 0500AD
 The Babylonian Talmud is the compilation of ancient law and tradition set down during the first five centuries A.D. which serves as the basis of Jewish religious, criminal and civil law. One problem discussed in the Talmud is the so
called marriage contract problem: a man has three wives whose marriage contracts specify that in the case of this death they receive 100, 200 and 300 respectively. The Talmud gives apparently contradictory recommendations. Where the man dies leaving an estate of only 100, the Talmud recommends equal division. However, if the estate is worth 300 it recommends proportional division (50,100,150), while for an estate of 200, its recommendation of (50,75,75) is a complete mystery. This particular Mishna has baffled Talmudic scholars for two millennia. In 1985, it was recognised that the Talmud anticipates the modern theory of cooperative games. Each solution corresponds to the nucleolus of an appropriately defined game.
 1713
 In a letter dated 13 November 1713 Francis Waldegrave provided the first, known, minimax mixed strategy solution to a twoperson game. Waldegrave wrote the letter, about a twoperson version of the card game le Her, to
PierreRemond de Montmort who in turn wrote to Nicolas Bernoulli, including in his letter a discussion of the Waldegrave solution. Waldegrave's solution is a minimax mixed strategy equilibrium, but he made no extension of his result to other games, and expressed concern that a mixed strategy "does not seem to be in the usual rules of play" of games of chance
 1838
 Publication of Augustin Cournot's Researches into the Mathematical Principles of the Theory of Wealth. In chapter 7, On the Competition of Producers, Cournot discusses the special case of duopoly and utilises a solution concept that
is a restricted version of the Nash equilibrium
 1871
 In the first edition of his book The Descent of Man, and Selection in Relation to Sex Charles Darwin gives the first (implicitly) game theoretic argument in evolutionary biology. Darwin argued that natural section will act to equalize the sex ratio. If, for example, births of females are less common than males, then a newborn female will have better mating prospects than a newborn male and therefore can expect to have more offspring. Thus parents genetically disposed to produce females tend to have more than the average numbers of grandchildren and thus the genes for femaleproducing tendencies spread, and female births become commoner. As the 1:1 sex ratio is approached, the advantage associated with producing females dies away. The same reasoning holds if males are substituted for females throughout. Therefore 1:1 is the equilibrium ratio.
 1881
 Publication of Francis Ysidro Edgeworth's Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences. Edgeworth proposed the contract curve as a solution to the problem of determining the
outcome of trading between individuals. In a world of two commodities and two types of consumers he demonstrated that the contract curve shrinks to the set of competitive equilibria as the number of consumers of each type becomes infinite. The concept of the core is a generalisation of Edgeworth's contract curve.
 1913
 The first 'theorem' of game theory asserts that in chess either white can force a win, or black can force a win, or both sides can force at least a draw. This 'theorem' was published by Ernst Zermelo in his paper Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels and hence is referred to as Zermelo's Theorem. Zermelo's results were extended and generalised in two papers by Denes Konig and Laszlo Kalmar. The Kalmar paper contains the first proof of Zermelo's theorem since Zermelo's own paper did not give one. An English translation of the Zermelo paper, along with a discussion its significance and its relationship to the work of Konig and Kalmar is contained in Zermelo and the Early History of Game Theory by U. Schwalbe and P. Walker.
 192127
 Emile Borel published four notes on strategic games and an erratum to one of them. Borel gave the first modern formulation of a mixed strategy along with finding the minimax solution for twoperson games with three or five possible
strategies. Initially he maintained that games with more possible strategies would not have minimax solutions, but by 1927, he considered this an open question as he had been unable to find a counterexample.
 1928
 John von Neumann proved the minimax theorem in his article Zur Theorie der Gesellschaftsspiele. It states that every two person zerosum game with finitely many pure strategies for each player is determined, ie: when mixed strategies are admitted, this variety of game has precisely one individually rational payoff vector. The proof makes involved use of some topology and of functional calculus. This paper also introduced the extensive form of a game.
