading
2088:Appeasement
1938:Equilibrium
1918:Solved game
1853:Determinacy
1836:Definitions
1829:game theory
1173:. pp.
1092:Ken Binmore
882:rationality
878:game theory
758:Derivatives
430:probability
422:Émile Borel
57:game theory
2875:Categories
2469:Trust game
2454:Kuhn poker
2123:Escalation
2118:Deterrence
2108:Cheap talk
2080:Strategies
1898:Preference
1827:Topics of
1731:, chapter
1686:2017-03-08
1662:2017-03-08
1637:2017-03-08
1612:2018-02-25
1487:2023-04-24
1268:2021-04-25
1209:2022-04-28
1203:Neos Guide
1134:(3): 216.
1074:2021-04-25
1016:2022-04-28
959:References
844:Extensions
826:Complexity
582:Minimize:
123:Definition
111:, or with
2653:John Nash
2359:Stag hunt
2103:Collusion
1735:, (1994)
1706:, series
1527:0046-3892
1406:830323721
1319:830323721
1148:0952-8091
1050:830323721
991:741548935
848:In 1944,
647:M u
633:M u
592:∑
401:A game's
194:Option 2
183:Option 1
178:Option 2
175:Option 1
151:Choice 2
140:Choice 1
135:Choice 2
132:Choice 1
36:Zero game
32:Empty sum
2794:Lazy SMP
2488:Theorems
2439:Deadlock
2294:Checkers
2175:of games
1942:concepts
1737:Elsevier
1094:(2007).
915:See also
435:expected
232:Solution
2546:figures
2329:Chicken
2183:Auction
2173:Classes
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1464:2289856
765:options
532:Solving
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263:Example
253:maximin
249:minimax
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146:B, −B
143:−A, A
89:bridge
2284:Chess
2271:Games
1531:JSTOR
1460:S2CID
1177:–36.
886:games
787:Swaps
85:Sport
81:chess
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51:is a
1965:Core
1758:ISBN
1741:ISBN
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1712:ESPN
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1575:ISBN
1523:ISSN
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