Contents 1 History 1.1 Prize-winning achievements 2 Game types 2.1
3 Representation of games 3.1 Extensive form 3.2 Normal form 3.3 Characteristic function form 4 General and applied uses 4.1 Description and modeling
4.2 Prescriptive or normative analysis
4.3
5 In popular culture 6 See also 7 Notes 8 References and further reading 8.1 Textbooks and general references 8.2 Historically important texts 8.3 Other print references 9 External links History[edit]
John von Neumann
John Nash
Early discussions of examples of two-person games occurred long before
the rise of modern, mathematical game theory. The first known
discussion of game theory occurred in a letter written by Charles
Waldegrave, an active Jacobite, and uncle to James Waldegrave, a
British diplomat, in 1713.[2] In this letter, Waldegrave
provides a minimax mixed strategy solution to a two-person version of
the card game le Her, and the problem is now known as Waldegrave
problem. In his 1838 Recherches sur les principes mathématiques de la
théorie des richesses (Researches into the Mathematical Principles of
the Theory of Wealth),
Prize-winning achievements[edit]
In 1965,
Game types[edit]
Symmetric / asymmetric[edit] E F E 1, 2 0, 0 F 0, 0 1, 2 An asymmetric game Main article: Symmetric game 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 2×2 games are symmetric. The standard representations of chicken, the prisoner's dilemma, and the stag hunt are all symmetric games. Some[who?] 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. Zero-sum / non-zero-sum[edit] A B A –1, 1 3, –3 B 0, 0 –2, 2 A zero-sum game Main article: Zero-sum game
Zero-sum games are a special case of constant-sum games, in which
choices by players can neither increase nor decrease the available
resources. In zero-sum games the total benefit to all players in the
game, for every combination of strategies, always adds to zero (more
informally, a player benefits only at the equal expense of
others).[11]
Simultaneous / sequential[edit]
Main articles:
Sequential Simultaneous Normally denoted by Decision trees Payoff matrices Prior knowledgeof opponent's move? Yes No Time axis? Yes No Also known as Extensive-form gameExtensive game Strategy gameStrategic game
Combinatorial games[edit] Games in which the difficulty of finding an optimal strategy stems from the multiplicity of possible moves are called combinatorial games. Examples include chess and go. Games that involve imperfect information may also have a strong combinatorial character, for instance backgammon. There is no unified theory addressing combinatorial elements in games. There are, however, mathematical tools that can solve particular problems and answer general questions.[18] Games of perfect information have been studied in combinatorial game theory, which has developed novel representations, e.g. surreal numbers, as well as combinatorial and algebraic (and sometimes non-constructive) proof methods to solve games of certain types, including "loopy" games that may result in infinitely long sequences of moves. These methods address games with higher combinatorial complexity than those usually considered in traditional (or "economic") game theory.[19][20] A typical game that has been solved this way is hex. A related field of study, drawing from computational complexity theory, is game complexity, which is concerned with estimating the computational difficulty of finding optimal strategies.[21] Research in artificial intelligence has addressed both perfect and imperfect information games that have very complex combinatorial structures (like chess, go, or backgammon) for which no provable optimal strategies have been found. The practical solutions involve computational heuristics, like alpha–beta pruning or use of artificial neural networks trained by reinforcement learning, which make games more tractable in computing practice.[18][22] Infinitely long games[edit] Main article: Determinacy Games, as studied by economists and real-world game players, are generally finished in finitely many moves. Pure mathematicians are not so constrained, and 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. The focus of attention is usually not so much on the best way to play such a game, but whether one player has a winning strategy. (It can be proven, using the axiom of choice, that there are games – even with perfect information and where the only outcomes are "win" or "lose" – for which neither player has a winning strategy.) The existence of such strategies, for cleverly designed games, has important consequences in descriptive set theory. Discrete and continuous games[edit]
Much of game theory is concerned with finite, discrete games, that
have a finite number of players, moves, events, outcomes, etc. Many
concepts can be extended, however. Continuous games allow players to
choose a strategy from a continuous strategy set. For instance,