 1930
 Publication of F. Zeuthen's book Problems of Monopoly and Economic Warfare. In chapter IV he proposed a solution to the bargaining problem which Harsanyi later showed is equivalent to Nash's bargaining solution.
 1934
 R.A. Fisher independently discovers Waldegrave's solution to the card game le Her. Fisher reported his work in the paper Randomisation and an Old Enigma of Card Play.
 1938
 Ville gives the first elementary, but still partially topological, proof of the minimax theorem. Von Neumann and Morgenstern's (1944) proof of the theorem is a revised, and more elementary, version of Ville's proof.
 1944
 Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern is published. As well as expounding twoperson zero sum theory this book is the seminal work in areas of game theory such as the notion of a
cooperative game, with transferable utility (TU), its coalitional form and its von NeumannMorgenstern stable sets. It was also the account of axiomatic utility theory given here that led to its wide spread adoption within economics.
 1945
 Herbert Simon writes the first review of von NeumannMorgenstern.
 1946
 The first entirely algebraic proof of the minimax theorem is due to L. H. Loomis's, On a Theorem of von Neumann, paper.
 1950
 Contributions to the Theory of Games I, H. W. Kuhn and A. W. Tucker eds., published.
 1950
 In January 1950 Melvin Dresher and Merrill Flood carry out, at the Rand Corporation, the experiment which introduced the game now known as the Prisoner's Dilemma. The famous story associated with this game is due to A. W. Tucker, A TwoPerson Dilemma, (memo, Stanford University). Howard Raiffa independently conducted, unpublished, experiments with the Prisoner's Dilemma.
 1950
 John McDonald's Strategy in Poker, Business and War published. This was the first introduction to game theory for the general reader.
 195053
 Extensive form games allow the modeller to specify the exact order in which players have to make their decisions and to formulate the assumptions about the information possessed by the players in all stages of the game. In two papers, Extensive Games (1950) and Extensive Games and the Problem of Information (1953), H. W. Kuhn included the formulation of extensive form games which is currently used, and also some basic theorems pertaining to this class of games.
 195053
 In four papers between 1950 and 1953 John Nash made seminal contributions to both noncooperative game theory and to bargaining theory. In two papers, Equilibrium Points in N Person Games (1950) and Noncooperative Games (1951), Nash proved the existence of a strategic equilibrium for noncooperative gamesthe Nash equilibriumand proposed the "Nash program", in which he suggested approaching the study of cooperative games via their reduction to noncooperative form. In his two papers on bargaining theory, The Bargaining Problem (1950) and TwoPerson Cooperative Games (1953), he founded axiomatic bargaining theory, proved the existence of the Nash bargaining solution and provided the first execution of the Nash program.
 1951
 George W. Brown described and discussed a simple iterative method for approximating solutions of discrete zerosum games in his paper Iterative Solutions of Games by Fictitious Play.
 1952
 The first textbook on game theory was John Charles C. McKinsey, Introduction to the Theory of Games.
 1952
 Merrill Flood's report, (Rand Corporation research memorandum, Some Experimental Games, RM789, June), on the 1950 Dresher/Flood experiments appears.
 1952
 The Ford Foundation and the University of Michigan sponsor a seminar on the "Design of Experiments in Decision Processes" in Santa Monica. This was the first experimental economics/experimental game theory conference
 195253
 The notion of the Core as a general solution concept was developed by L. S. Shapley (Rand Corporation research memorandum, Notes on the NPerson Game III: Some Variants of the vonNeumannMorgenstern Definition of Solution, RM 817, 1952) and D. B. Gillies (Some Theorems on NPerson Games, Ph.D. thesis, Department of Mathematics, Princeton University, 1953). The core is the set of allocations that cannot be improved upon by any coalition.
 1953
 Lloyd Shapley in his paper A Value for NPerson Games characterised, by a set of axioms, a solution concept that associates with each coalitional game,v, a unique outcome, v. This solution in now known as the Shapley Value.
 1953
 Lloyd Shapley's paper Stochastic Games showed that for the strictly competitive case, with future payoff discounted at a fixed rate, such games are determined and that they have optimal strategies that depend only on the game being played, not on the history or even on the date, ie: the strategies are stationary.
