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:''For other uses, see: [[game (disambiguation)]], a band named [[Game Theory (band)|Game Theory]], or [[combinatorial game theory]] (used to study games like [[nim]], [[chess]], and [[go (board game)|go]]).''


'''Game theory''' is a branch of [[applied mathematics]] that studies strategic situations where players choose different actions in an attempt to maximize their returns. First developed as a tool for understanding [[economics|economic]] [[behavior]] and then by the [[RAND|RAND Corporation]] to define [[nuclear strategies]], game theory is now used in many diverse academic fields, ranging from [[biology]] and [[psychology]] to [[sociology]] and [[philosophy]]. Beginning in the 1970s, game theory has been applied to animal behavior, including species' development by [[natural selection]]. Because of interesting games like the [[prisoner's dilemma]], in which rational self-interest hurts everyone, game theory has been used in [[political science]], [[ethics]] and philosophy. Finally, game theory has recently drawn attention from [[computer scientist]]s because of its use in [[artificial intelligence]] and [[cybernetics]].
'''= "Game Theory is the science of logical decision making in humans, animals, and computers".''': "We now have ''mathematical and theoretical approaches to predict how people will act, given certain adversarial conditions''." [https://medium.com/blockchannel/cryptoeconomic-theory-game-theory-basics-fb3a49aab1a8]


In addition to its academic interest, game theory has received attention in popular culture. A [[Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel|Nobel Prize]]-winning game theorist, [[John Forbes Nash|John Nash]] was the subject of the 1998 biography by [[Sylvia Nasar]] and the 2001 film ''[[A Beautiful Mind]]''. Game theory was also a theme in the 1983 film ''[[WarGames]]''. Several [[game show]]s have adopted game theoretic situations, including  ''[[Friend or Foe?]]'' and to some extent ''[[Survivor (TV series)|Survivor]]''.  The character of [[Jack Bristow]] on the [[television]] show ''[[Alias (TV series)|Alias]]'' is one of the few fictional game theorists in popular culture.  <ref>[http://www.gametheory.net GameTheory.net] has an extensive list of [http://www.gametheory.net/popular/ references to game theory in popular culture].</ref>


Although similar to [[decision theory]], game theory studies decisions that are made in an environment where various players interact. In other words, game theory studies choice of optimal behavior when costs and benefits of each option are not fixed, but depend upon the choices of other individuals.
=Context=


==Representation of games==
Game Theory is often used to discuss the nature of human cooperation.


The '''games''' studied by game theory are well-defined mathematical objects. A game consists of a set of players, a set of moves (or [[strategy (game theory)|strategies]]) available to those players, and a specification of payoffs for each combination of strategies. There are two ways of representing games that are common in the literature.
See our entries on the [[Prisoner's Dilemman]] and the [[Assurance Game]]


See also [[List of games in game theory]].
Our interest is focused on [[Cooperative Game Theory]] and the calculation and distribution of cooperative surplus.‎


===Normal form===
{| align=right border="1" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 1em; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse; font-size: 95%;"
|+ align=bottom |''A normal form game''
|-
|
! scope="col" style="color: #900;width: 90px;"|''Player 2 chooses left''
! scope="col" style="color: #900;width: 90px;"|''Player 2 chooses right''
|-
! scope="col" style="color: #009;width: 90px;"|''Player 1 chooses top''
|align=center| <span style="color: #009">4</span>, <span style="color: #900">3</span>
|align=center| <span style="color: #009">-1</span>, <span style="color: #900">-1</span>
|-
! scope="col" style="color: #009;width: 100px;"|''Player 1 chooses bottom''
|align=center| <span style="color: #009">0</span>, <span style="color: #900">0</span>
|align=center| <span style="color: #009">3</span>, <span style="color: #900">4</span>
|}
{{main|Normal form game}}
The normal (or strategic form) game is a [[Matrix (mathematics)|matrix]] which shows the players, strategies, and payoffs (see the example to the right). Here there are two players; one chooses the row and the other chooses the column. Each player has two strategies, which are specified by the number of rows and the number of columns. The payoffs are provided in the interior. The first number is the payoff received by the row player (''Player 1'' in our example); the second is the payoff for the column player (''Player 2'' in our example). Suppose that ''Player 1'' plays top and that ''Player 2'' plays left. Then ''Player 1'' gets 4, and ''Player 2'' gets 3.