Differential games[edit] Differential games such as the continuous pursuit and evasion game are continuous games where the evolution of the players' state variables is governed by differential equations. The problem of finding an optimal strategy in a differential game is closely related to the optimal control theory. In particular, there are two types of strategies: the open-loop strategies are found using the Pontryagin maximum principle while the closed-loop strategies are found using Bellman's Dynamic Programming method. A particular case of differential games are the games with a random time horizon.[23] In such games, the terminal time is a random variable with a given probability distribution function. Therefore, the players maximize the mathematical expectation of the cost function. It was shown that the modified optimization problem can be reformulated as a discounted differential game over an infinite time interval. Evolutionary game theory[edit]
Stochastic outcomes (and relation to other fields)[edit]
Individual decision problems with stochastic outcomes are sometimes
considered "one-player games". These situations are not considered
game theoretical by some authors.[by whom?] They may be
modeled using similar tools within the related disciplines of decision
theory, operations research, and areas of artificial intelligence,
particularly
Metagames[edit] These are games the play of which is the development of the rules for another game, the target or subject game. Metagames seek to maximize the utility value of the rule set developed. The theory of metagames is related to mechanism design theory. The term metagame analysis is also used to refer to a practical approach developed by Nigel Howard.[28] whereby a situation is framed as a strategic game in which stakeholders try to realise their objectives by means of the options available to them. Subsequent developments have led to the formulation of confrontation analysis. Pooling games[edit] These are games prevailing over all forms of society. Pooling games are repeated plays with changing payoff table in general over an experienced path and their equilibrium strategies usually take a form of evolutionary social convention and economic convention. Pooling game theory emerges to formally recognize the interaction between optimal choice in one play and the emergence of forthcoming payoff table update path, identify the invariance existence and robustness, and predict variance over time. The theory is based upon topological transformation classification of payoff table update over time to predict variance and invariance, and is also within the jurisdiction of the computational law of reachable optimality for ordered system.[29] Mean field game theory[edit]
Representation of games[edit] See also: List of games in game theory The games studied in game theory are well-defined mathematical objects. To be fully defined, a game must specify the following elements: the players of the game, the information and actions available to each player at each decision point, and the payoffs for each outcome. (Eric Rasmusen refers to these four "essential elements" by the acronym "PAPI".)[30] A game theorist typically uses these elements, along with a solution concept of their choosing, to deduce a set of equilibrium strategies for each player such that, when these strategies are employed, no player can profit by unilaterally deviating from their strategy. These equilibrium strategies determine an equilibrium to the game—a stable state in which either one outcome occurs or a set of outcomes occur with known probability. Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games. Extensive form[edit] Main article: Extensive form game An extensive form game The extensive form can be used to formalize games with a time sequencing of moves. Games here are played on trees (as pictured here). 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. The extensive form can be viewed as a multi-player generalization of a decision tree.[31] To solve any extensive form game, backward induction must be used. It involves working backward up the game tree to determine what a rational player would do at the last vertex of the tree, what the player with the previous move would do given that the player with the last move is rational, and so on until the first vertex of the tree is reached.[32] The game pictured consists of two players. The way this particular game is structured (i.e., with sequential decision making and perfect information), Player 1 "moves" first by choosing either F or U (Fair or Unfair). Next in the sequence, Player 2, who has now seen Player 1's move, chooses to play either A or R. Once Player 2 has made his/ her choice, the game is considered finished and each player gets their respective payoff. Suppose that Player 1 chooses U and then Player 2 chooses A: Player 1 then gets a payoff of "eight" (which in real-world terms can be interpreted in many ways, the simplest of which is in terms of money but could mean things such as eight days of vacation or eight countries conquered or even eight more opportunities to play