 1953
 Contributions to the Theory of Games II, H. W. Kuhn and A. W. Tucker eds., published.
 1954
 One of the earliest applications of game theory to political science is L. S. Shapley and M. Shubik with their paper A Method for Evaluating the Distribution of Power in a Committee System. They use the Shapley value to
determine the power of the members of the UN Security Council.
 195455
 Differential Games were developed by Rufus Isaacs in the early 1950s. They grew out of the problem of forming and solving military pursuit games. The first publications in the area were Rand Corporation research memoranda, by Isaacs, RM1391 (30 November 1954), RM1399 (30 November 1954), RM1411 (21 December 1954) and RM1486 (25 March 1955) all entitled, in part, Differential Games.
 1955
 One of the first applications of game theory to philosophy is R. B. Braithwaite's Theory of Games as a Tool for the Moral Philosopher.
 1957
 Games and Decisions: Introduction and Critical Survey by Robert Duncan Luce and Howard Raiffa published.
 1957
 Contributions to the Theory of Games III, M. A. Dresher, A. W. Tucker and P. Wolfe eds., published.
 1959
 The notion of a Strong Equilibrium was introduced by R. J. Aumann in the paper Acceptable Points in General Cooperative NPerson Games.
 1959
 The relationship between Edgeworth's idea of the contract curve and the core was pointed out by Martin Shubik in his paper Edgeworth Market Games. One limitation with this paper is that Shubik worked within the confines of TU games whereas Edgeworth's idea is more appropriately modelled as an NTU game.
 1959
 Contributions to the Theory of Games IV, A. W. Tucker and R. D. Luce eds., published.
 1959
 Publication of Martin Shubik's Strategy and Market Structure: Competition, Oligopoly, and the Theory of Games. This was one of the first books to take an explicitly noncooperative game theoretic approach to modelling oligopoly. It also contains an early statement of the Folk Theorem.
 Late 50's
 Near the end of this decade came the first studies of repeated games. The main
result to appear at this time was the Folk Theorem. This states that the equilibrium outcomes
in an infinitely repeated game
coincide with the feasible and strongly individually rational outcomes of the oneshot game
on which it is based. Authorship of the theorem is obscure.
 1960
 The development of NTU (nontransferable utility) games made cooperative game
theory more widely applicable. Von Neumann and Morgenstern stable sets were investigated
in the NTU context in the Aumann and Peleg paper Von Neumann and
Morgenstern Solutions to Cooperative Games Without Side Payments.
 1960
 Publication of Thomas C. Schelling's The Strategy of
Conflict. It is in this book that Schelling introduced the idea of a focalpoint
effect.
 1961
 The first explicit application to evolutionary biology was by R. C. Lewontin in Evolution and the Theory of Games.
 1961
 The Core was extended to NTU games by R. J. Aumann in his paper The Core of a Cooperative Game Without Side Payments.
 1962
 In their paper College Admissions and the Stability of
Marriage, D. Gale and L. Shapley asked whether it is possible to match m women
with m men so that there is no pair consisting of a woman and a man who prefer each other
to the partners with whom they are currently matched. Game theoretically the question is,
does the appropriately defined NTU coalitional game have a nonempty core? Gale and
Shapley proved not only nonemptiness but also provided an algorithm for finding a point in
it.
 1962
 One of the first applications of game theory to cost allocation is Martin Shubik's
paper Incentives, Decentralized Control, the Assignment of Joint Costs
and Internal Pricing. In this paper Shubik argued that the Shapley value could be used
to provide a means of devising incentivecompatible cost assignments and internal pricing in
a firm with decentralised decision making.
 1962
 An early use of game theory in insurance is Karl Borch's paper Application of Game Theory to Some Problems in Automobile
Insurance. The article indicates how game theory can be applied to determine
premiums for different classes of insurance, when required total premium for all classes is
given. Borch suggests that the Shapley value will give reasonable premiums for all classes of
risk.