When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other. If players have some information about the choices of other players, the game is usually presented in extensive form.
=Description=


===Extensive form===
From the Wikipedia at http://en.wikipedia.org/wiki/Game_theory:
{{main|Extensive form game}}
[[Image:Ult.png|thumb|left|An extensive form game]]
Extensive form games attempt to capture games with some important order. Games here are presented as [[tree (graph theory)|trees]] (as pictured to the left). Here each [[vertex]] (or node) represents a point of choice for a player. The player is specified by a number listed by the vertex. The lines out of the vertex represent a possible action for that player. The payoffs are specified at the bottom of the tree.


In the game pictured here, there are two players. ''Player 1'' moves first and chooses either ''F'' or ''U''. ''Player 2'' sees ''Player 1'''s move and then chooses ''A'' or ''R''. Suppose that ''Player 1'' chooses ''U'' and then ''Player 2'' chooses ''A'', then ''Player 1'' gets 8 and ''Player 2'' gets 2.
"Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. First developed as a tool for understanding economic behavior and then by the RAND Corporation to define nuclear strategies, game theory is now used in many diverse academic fields, ranging from biology and psychology to sociology and philosophy. Beginning in the 1970s, game theory has been applied to animal behavior, including species' development by natural selection. Because of interesting games like the prisoner's dilemma, in which rational self-interest hurts everyone, game theory has been used in political science, ethics and philosophy. Finally, game theory has recently drawn attention from computer scientists because of its use in artificial intelligence and cybernetics."
(http://en.wikipedia.org/wiki/Game_theory)


Extensive form games can also capture simultaneous-move games as well. Either a dotted line or circle is drawn around two different vertices to represent them as being part of the same [[information set]] (i.e., the players do not know at which point they are).


==Types of games==
=Applications=


===Symmetric and asymmetric===
"* In public policy, game theory is used to predict how nations will act and react.
{{main|Symmetric game}}


{| border="1" align=right cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 1em; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse; font-size: 95%;"
* In war, game theory is used to predict the moves of the opponent.
|+ align=bottom|''An asymmetric game''
|
! ''E''
! ''F''
|-
! ''E''
| 1, 2
| 0, 0
|-
! ''F''
| 0, 0
| 1, 2
|}
A symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. If the identities of the players can be changed without changing the payoff to the strategies, then a game is symmetric. Many of the commonly studied 2&times;2 games are symmetric. The standard representations of [[Game of chicken|chicken]], the [[prisoner's dilemma]], and the [[stag hunt]] are all symmetric games. Some scholars would consider certain asymmetric games as examples of these games as well.  However, the most common payoffs for each of these games are symmetric.


Most commonly studied asymmetric games are games where there are not identical strategy sets for both players. For instance, the [[ultimatum game]] and similarly the [[dictator game]] have different strategies for each player. It is possible, however, for a game to have identical strategies for both players, yet be asymmetric. For example, the game pictured to the right is asymmetric despite having identical strategy sets for both players.
* In cryptography, game theory is used to predict potential cyberattacks.


===Zero sum and non-zero sum===
* '''In token design, game theory is used to predict the actions of token-holders in response to embedded incentives'''.
{{main|Zero-sum}}


{| border="1" align=right cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 1em; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse; font-size: 95%;"
* In financial markets, game theory is used to predict stock market decisions
|+ align=bottom|''A Zero-Sum Game''
|
! ''A''
! ''B''
|-
! ''A''
| 2, &minus;2
| &minus;1, 1
|-
! ''B''
| &minus;1, 1
| 3, &minus;3
|}
In [[zero-sum]] games the total benefit to all players in the game, for every combination of strategies, always adds to zero (or more informally put, a player benefits only at the expense of others). [[Poker]] exemplifies a zero-sum game (ignoring the possibility of the house's cut), because one wins exactly the amount one's opponents lose. Other zero sum games include [[matching pennies]] and most classical board games including [[go (board game)|go]] and [[chess]]. Many games studied by game theorists (including the famous [[prisoner's dilemma]]) are non-zero-sum games, because some [[Outcome (Game theory)|outcomes]] have net results greater or less than zero. Informally, in non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another.