the same game against other players) and Player 2 gets a payoff of "two". The extensive form can also capture simultaneous-move games and games with imperfect information. To represent it, either a dotted line connects 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), or a closed line is drawn around them. (See example in the imperfect information section.) Normal form[edit] Player 2chooses Left Player 2chooses Right Player 1chooses Up 4, 3 –1, –1 Player 1chooses Down 0, 0 3, 4 Normal form or payoff matrix of a 2-player, 2-strategy game Main article: Normal-form game The normal (or strategic form) game is usually represented by a matrix which shows the players, strategies, and payoffs (see the example to the right). More generally it can be represented by any function that associates a payoff for each player with every possible combination of actions. In the accompanying example 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 Up and that Player 2 plays Left. Then Player 1 gets a payoff of 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. Every extensive-form game has an equivalent normal-form game, however the transformation to normal form may result in an exponential blowup in the size of the representation, making it computationally impractical.[33] Characteristic function form[edit]
Main article:
C displaystyle mathbf C appears, it works against the fraction ( N C ) displaystyle left( frac mathbf N mathbf C right) as if two individuals were playing a normal game. The balanced payoff of C is a basic function. Although there are differing examples that help determine coalitional amounts from normal games, not all appear that in their function form can be derived from such. Formally, a characteristic function is seen as: (N,v), where N represents the group of people and v : 2 N → R displaystyle v:2^ N to mathbf R is a normal utility. Such characteristic functions have expanded to describe games where there is no removable utility. General and applied uses[edit]
As a method of applied mathematics, game theory has been used to study
a wide variety of human and animal behaviors. It was initially
developed in economics to understand a large collection of economic
behaviors, including behaviors of firms, markets, and consumers. The
first use of game-theoretic analysis was by Antoine Augustin Cournot
in 1838 with his solution of the Cournot duopoly. The use of game
theory in the social sciences has expanded, and game theory has been
applied to political, sociological, and psychological behaviors as
well.
Although pre-twentieth century naturalists such as
Description and modeling[edit]
A four-stage centipede game
The primary use of game theory is to describe and model how human
populations behave. Some[who?] 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 been
criticized. It is argued that the assumptions made by game theorists
are often violated when applied to real-world situations. Game
theorists usually assume players act rationally, but in practice human
behavior often deviates from this model. 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 ideal akin to the models used by physicists.
However, empirical work has shown that in some classic games, such as
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 and
whether the analysis of the experiments fully captures all aspects of
the relevant situation.[38]
Some game theorists, following the work of
Prescriptive or normative analysis[edit] Cooperate Defect Cooperate -1, -1 -10, 0 Defect 0, -10 -5, -5 The Prisoner's Dilemma 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 strategy, corresponding to a
Political science[edit]
The application of game theory to political science is focused in the
overlapping areas of fair division, political economy, public choice,
war bargaining, positive political theory, and social choice theory.
In each of these areas, researchers have developed game-theoretic
models in which the players are often voters, states, special interest
groups, and politicians.
Early examples of game theory applied to political science are
provided by Anthony Downs. In his book An Economic Theory of
Democracy,[51] he applies the Hotelling firm location model to
the political process. In the Downsian model, political candidates
commit to ideologies on a one-dimensional policy space. Downs first
shows how the political candidates will converge to the ideology
preferred by the median voter if voters are fully informed, but then
argues that voters choose to remain rationally ignorant which allows
for candidate divergence. Game Theory was applied in 1962 to the Cuban
missile crisis during the presidency of John F. Kennedy.[52]
It has also been proposed that game theory explains the stability of
any form of political government. Taking the simplest case of a
monarchy, for example, the king, being only one person, does not and
cannot maintain his authority by personally exercising physical
control over all or even any significant number of his subjects.