 1963
 O. N. Bondareva established that for a TU game its core is nonempty iff it is
balanced. The reference, which is in Russian, translates as Some Applications of Linear
Programming Methods to the Theory of Cooperative Games.
 1963
 In their paper A Limit Theorem on the Core of an
Economy G. Debreu and H. Scarf generalised Edgeworth, in the context of a NTU
game, by allowing an arbitrary number of commodities and an arbitrary but finite number of
types of traders.
 1964
 Robert J. Aumann further extended Edgeworth by assuming that the agents
constitute a (nonatomic) continuum in his paper Markets with a
Continuum of Traders.
 1964
 The idea of the Bargaining Set was introduced and discussed in the paper by R. J.
Aumann and M. Maschler, The Bargaining Set for Cooperative
Games. The bargaining set includes the core but unlike it, is never empty for TU
games.
 1964
 Carlton E. Lemke and J.T. Howson, Jr., describe an algorithm for finding a Nash
equilibrium in a bimatrix game, thereby giving a constructive proof of the existence of an
equilibrium point, in their paper Equilibrium Points in Bimatrix
Games. The paper also shows that, except for degenerate situations, the number of
equilibria in a bimatrix game is odd.
 1965
 Publication of Rufus Isaacs's Differential Games: A
Mathematical Theory with Applications to Warfare and Pursuit, Control and
Optimization.
 1965
 R. Selten, Spieltheoretische Behandlung eines Oligopolmodells
mit Nachfragetraegheit. In this article Selten introduced the idea of refinements of the
Nash equilibrium with the concept of (subgame) perfect equilibria.
 1965
 The concept of the Kernel is due to M. Davis and M. Maschler, The Kernel of a Cooperative Game. The kernel is always included in
the bargaining set but is often much smaller.
 1966
 Infinitely repeated games with incomplete information were born in a paper by R. J.
Aumann and M. Maschler, GameTheoretic Aspects of Gradual
Disarmament.
 1966
 In his paper A General Theory of Rational Behavior in Game
Situations John Harsanyi gave the, now, most commonly used definition to distinguish
between cooperative and noncooperative games. A game is cooperative if
commitmentsagreements, promises, threatsare fully binding and enforceable. It is
noncooperative if commitments are not enforceable.
 1967
 Lloyd Shapley, independently of O.N. Bondareva, showed that the core of a TU
game is nonempty iff it is balanced in his paper On Balanced Sets and
Cores.
 1967
 In the articleThe Core of a NPerson Game, H. E. Scarf
extended the notion of balancedness to NTU games, then showed that every balanced NTU
game has a nonempty core.
 196768
 In a series of three papers, Games with Incomplete Information
Played by 'Bayesian' Players, Parts I, II and III, John Harsanyi constructed the
theory of games of incomplete information. This laid the theoretical groundwork for
information economics that has become one of the major themes of economics and game
theory.
 1968
 The longstanding question as to whether stable sets always exist was answered in the
negative by William Lucas in his paper A Game with no
Solution.
 1969
 David Schmeidler introduced the Nucleolus in this paper The
Nucleolus of a Characteristic Game. The Nucleolus always exists, is unique, is a
member of the Kernel and for any non empty core is always in it.
 1969
 Shapley defined a value for NTU games in his article Utility
Comparison and the Theory of Games.
 1969
 For a coalitional game to be a market game it is necessary that it and all its
subgames have nonempty cores, ie: that the game be totally balanced. In Market Games L. S. Shapley and Martin Shubik prove that this
necessary condition is also sufficient.
 1972
 International Journal of Game Theory was founded by Oskar Morgenstern.
 1972
 The concept of an Evolutionarily Stable Strategy (ESS), was introduced to
evolutionary game theory by John Maynard Smith in an essay Game
Theory and The Evolution of Fighting. The ESS concept has since found increasing
use within the economics (and biology!) literature.
 1973
 In the traditional view of strategy randomization, the players use a randomising
device to decide on their actions. John Harsanyi was the first to break away from this view
with his paper Games with Randomly Disturbed Payoffs: A New
Rationale for Mixed Strategy Equilibrium Points. For Harsanyi nobody really
randomises. The appearance of randomisation is due to the payoffs not being exactly known
to all; each player, who knows his own payoff exactly, has a unique optimal action against
his estimate of what the others will do.