It is possible to transform any game into a zero-sum game by adding an additional dummy player (often called "the board"), whose losses compensate the players' net winnings.
=Typology=


===Simultaneous and sequential===
==[[Cooperative vs Non-Cooperative Games]]==
{{main|Sequential game}}


Simultaneous games are games where both players move simultaneously, or if they do not move simultaneously, the later players are unaware of the earlier players' actions (making them ''effectively'' simultaneous). Sequential games (or dynamic games) are games where later players have some knowledge about earlier actions. This need not be [[perfect information|perfect knowledge]] about every action of earlier players; it might be very little information. For instance, a player may know that an earlier player did not perform one particular action, while she does not know which of the other available actions the first player actually performed.
Kyle Birchard:


The difference between simultaneous and sequential games is captured in the different representations discussed above. [[Normal form game|Normal form]] is used to represent simultaneous games, and [[extensive form game|extensive form]] is used to represent sequential ones.
"Cooperative Games: Imagine an interaction for which it is the case that everything that both is affected by the actions of the players and is of concern to any of the players is subject to binding (meaning costlessly enforceable) agreement. This is termed a cooperative game. The term does not refer to the feelings of the parties about each other but simply to the institutional arrangements governing their interactions.


===Perfect information and imperfect information===
Non-cooperative Games: More commonly, however, something about the interaction is not subject to binding agreement. Such situations are modeled as noncooperative games.
[[Image:PD with outside option.png|thumb|250px|right|A game of imperfect information (the dotted line represents ignorance on the part of player 2)]]
{{main|Perfect information}}


An important subset of sequential games consists of games of perfect information. A game is one of perfect information if all players know the moves previously made by all other players. Thus, only sequential games can be games of perfect information, since in simultaneous games not every player knows the actions of the others. Most games studied in game theory are imperfect information games, although some interesting games are games of perfect information, including the [[ultimatum game]] and [[centipede game]]. Many popular games are games of perfect information including [[chess]], [[go (board game)|go]], and [[mancala]].
Notice how this doesn’t necessarily refer to the ability or desire to cooperate, Cooperative Games simply refer to the enforcement level found in binding vs non-binding agreements.


Perfect information is often confused with [[complete information]], which is a similar concept. Complete information requires that every player know the strategies and payoffs of the other players but not necessarily the actions.
In the social arrangement between an employer and employee, part of the interaction may be addressed cooperatively, as when an employer and an employee bargain over a wage and working hours. Other aspects of the same interaction may be noncooperative because of the impossibility of writing or enforcing the relevant contracts.


===Infinitely long games===
Examples include how hard the worker works or whether the employer will invest the resulting profits back into the company. When the employer is measuring productivity, he/she plays a cooperative game if he/she has a ticker at the door that tracks when the employee walks in and out. However, if the employer can’t verify the quality of work or effort put in, then the game is non-cooperative.
{{main|Determinacy}}


For obvious reasons, games as studied by economists and real-world game players are generally finished in a finite number of moves. Pure mathematicians are not so constrained, and [[set theory|set theorists]] in particular study games that last for infinitely many moves, with the winner (or other payoff) not known until ''after'' all those moves are completed.
In technology jobs, and inside startups especially, it’s often difficult and costly to track worker productivity at work → making it a non-cooperative game. This is why we hear so often about ‘company culture’ and establishing a common ‘mission’. When an employer has no way enforce certain agreements, and rational employees can slack off without repercussions, therefore a narrative of ‘culture’ is used to imprint made-up social contracts.


The focus of attention is usually not so much on what is the best way to play such a game, but simply on whether one or the other player has a [[Determinacy#Basic notions|winning strategy]]. (It can be proved, using the [[axiom of choice]], that there are games&mdash;even with perfect information, and where the only outcomes are "win" or "lose"&mdash;for which ''neither'' player has a winning strategy.) The existence of such strategies, for cleverly designed games, has important consequences in [[descriptive set theory]].
Most commonly, social interactions are categorized based on whether the game representing it is cooperative or noncooperative and whether the payoffs of the game are common interest or conflict."
(https://medium.com/blockchannel/cryptoeconomic-theory-game-theory-basics-fb3a49aab1a8)


==Uses of game theory==


Games in one form or another are widely used in many different academic disciplines.
[[Category:Encyclopedia]]


===Economics and business===
[[Category:Relational]]