Sovereign control is instead explained by the recognition by each
citizen that all other citizens expect each other to view the king (or
other established government) as the person whose orders will be
followed. Coordinating communication among citizens to replace the
sovereign is effectively barred, since conspiracy to replace the
sovereign is generally punishable as a crime. Thus, in a process that
can be modeled by variants of the prisoner's dilemma, during periods
of stability no citizen will find it rational to move to replace the
sovereign, even if all the citizens know they would be better off if
they were all to act collectively.[53]
A game-theoretic explanation for democratic peace is that public and
open debate in democracies sends clear and reliable information
regarding their 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 non-democracy.[54]
On the other hand, game theory predicts that two countries may still
go to war even if their leaders are cognizant of the costs of
fighting. War may result from asymmetric information; two countries
may have incentives to mis-represent the amount of military resources
they have on hand, rendering them unable to settle disputes agreeably
without resorting to fighting. Moreover, war may arise because of
commitment problems: if two countries wish to settle a dispute via
peaceful means, but each wishes to go back on the terms of that
settlement, they may have no choice but to resort to warfare. Finally,
war may result from issue indivisibilities.[55]
Biology[edit] Hawk Dove Hawk 20, 20 80, 40 Dove 40, 80 60, 60 The hawk-dove game Main article: Evolutionary game theory
Unlike those in economics, the payoffs for games in biology are often
interpreted as corresponding to fitness. In addition, the focus has
been less on equilibria that correspond to a notion of rationality and
more on ones that would be maintained by evolutionary forces. The
best-known equilibrium in biology is known as the evolutionarily
stable strategy (ESS), first introduced in (Smith &
Philosophy[edit] Stag Hare Stag 3, 3 0, 2 Hare 2, 0 2, 2 Stag hunt
In popular culture[edit]
Based on the 1998 book by Sylvia Nasar,[74] the life story of
game theorist and mathematician John Nash was turned into the 2001
biopic A Beautiful Mind, starring
Applied ethics Chainstore paradox Chemical game theory Collective intentionality Combinatorial game theory Confrontation analysis Glossary of game theory Intra-household bargaining Kingmaker scenario Law and economics Parrondo's paradox Precautionary principle Quantum game theory Quantum refereed game Rationality Reverse game theory Risk management Self-confirming equilibrium Tragedy of the commons Zermelo's theorem Lists List of cognitive biases List of emerging technologies List of games in game theory Outline of artificial intelligence Notes[edit] ^ a b Myerson, Roger B. (1991). Game Theory: Analysis of Conflict, Harvard University Press, p. 1. Chapter-preview links, pp. vii–xi. ^ Bellhouse, David (2007), "The Problem of Waldegrave" (PDF), Journal Électronique d'Histoire des Probabilités et de la Statistique, 3 (2).mw-parser-output cite.citation font-style:inherit .mw-parser-output .citation q quotes:"""""""'""'" .mw-parser-output .citation .cs1-lock-free a background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center .mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center .mw-parser-output .citation .cs1-lock-subscription a background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center .mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration color:#555 .mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span border-bottom:1px dotted;cursor:help .mw-parser-output .cs1-ws-icon a background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center .mw-parser-output code.cs1-code color:inherit;background:inherit;border:inherit;padding:inherit .mw-parser-output .cs1-hidden-error display:none;font-size:100% .mw-parser-output .cs1-visible-error font-size:100% .mw-parser-output .cs1-maint display:none;color:#33aa33;margin-left:0.3em .mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format font-size:95% .mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left padding-left:0.2em .mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right padding-right:0.2em ^ Screpanti; Ernesto; Zamagni; Stefano (2005). An Outline of the History of Economic Thought' (2nd ed.). Oxford University Press. ^ Kim, Sungwook, ed. (2014).