 1973
 The major impetus for the use of the ESS concept was the publication of J. Maynard
Smith and G. Price's paper The Logic of Animal Conflict.
 1973
 The revelation principle can be traced back to Gibbard's paper Manipulation of Voting Schemes: A General Result
 1974
 Publication of R. J. Aumann and L. S. Shapley's book Values
of NonAtomic Games. It deals with values for large games in which all the players
are individually insignificant (nonatomic games).
 1974
 R. J. Aumann proposed the concept of a correlated equilibrium in his paper Subjectivity and Correlation in Randomized Strategies.
 1975
 The introduction of trembling hand perfect equilibria occurred in the paper Reexamination of the Perfectness Concept for Equilibrium Points in
Extensive Games by Reinhard Selten. This paper was the true catalyst for the
'refinement industry' that has developed around the Nash equilibrium.
 1975
 E. Kalai and M. Smorodinsky, in their article Other Solutions
to Nash's Bargaining Problem, replace Nash's independence of irrelevant alternatives
axiom with a monotonicity axiom. The resulting solution is known as the KalaiSmorodinsky
solution.
 1975
 In his paper CrossSubsidization: Pricing in Public
Enterprises, G. Faulhaber shows that the set of subsidyfree prices are those prices for
which the resulting revenue (ri = piqi for given demand levels qi) vector lies in the core of
the cost allocation game.
 1976
 An event is common knowledge among a set of agents if all know it and all know
that they all know it and so on ad infinitum. Although the idea first appeared in the work of
the philosopher D. K. Lewis in the late 1960s it was not until its
formalisation in Robert Aumann's Agreeing to Disagree that
game theorists and economists came to fully appreciate its importance.
 1977
 S. C. Littlechild and G. F. Thompson are among the first to apply the nucleolus to
the problem of cost allocation with their article Aircraft Landing Fees:
A Game Theory Approach. They use the nucleolus, along with the core and Shapley
value, to calculate fair and efficient landing and takeoff fees for Birmingham airport.
 1981
 Elon Kohlberg introduced the idea of forward induction in a conference paper Some Problems with the Concept of Perfect Equilibria.
 1981
 R. J. Aumann published a Survey of Repeated Games.
This survey firstly proposed the idea of applying the notion of an automaton to describe a
player in a repeated game. A second idea from the survey is to study the interactive
behaviour of bounded players by studying a game with appropriately restricted set of
strategies. These ideas have given birth to a large and growing literature.
 1982
 David M. Kreps and Robert Wilson extend the idea of a subgame perfect equilibrium
to subgames in the extensive form that begin at information sets with imperfect information.
They call this extended idea of equilibrium sequential. It is detailed in their paper Sequential Equilibria.
 1982
 A. Rubinstein considered a noncooperative approach to bargaining in his paper Perfect Equilibrium in a Bargaining Model. He considered an
alternatingoffer game were offers are made sequentially until one is accepted. There is no
bound on the number of offers that can be made but there is a cost to delay for each player.
Rubinstein showed that the subgame perfect equilibrium is unique when each player's cost of
time is given by some discount factor delta.
 1982
 Publication of Evolution and the Theory of Games by
John Maynard Smith.
 1984
 Following the work of Gale and Shapley, A. E. Roth applied the core to the problem
of the assignment of interns to hospitals. In his paper The Evolution of
the Labour Market for Medical Interns and Residents: A Case Study in Game Theory
he found that American hospitals developed in 1950 a method of assignment that is a point in
the core.
 1984
 The idea of a rationalizability was introduced in two papers; B. D. Bernheim, Rationalizable Strategic Behavior and D. G. Pearce, Rationalizable Strategic Behavior and the Problem of
Perfection.
 1984
 Publication of The Evolution of Cooperation by Robert
Axelrod.