Economists have used game theory to analyze a wide array of economic phenomena, including [[auction]]s, [[bargaining]], [[duopoly|duopolies]], [[oligopoly|oligopolies]], [[social network]] formation, and [[voting systems]].  This research usually focuses on particular sets of strategies known as [[solution concept|equilibria]] in games.  These "solution concepts" are usually based on what is required by norms of [[perfect rationality|rationality]].  The most famous of these is the [[Nash equilibrium]].  A set of strategies is a Nash equilibrium if each represents a best response to the other strategies.  So, if all the players are playing the strategies in a Nash equilibrium, they have no incentive to deviate, since their strategy is the best they can do given what others are doing.
[[Category:P2P Theory]]


The payoffs of the game are generally taken to represent the [[utility function|utility]] of individual players. Often in modeling situations the payoffs represent money, which presumably corresponds to an individual's utility. This assumption, however, can be faulty.
[[Category:Gaming]]
 
A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of some particular economic situation.  One or more solution concepts are chosen, and the author demonstrates which strategy sets in the presented game are equilibria of the appropriate type.  Naturally one might wonder to what use should this information be put.  Economists and business professors suggest two primary uses.
 
====Descriptive====
[[Image:Centipede game.png|thumb|300px|right|A three stage Centipede Game]]
The first use is to inform us about how actual human populations behave.  Some scholars believe that by finding the equilibria of games they can predict how actual human populations will behave when confronted with situations analogous to the game being studied.  This particular view of game theory has come under recent criticism.  First, it is criticized because the assumptions made by game theorists are often violated.  Game theorists may assume players always act rationally to maximize their wins (the [[Homo economicus]] model), but real humans often act either irrationally, or act rationally to maximize the wins of some larger group of people ([[altruism]]).  Game theorists respond by comparing their assumptions to those used in physics. Thus while their assumptions do not always hold, they can treat game theory as a reasonable scientific [[Idealization|ideal]] akin to the models used by [[physicist]]s.  However, additional criticism of this use of game theory has been levied because some experiments have demonstrated that individuals do not play equilibrium strategies.  For instance, in the [[Centipede game]], [[Guess 2/3 of the average]] game, and the [[Dictator game]], people regularly do not play Nash equilibria. There is an ongoing debate regarding the importance of these experiments. <ref>Experimental work in game theory goes by many names, [[experimental economics]], [[behavioral economics]], and [[behavioral game theory]] are several.  For a recent discussion on this field see Camerer 2003.</ref>
 
Alternatively, some authors claim that Nash equilibria do not provide predictions for human populations, but rather provide an explanation for why populations that play Nash equilibria remain in that state.  However, the question of how populations reach those points remains open.
 
Some game theorists have turned to [[evolutionary game theory]] in order to resolve these worries.  These models presume either no rationality or [[bounded rationality]] on the part of players.  Despite the name, evolutionary game theory does not necessarily presume [[natural selection]] in the biological sense.  Evolutionary game theory includes both biological as well as cultural evolution and also models of individual learning (for example, [[fictitious play]] dynamics).
 
====Normative====
{| border="1" align=right cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 1em; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse; font-size: 95%;"
|+ align=bottom|''The Prisoner's Dilemma''
|
! ''Cooperate''
! ''Defect''
|-
! ''Cooperate''
| 2, 2
| 0, 3
|-
! ''Defect''
| 3, 0
| 1, 1
|}
 
On the other hand, some scholars see game theory not as a predictive tool for the behavior of human beings, but as a suggestion for how people ought to behave.  Since a [[Nash equilibrium]] of a game constitutes one's [[best response]] to the actions of the other players, playing a strategy that is part of a Nash equilibrium seems appropriate.  However, this use for game theory has also come under criticism.  First, in some cases it is appropriate to play a non-equilibrium strategy if one expects others to play non-equilibrium strategies as well.  For an example, see [[Guess 2/3 of the average]]. 
 
Second, the [[Prisoner's Dilemma]] presents another potential counterexample.  In the Prisoner's Dilemma, each player pursuing his own self-interest leads both players to be worse off than had they not pursued their own self-interests.  Some scholars believe that this demonstrates the failure of game theory as a recommendation for behavior.
 