^ Neumann, J. v. (1928), "Zur Theorie der Gesellschaftsspiele", Mathematische Annalen, 100 (1): 295–320, doi:10.1007/BF01448847 English translation: Tucker, A. W.; Luce, R. D., eds. (1959), "On the Theory of Games of Strategy", Contributions to the Theory of Games, 4, pp. 13–42 ^ Mirowski, Philip (1992). "What Were von Neumann and Morgenstern Trying to Accomplish?". In Weintraub, E. Roy (ed.). Toward a History of Game Theory. Durham: Duke University Press. pp. 113–147. ISBN 978-0-8223-1253-6. ^ Leonard, Robert (2010), Von Neumann, Morgenstern, and the Creation of Game Theory, New York: Cambridge University Press, ISBN 9780521562669 ^ Prisoner's Dilemma. Plato.stanford.edu (4 September 1997). Retrieved on 3 January 2013. ^ Wolfram, Stephen (2002). A New Kind of Science. Wolfram Media, Inc. p. 1104. ISBN 978-1-57955-008-0. ^ 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. ^ Owen, Guillermo (1995). Game Theory: Third Edition. Bingley: Emerald Group Publishing. p. 11. ISBN 978-0-12-531151-9. ^ Ferguson, Thomas S. "Game Theory" (PDF). UCLA Department of Mathematics. pp. 56–57. ^ "Complete vs Perfect Infomation in Combinatorial Game Theory". Stack Exchange. 24 June 2014. ^ Mycielski, Jan (1992). "Games with Perfect Information". Handbook of Game Theory with Economic Applications. Volume 1. pp. 41–70. doi:10.1016/S1574-0005(05)80006-2. ISBN 9780444880987. ^ "Infinite Chess". PBS Infinite Series. 2 March 2017. Perfect information defined at 0:25, with academic sources arXiv:1302.4377 and arXiv:1510.08155. ^ Owen, Guillermo (1995). Game Theory: Third Edition. Bingley: Emerald Group Publishing. p. 4. ISBN 978-0-12-531151-9. ^ Leyton-Brown & Shoham (2008), p. 60. ^ a b
^ Albert, Michael H.; Nowakowski, Richard J.; Wolfe, David (2007), Lessons in Play: In Introduction to Combinatorial Game Theory, A K Peters Ltd, pp. 3–4, ISBN 978-1-56881-277-9 ^ Beck, József (2008), Combinatorial games: tic-tac-toe theory, Cambridge University Press, pp. 1–3, ISBN 978-0-521-46100-9 ^ Robert A. Hearn; Erik D. Demaine (2009), Games, Puzzles, and Computation, A K Peters, Ltd., ISBN 978-1-56881-322-6 ^ M. Tim Jones (2008), Artificial Intelligence: A Systems Approach, Jones & Bartlett Learning, pp. 106–118, ISBN 978-0-7637-7337-3 ^ (in Russian) Petrosjan, L.A. and Murzov, N.V. (1966). Game-theoretic problems of mechanics. Litovsk. Mat. Sb. 6, 423–433. ^ Newton, Jonathan (2018). "Evolutionary Game Theory: A Renaissance". Games. 9 (2): 31. doi:10.3390/g9020031. ^ Webb (2007). ^ Osborne & Rubinstein (1994). ^ a b Hugh Brendan McMahan (2006), Robust Planning in Domains with Stochastic Outcomes, Adversaries, and Partial Observability, CMU-CS-06-166, pp. 3–4 ^ Howard (1971). ^ Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. ISBN 978-1507658246. ^ a b
Eric Rasmusen (2007). Games and Information, 4th ed. Description and
chapter-preview.