 1985
 For a Bayesian game the question arises as to whether or not it is possible to construct a
situation for which there is no sets of types large enough to contain all the private information
that players are supposed to have. In their paper, Formulation of Bayesian
Analysis for Games with Incomplete Information, J.F. Mertens and S. Zamir show that
it is not possible to do so.
 198586
 Following Aumann, the theory of automata is now being used to formulate the idea
of bounded rationality in repeated games. Two of the first articles to take this approach were
A. Neyman's 1985 paper Bounded Complexity Justifies Cooperation in
the Finitely Repeated Prisoner's Dilemma and A. Rubinstein's 1986 article Finite Automata Play the Repeated Prisoner's Dilemma.
 1986
 In their paper On the Strategic Stability of Equilibria
Elon Kohlberg and JeanFrancois Mertens deal with the problem of he refinement of Nash
equilibria in the normal form, rather than the extensive form of a game as with the Selten
and Kreps and Wilson papers. This paper is also one of the first, published, discussions of
the idea of forward induction.
 1988
 John C. Harsanyi and Reinhard Selten produced the first general theory of selecting
between equilibria in their book A General Theory of Equilibrium
Selection in Games. They provide criteria for selecting one particular equilibrium
point for any noncooperative or cooperative game.
 1988
 With their paper The Bayesian Foundations of Solution Concepts of
Games Tan and Werlang are among the first to formally discuss the assumptions about a
player's knowledge that lie behind the concepts of Nash equilibria and rationalizability.
 1988
 One interpretation of the Nash equilibrium is to think of it as an accepted (learned)
'standard of behaviour' which governs the interaction of various agents in repetitions of
similar situations. The problem then arises of how agents learn the equilibrium. One of the
earliest works to attack the learning problem was Drew Fudenberg and David Kreps's A
Theory of Learning, Experimentation and Equilibria, (MIT and Stanford Graduate School of
Business, unpublished), which uses an learning process similar to Brown's fictitious play,
except that player occasionally experiment by choosing strategies at random, in the context of
iterated extensive form games. Evolutionary game models are also commonly utilised within
the learning literature.
 1989
 The journal Games and Economic Behavior founded.
 1990
 The first graduate level microeconomics textbook to fully integrate game theory into
the standard microeconomic material was David M. Krep's A Course
in Microeconomic Theory.
 1990
 In the article Equilibrium without Independence Vincent
Crawford discusses mixed strategy Nash equilibrium when the players preferences do not
satisfy the assumptions necessary to be represented by expected utility functions.
 1991
 An early published discussion of the idea of a Perfect Bayesian Equilibrium is the
paper by D. Fudenberg and J. Tirole, Perfect Bayesian Equilibrium and
Sequential Equilibrium.
 1992
 Publication of the Handbook of Game Theory with Economic Applications, Volume 1 edited by Robert J. Aumann and Sergiu Hart.
 1994
 Game Theory and the Law by Douglas G. Baird, Robert H. Gertner and Randal C. Picker is one of the first books in law and economics to take an explicitly game theoretic approach to the subject.
 1994
 Publication of the Handbook of Game Theory with Economic Applications, Volume 2 edited by Robert J. Aumann and Sergiu Hart.
 1994
 The Sveriges Riksbank (Bank of Sweden) Prize in Economic Sciences in Memory of Alfred Nobel was award to John Nash, John C. Harsanyi and Reinhard Selten "for their pioneering analysis of equilibria in the theory of noncooperative games".
 2002
 Publication of the Handbook of Game Theory with Economic Applications, Volume 3 edited by Robert J. Aumann and Sergiu Hart.
 2005
 The Sveriges Riksbank (Bank of Sweden) Prize in Economic Sciences in Memory of Alfred Nobel was award to Robert J. Aumann and Thomas C. Schelling "for having enhanced our understanding of conflict and cooperation through gametheory analysis".
 2012
 The Sveriges Riksbank (Bank of Sweden) Prize in Economic Sciences in Memory of Alfred Nobel was award to Alvin E. Roth
and Lloyd S. Shapley "for the theory of stable allocations and the practice of market design".