===Biology===
{| border="1" align=right cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 1em; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse; font-size: 95%;"
|+ align=bottom|''Hawk-Dove''
|
! ''Hawk''
! ''Dove''
|-
! ''Hawk''
| (V-C)/2, (V-C)/2
| V, 0
|-
! ''Dove''
| 0, V
| V/2, V/2
|}
 
Unlike economics, the payoffs for games in [[biology]] are often interpreted as corresponding to [[fitness (biology)|fitness]].  In addition, the focus has been less on [[solution concept|equilibria]] that correspond to a notion of rationality, but rather on ones that would be maintained by [[evolution]]ary forces.  The most well-known equilibrium in biology is known as the [[Evolutionary stable strategy]] or (ESS), and was first introduced by [[John Maynard Smith]] (described in his 1982 book).  Although its initial motivation did not involve any of the mental requirements of the [[Nash equilibrium]], every ESS is a Nash equilibrium.
 
In biology, game theory has been used to understand many different phenomena.  It was first used to explain the evolution (and stability) of the approximate 1:1 [[sex ratio]]s.  [[Ronald Fisher]] (1930) suggested that the 1:1 sex ratios are a result of evolutionary forces acting on individuals who could be seen as trying to maximize their number of grandchildren.
 
Additionally, biologists have used [[evolutionary game theory]] and the ESS to explain the emergence of [[animal communication]] ([[John Maynard Smith|Maynard Smith]] & Harper, 2003).  The analysis of [[signaling games]] and [[cheap talk|other communication games]] has provided some insight into the evolution of communication among animals. 
 
Finally, biologists have used the [[hawk-dove game]] (also known as chicken) to analyze fighting behavior and territoriality.
 
===Computer science and logic===
 
Game theory has come to play an increasingly important role in [[logic]] and in [[computer science]]. Several logical theories have a basis in [[game semantics]]. In addition, computer scientists have used games to model [[interactive computation]]s.
 
===Political science===
Research in [[political science]] has also used game theory. A game-theoretic explanation for the [[democratic peace theory |democratic peace]] is that the public and open debate in democracies send clear and reliable information regarding the intentions to other states. In contrast, it is difficult to know the intentions of nondemocratic leaders, what effect concessions will have, and if promises will be kept. Thus there will be mistrust and unwillingness to make concessions if at least one of the parties in a dispute is a nondemocracy.[http://papers.ssrn.com/sol3/papers.cfm?abstract_id=433844]
 
===Philosophy===
 
Game theory has been put to several uses in [[philosophy]].  Responding to two papers by [[W.V.O. Quine]] (1960, 1967), [[David Lewis]] (1969) used game theory to develop a philosophical account of [[Convention (norm)|convention]].  In so doing, he provided the first analysis of [[Common knowledge (logic)|common knowledge]] and employed it in analyzing play in [[coordination game]]s.  In addition, he first suggested that one can understand [[meaning]] in terms of [[signaling game]]s.  This later suggestion has been pursued by several philosophers since Lewis (Skyrms 1996, Grim et al. 2004).
{| border="1" align=right cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 1em; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse; font-size: 95%;"
|+ align=bottom|''The Stag Hunt''
|
! ''Stag''
! ''Hare''
|-
! ''Stag''
| 3, 3
| 0, 2
|-
! ''Hare''
| 2, 0
| 2, 2
|}
 
In [[ethics]], some authors have attempted to pursue the project, begun by [[Thomas Hobbes]], of deriving morality from self-interest.  Since games like the [[Prisoner's Dilemma]] present an apparent conflict between morality and self-interest, explaining why cooperation is required by self-interest is an important component of this project.  This general strategy is a component of the general [[social contract]] view in [[political philosophy]] (for examples, see Gauthier 1987 and Kavka 1986). <ref>For a more detailed discussion of the use of Game Theory in ethics see the Stanford Encyclopedia of Philosophy's entry [http://plato.stanford.edu/entries/game-ethics/ game theory and ethics].</ref>
 
Finally, other authors have attempted to use [[evolutionary game theory]] in order to explain the emergence of human attitudes about morality and corresponding animal behaviors.  These authors look at several games including the Prisoner's Dilemma, [[Stag hunt]], and the [[Nash bargaining game]] as providing an explanation for the emergence of attitudes about morality (see, e.g., Skyrms 1996, 2004; Sober and Wilson 1999).
 