^ Fudenberg & Tirole (1991), p. 67. ^ Williams, Paul D. (2013). Security Studies: an Introduction (second edition). 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN: Routledge. pp. 55–56. ^ Leyton-Brown & Shoham (2008), p. 35. ^ "On economic applications of evolutionary game theory" (PDF). J Evol Econ. ^ a b
^ Ross, Don. "Game Theory". The Stanford Encyclopedia of Philosophy (Spring 2008 Edition). Edward N. Zalta (ed.). Retrieved 21 August 2008. ^ Velegol, Darrell; Suhey, Paul; Connolly, John; Morrissey, Natalie; Cook, Laura (14 September 2018). "Chemical Game Theory". Industrial & Engineering Chemistry Research. 57 (41): 13593–13607. doi:10.1021/acs.iecr.8b03835. ISSN 0888-5885. ^ Experimental work in game theory goes by many names, experimental
economics, behavioral economics, and behavioural game theory are
several. For a recent discussion, see
^ • At JEL:C7 of the
^ N. Agarwal and P. Zeephongsekul. Psychological Pricing in Mergers & Acquisitions using Game Theory, School of Mathematics and Geospatial Sciences, RMIT University, Melbourne ^ •
^ • From
^ Brams, Steven J. (1994). Chapter 30 Voting procedures. Handbook of Game Theory with Economic Applications. 2. pp. 1055–1089. doi:10.1016/S1574-0005(05)80062-1. ISBN 9780444894274. and Moulin, Hervé (1994). Chapter 31 Social choice. Handbook of Game Theory with Economic Applications. 2. pp. 1091–1125. doi:10.1016/S1574-0005(05)80063-3. ISBN 9780444894274. ^
Vernon L. Smith, 1992. "Game Theory and Experimental Economics:
Beginnings and Early Influences," in E. R. Weintraub, ed., Towards a
History of Game Theory, pp. 241–282
Smith, V.L. (2001). "Experimental Economics". International
Encyclopedia of the Social & Behavioral Sciences.
pp. 5100–5108. doi:10.1016/B0-08-043076-7/02232-4.
ISBN 9780080430768.
http://www.sciencedirect.com/science/handbooks/15740722. Missing or
empty |title= (help)
Vincent P. Crawford (1997). "Theory and Experiment in the Analysis of
Strategic Interaction," in Advances in
^ From
^ •
^ •
^ •
^ Game-theoretic model to examine the two tradeoffs in the acquisition
of information for a careful balancing act Archived 24 May 2013 at the
^ Options Games: Balancing the trade-off between flexibility and commitment Archived 20 June 2013 at the Wayback Machine. Europeanfinancialreview.com (15 February 2012). Retrieved on 2013-01-03. ^ (Downs 1957) ^ Steven J. Brams,
^ Morrison, A. S. (2013). "Yes, Law is the Command of the Sovereign". doi:10.2139/ssrn.2371076. ^ Levy, G.; Razin, R. (2004). "It Takes Two: An Explanation for the Democratic Peace". Journal of the European Economic Association. 2 (1): 1–29. doi:10.1162/154247604323015463. JSTOR 40004867. ^ Fearon, James D. (1 January 1995). "Rationalist Explanations for War". International Organization. 49 (3): 379–414. doi:10.1017/s0020818300033324. JSTOR 2706903. ^ Wood, Peter John (2011). "Climate change and game theory" (PDF).
Ecological
^ Harper & Maynard Smith (2003). ^ Maynard Smith, J. (1974). "The theory of games and the evolution of animal conflicts" (PDF). Journal of Theoretical Biology. 47 (1): 209–221. doi:10.1016/0022-5193(74)90110-6. PMID 4459582. ^ Evolutionary Game Theory (Stanford Encyclopedia of Philosophy). Plato.stanford.edu. Retrieved on 3 January 2013. ^ a b Biological Altruism (Stanford Encyclopedia of Philosophy). Seop.leeds.ac.uk. Retrieved on 3 January 2013. ^ Yoav Shoham; Kevin Leyton-Brown (15 December 2008). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press. ISBN 978-1-139-47524-2. ^ (Ben David, Borodin & Karp et al. 1994) ^
^ Nisan, Noam; Ronen, Amir (2001), "Algorithmic Mechanism Design" (PDF), Games and Economic Behavior, 35 (1–2): 166–196, CiteSeerX 10.1.1.21.1731, doi:10.1006/game.1999.0790 ^ •
^ (Skyrms (1996), Grim, Kokalis, and Alai-Tafti et al. (2004)). ^ Ullmann-Margalit, E. (1977), The Emergence of Norms, Oxford University Press, ISBN 978-0198244110 ^ Bicchieri, C. (2006), The Grammar of Society: the Nature and Dynamics of Social Norms, Cambridge University Press, ISBN 978-0521573726 ^ Bicchieri, Cristina (1989), "Self-Refuting Theories of Strategic Interaction: A Paradox of Common Knowledge", Erkenntnis, 30 (1–2): 69–85, doi:10.1007/BF00184816 ^ Bicchieri, Cristina (1993),
^ The Dynamics of Rational Deliberation, Harvard University Press, 1990, ISBN 978-0674218857 ^ Bicchieri, Cristina; Jeffrey, Richard; Skyrms, Brian, eds. (1999), "Knowledge, Belief, and Counterfactual Reasoning in Games", The Logic of Strategy, New York: Oxford University Press, ISBN 978-0195117158 ^ For a more detailed discussion of the use of game theory in ethics, see the Stanford Encyclopedia of Philosophy's entry game theory and ethics. ^ Nasar, Sylvia (1998) A Beautiful Mind, Simon & Schuster. ISBN 0-684-81906-6. ^ Singh, Simon (14 June 1998) "Between Genius and Madness", New York Times. ^ Heinlein, Robert A. (1959), Starship Troopers ^ Guzman, Rafer (6 March 1996). "Star on hold: Faithful following, meager sales". Pacific Sun. Archived from the original on 6 November 2013. Retrieved 25 July 2018.. References and further reading[edit] Wikiquote has quotations related to: Game theory Wikimedia
Textbooks and general references[edit]
Aumann, Robert J (1987), "game theory", The New Palgrave: A Dictionary
of Economics, 2, pp. 460–82.
Camerer, Colin (2003), "Introduction", Behavioral Game Theory:
Experiments in Strategic Interaction, Russell Sage Foundation,
pp. 1–25, ISBN 978-0-691-09039-9, Description.
Dutta, Prajit K. (1999), Strategies and games: theory and practice,
MIT Press, ISBN 978-0-262-04169-0. Suitable for undergraduate and
business students.
Fernandez, L F.; Bierman, H S. (1998),
n displaystyle n -person games in partition function form", Naval Research Logistics
Quarterly, 10 (4): 281–298, doi:10.1002/nav.3800100126
Dolev, Shlomi; Panagopoulou, Panagiota; Rabie, Mikael; Schiller, Elad
Michael; Spirakis, Paul (2011), "
Look up game theory in Wiktionary, the free dictionary. Wikiversity has learning resources about Game Theory Wikibooks has a book on the topic of: Introduction to Game Theory James Miller (2015): Introductory Game Theory Videos.
Hazewinkel, Michiel, ed. (2001) [1994], "Games, theory of",
Encyclopedia of Mathematics, Springer Science+Business Media B.V. /
Kluwer Academic Publishers, ISBN 978-1-55608-010-4
Paul Walker: History of Game Theory Page.
David Levine: Game Theory. Papers, Lecture Notes and much more stuff.
Alvin Roth:"Game Theory and Experimental
vteTopics in game theoryDefinitions
vteAreas of mathematicsFoundations
Category Portal Commons WikiProject vteMicroeconomicsMajor topics
Aggregation
Budget set
Consumer choice
Convexity and non-convexity
Cost
Average
Marginal
Opportunity
Social
Sunk
Transaction
Cost–benefit analysis
Deadweight loss
Distribution
Economies of scale
Economies of scope
Elasticity
Equilibrium
General
Exchange
Externality
Firms
Category vtePropertyBy owner
Common
Communal
Community
Crown
Customary
Cooperative
Estate
Private
Public
Self
Social
State
By nature
Croft
Intangible
Intellectual
indigenous
Personal
Tangible
immovable
real
Commons
Common land
Common-pool resource
Digital
Global
Information
Knowledge
Theory
Bundle of rights
Commodity
fictitious commodities
Common good (economics)
Excludability
First possession
appropriation
homestead principle
Free-rider problem
Game theory
Georgism
Gift economy
Labor theory of property
Law of rent
rent-seeking
Legal plunder
Natural rights
Ownership
Categories: Property
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