==History of game theory==
 
The first known discussion of game theory occurred in a letter written by [[James Waldegrave]] in 1713.  In this letter, Waldegrave provides a [[minimax]] [[mixed strategy]] solution to a two-person version of the card game [[le Her]].  It was not until the publication of [[Antoine Augustin Cournot]]'s ''Researches into the Mathematical Principles of the Theory of Wealth'' in 1838 that a general game theoretic analysis was pursued.  In this work Cournot considers a [[duopoly]] and presents a solution that is a restricted version of the [[Nash equilibrium]].
 
Although Cournot's analysis is more general than Waldegrave's, game theory did not really exist as a unique field until [[John von Neumann]] published a series of papers in 1928. While the French mathematician [[Emile Borel|Borel]] did some earlier work on games, von Neumann can rightfully be credited as the inventor of game theory. Von Neumann was a brilliant mathematician whose work was far-reaching from set theory to his calculations that were key to development of both the Atom and Hydrogen bombs and finally to his work developing computers. Von Neumann's work culminated in the 1944 book ''The Theory of Games and Economic Behavior'' by von Neumann and [[Oskar Morgenstern]]. This profound work contains the method for finding optimal solutions for two-person zero-sum games.  During this time period, work on game theory was primarily focused on [[cooperative game]] theory, which analyzes optimal strategies for groups of individuals, presuming that they can enforce agreements between them about proper strategies.
 
In 1950, the first discussion of the [[Prisoner's dilemma]] appeared, and an experiment was undertaken on this game at the [[RAND corporation]]. Around this same time, [[John Forbes Nash|John Nash]] developed a definition of an "optimum" strategy for multiplayer games where no such optimum was previously defined, known as [[Nash equilibrium]]. This equilibrium is sufficiently general, allowing for the analysis of [[non-cooperative game]]s in addition to cooperative ones.
 
Game theory experienced a flurry of activity in the 1950s, during which time the concepts of the [[core (economics)|core]], the [[extensive form game]], [[fictitious play]], [[repeated game]]s, and the [[Shapley value]] were developed. In addition, the first applications of Game theory to [[philosophy]] and [[political science]] occurred during this time.
 
In 1965, [[Reinhard Selten]] introduced his [[solution concept]] of [[subgame perfect equilibrium|subgame perfect equilibria]], which further refined the [[Nash equilibrium]] (later he would introduce [[trembling hand perfection]] as well). In 1967, [[John Harsanyi]] developed the concepts of [[complete information]] and [[Bayesian game]]s.  He, along with John Nash and Reinhard Selten, won the [[Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel]] in 1994.
 
In the 1970s, game theory was extensively applied in [[biology]], largely as a result of the work of [[John Maynard Smith]] and his [[evolutionary stable strategy]].  In addition, the concepts of [[correlated equilibrium]], trembling hand perfection, and [[Common knowledge (logic)|common knowledge]]<ref>Although common knowledge was first discussed by the philosopher [[David Lewis]] in his dissertation (and later book) ''Convention'' in the late 1960s, it was not widely considered by economists until [[Robert Aumann]]'s work in the 1970s.</ref> were introduced and analyzed. 
 
In 2005, game theorists [[Thomas Schelling]] and [[Robert Aumann]] won the [[Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel|Bank of Sweden Prize in Economic Sciences]].  Schelling worked on dynamic models, early examples of [[evolutionary game theory]]. Aumann contributed more to the [[solution concept|equilibrium school]], developing an equilibrium coarsening correlated equilibrium and developing extensive analysis of the assumption of [[Common knowledge (logic)|common knowledge]].
 
==Notes==
 
<references/>
 
==References==
;Textbooks and general reference texts
 
* Bierman, H. S. and L. Fernandez: ''Game Theory with economic applications'', Addison-Wesley, 1998. (suitable for upper-level undergraduates)
* Fudenberg, Drew and [[Jean Tirole]]: ''Game Theory'', MIT Press, 1991, ISBN 0262061414 (the definitive reference text)
* Dutta, Prajit: ''Strategies and Games: Theory and Practice'', MIT Press, 2000, ISBN 0262041693 (suitable for undergraduate and business students)
* Gibbons, Robert (1992): ''Game Theory for Applied Economists'', Princeton University Press ISBN 0691003955 (suitable for advanced undergraduates. Published in Europe by Harvester Wheatsheaf (London) with the title ''A primer in game theory'')
* Gintis, Herbert (2000): ''Game Theory Evolving'',  Princeton University Press ISBN 0691009430
* Osborne, Martin J.: ''An Introduction to Game Theory'', Oxford University Press, New York, 2004, ISBN 0-19-512895-8 (undergraduate textbook)
* Osborne, Martin J. and [[Ariel Rubinstein]]: ''A Course in Game Theory'', MIT Press, 1994, ISBN 0-262-65040-1 (a modern introduction at the graduate level)
* Rasmusen, Erik: ''Games and information'', 4th edition, Blackwell, 2006. Available online [http://www.rasmusen.org/GI/index.html].
* Mas-Colell, Whinston and Green (1995): '' Microeconomic Theory'', 1995. Oxford University Press, 1995, ISBN0-19-507340-1. (Presents game theory in formal way suitable for graduate level)
;Historically important texts
 
* [[Ronald Fisher|Fisher, Ronald]] (1930) ''[[The Genetical Theory of Natural Selection]]'' Clarendon Press, Oxford.
* Luce, Duncan and Howard Raiffa ''Games and Decisions: Introduction and Critical Survey'' Dover ISBN 0486659437
* [[John Maynard Smith|Maynard Smith, John]] ''[[Evolution and the Theory of Games]]'', Cambridge University Press 1982
* [[Oskar Morgenstern|Morgenstern, Oskar]] and [[John von Neumann]] (1947) ''The Theory of Games and Economic Behavior'' Princeton University Press
* [[John Forbes Nash|Nash, John]] (1950)  "Equilibrium points in n-person games" ''Proceedings of the National Academy of the USA'' 36(1):48-49.
* Poundstone, William ''Prisoner's Dilemma: [[John von Neumann]], Game Theory and the Puzzle of the Bomb'', ISBN 038541580X
 
;Other print references
 
* Camerer, Colin  (2003) ''Behavioral Game Theory'' Princeton University Press ISBN 0691090394
* [[David Gauthier|Gauthier, David]] (1987) ''Morals by Agreement'' Oxford University Press ISBN 0198249926
* Grim, Patrick, Trina Kokalis, Ali Alai-Tafti, Nicholas Kilb, and Paul St Denis (2004) "Making meaning happen."  ''Journal of Experimental & Theoretical Artificial Intelligence'' 16(4): 209-243.
* Kavka, Gregory  (1986) ''Hobbesian Moral and Political Theory''  Princeton University Press. ISBN 069102765X
* [[David Lewis|Lewis, David]] (1969) ''Convention: A Philosophical Study''
* [[John Maynard Smith|Maynard Smith]], J. and Harper, D. (2003) ''Animal Signals''. Oxford University Press. ISBN 0198526857
* [[W.V.O. Quine|Quine, W.v.O]] (1967) "Truth by Convention" in ''Philosophica Essays for A.N. Whitehead'' Russel and Russel Publishers.  ISBN 0846209705
* Quine, W.v.O (1960) "Carnap and Logical Truth"  ''Synthese''  12(4):350-374.
* Skyrms, Brian (1996)  ''Evolution of the Social Contract'' Cambridge University Press. ISBN 0521555833
* Skyrms, Brian (2004) ''The Stag Hunt and the Evolution of Social Structure'' Cambridge University Press.  ISBN 0521533929.
* Sober, Elliot and David Sloan Wilson (1999) ''Unto Others: The Evolution and Psychology of Unselfish Behavior''  Harvard University Press. ISBN 0674930479
* Sober, Elliot and David Sloan Wilson (1999) ''Unto Others: The Evolution and Psychology of Unselfish Behavior''  Harvard University Press. ISBN 0674930479
 
;Websites
 
*Yale Economic Review: [http://www.yaleeconomicreview.com/issues/spring2006/gametheory.php The Rise of Game Theory].
* Paul Walker: [http://www.econ.canterbury.ac.nz/personal_pages/paul_walker/gt/hist.htm History of Game Theory Page].
* David Levine: [http://dklevine.com Game Theory. Papers, Lecture Notes and much more stuff.]
* Alvin Roth: [http://www.economics.harvard.edu/~aroth/alroth.html Game Theory and Experimental Economics page] - Comprehensive list of links to game theory information on the Web
* Mike Shor: [http://www.gametheory.net Game Theory .net] - Lecture notes, interactive illustrations and other information.
* Jim Ratliff's [http://virtualperfection.com/gametheory/ Graduate Course in Game Theory] (lecture notes).
* [http://homepages.cwi.nl/~robu/ Valentin Robu's] [http://homepages.cwi.nl/~robu/aamas/aamas_demo.html software tool] for simulation of bilateral negotiation (bargaining)
* Don Ross: [http://plato.stanford.edu/entries/game-theory/ Review Of Game Theory].
* Bruno Verbeek and Christopher Morris: [http://plato.stanford.edu/entries/game-ethics/ Game Theory and Ethics]
* Chris Yiu's [http://www.yiu.co.uk/gametheory/ Game Theory Lounge]
* Elmer G. Wiens: [http://www.egwald.com/operationsresearch/gameintroduction.php Game Theory] - Introduction, worked examples, play online two-person zero-sum games.
* [http://www.socialcapitalgateway.org/eng-gametheory.htm Web sites on game theory and social interactions]
 
 
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Latest revision as of 12:24, 14 October 2018

= "Game Theory is the science of logical decision making in humans, animals, and computers".: "We now have mathematical and theoretical approaches to predict how people will act, given certain adversarial conditions." [1]


Context

Game Theory is often used to discuss the nature of human cooperation.

See our entries on the Prisoner's Dilemman and the Assurance Game

Our interest is focused on Cooperative Game Theory and the calculation and distribution of cooperative surplus.‎


Description

From the Wikipedia at http://en.wikipedia.org/wiki/Game_theory:

"Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. First developed as a tool for understanding economic behavior and then by the RAND Corporation to define nuclear strategies, game theory is now used in many diverse academic fields, ranging from biology and psychology to sociology and philosophy. Beginning in the 1970s, game theory has been applied to animal behavior, including species' development by natural selection. Because of interesting games like the prisoner's dilemma, in which rational self-interest hurts everyone, game theory has been used in political science, ethics and philosophy. Finally, game theory has recently drawn attention from computer scientists because of its use in artificial intelligence and cybernetics." (http://en.wikipedia.org/wiki/Game_theory)


Applications

"* In public policy, game theory is used to predict how nations will act and react.

  • In war, game theory is used to predict the moves of the opponent.
  • In cryptography, game theory is used to predict potential cyberattacks.
  • In token design, game theory is used to predict the actions of token-holders in response to embedded incentives.
  • In financial markets, game theory is used to predict stock market decisions

Typology

Cooperative vs Non-Cooperative Games

Kyle Birchard:

"Cooperative Games: Imagine an interaction for which it is the case that everything that both is affected by the actions of the players and is of concern to any of the players is subject to binding (meaning costlessly enforceable) agreement. This is termed a cooperative game. The term does not refer to the feelings of the parties about each other but simply to the institutional arrangements governing their interactions.

Non-cooperative Games: More commonly, however, something about the interaction is not subject to binding agreement. Such situations are modeled as noncooperative games.

Notice how this doesn’t necessarily refer to the ability or desire to cooperate, Cooperative Games simply refer to the enforcement level found in binding vs non-binding agreements.

In the social arrangement between an employer and employee, part of the interaction may be addressed cooperatively, as when an employer and an employee bargain over a wage and working hours. Other aspects of the same interaction may be noncooperative because of the impossibility of writing or enforcing the relevant contracts.

Examples include how hard the worker works or whether the employer will invest the resulting profits back into the company. When the employer is measuring productivity, he/she plays a cooperative game if he/she has a ticker at the door that tracks when the employee walks in and out. However, if the employer can’t verify the quality of work or effort put in, then the game is non-cooperative.

In technology jobs, and inside startups especially, it’s often difficult and costly to track worker productivity at work → making it a non-cooperative game. This is why we hear so often about ‘company culture’ and establishing a common ‘mission’. When an employer has no way enforce certain agreements, and rational employees can slack off without repercussions, therefore a narrative of ‘culture’ is used to imprint made-up social contracts.

Most commonly, social interactions are categorized based on whether the game representing it is cooperative or noncooperative and whether the payoffs of the game are common interest or conflict." (https://medium.com/blockchannel/cryptoeconomic-theory-game-theory-basics-fb3a49aab1a8)

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