Extensive-form game
An extensive-form game is a specification of a game in game theory, allowing for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the information each player has about the other player's moves when they make a decision, their payoffs for all possible game outcomes. Extensive-form games allow for the representation of incomplete information in the form of chance events modeled as "moves by nature"; some authors in introductory textbooks define the extensive-form game as being just a game tree with payoffs, add the other elements in subsequent chapters as refinements. Whereas the rest of this article follows this gentle approach with motivating examples, we present upfront the finite extensive-form games as constructed here; this general definition was introduced by Harold W. Kuhn in 1953, who extended an earlier definition of von Neumann from 1928. Following the presentation from Hart, an n-player extensive-form game thus consists of the following: A finite set of n players A rooted tree, called the game tree Each terminal node of the game tree has an n-tuple of payoffs, meaning there is one payoff for each player at the end of every possible play A partition of the non-terminal nodes of the game tree in n+1 subsets, one for each player, with a special subset for a fictitious player called Chance.
Each player's subset of nodes is referred to as the "nodes of the player". Each node of the Chance player has a probability distribution over its outgoing edges; each set of nodes of a rational player is further partitioned in information sets, which make certain choices indistinguishable for the player when making a move, in the sense that: there is a one-to-one correspondence between outgoing edges of any two nodes of the same information set—thus the set of all outgoing edges of an information set is partitioned in equivalence classes, each class representing a possible choice for a player's move at some point—, every path in the tree from the root to a terminal node can cross each information set at most once the complete description of the game specified by the above parameters is common knowledge among the playersA play is thus a path through the tree from the root to a terminal node. At any given non-terminal node belonging to Chance, an outgoing branch is chosen according to the probability distribution.
At any rational player's node, the player must choose one of the equivalence classes for the edges, which determines one outgoing edge except the player doesn't know which one is being followed. A pure strategy for a player thus consists of a selection—choosing one class of outgoing edges for every information set. In a game of perfect information, the information sets are singletons. It's less evident, it is assumed that each player has a von Neumann–Morgenstern utility function defined for every game outcome. The above presentation, while defining the mathematical structure over which the game is played, elides however the more technical discussion of formalizing statements about how the game is played like "a player cannot distinguish between nodes in the same information set when making a decision"; these can be made precise using epistemic modal logic. A perfect information two-player game over a game tree can be represented as an extensive form game with outcomes. Examples of such games include tic-tac-toe and infinite chess.
A game over an expectminimax tree, like that of backgammon, has no imperfect information but has moves of chance. For example, poker has both moves of imperfect information. A complete extensive-form representation specifies: the players of a game for every player every opportunity they have to move what each player can do at each of their moves what each player knows for every move the payoffs received by every player for every possible combination of moves The game on the right has two players: 1 and 2; the numbers by every non-terminal node indicate. The numbers by every terminal node represent the payoffs to the players; the labels by every edge of the graph are the name of the action. The initial node belongs to player 1. Play according to the tree is as follows: player 1 chooses between U and D; the payoffs are as specified in the tree. There are four outcomes represented by the four terminal nodes of the tree:, and; the payoffs associated with each outcome are as follows, and. If player 1 plays D, player 2 will play U' to maximise their payoff and so player 1 will only receive 1.
However, if player 1 plays U, player 2 maximises their payoff by playing D' and player 1 receives 2. Player 1 prefers 2 to 1 and s
Discounting
Discounting is a financial mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. The party that owes money in the present purchases the right to delay the payment until some future date; the discount, or charge, is the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt. The discount is associated with a discount rate, called the discount yield; the discount yield is the proportional share of the initial amount owed that must be paid to delay payment for 1 year. Discount yield = Charge to delay payment for 1 year debt liability Since a person can earn a return on money invested over some period of time, most economic and financial models assume the discount yield is the same as the rate of return the person could receive by investing this money elsewhere over the given period of time covered by the delay in payment; the concept is associated with the opportunity cost of not having use of the money for the period of time covered by the delay in payment.
The relationship between the discount yield and the rate of return on other financial assets is discussed in economic and financial theories involving the inter-relation between various market prices, the achievement of Pareto optimality through the operations in the capitalistic price mechanism, as well as in the discussion of the efficient market hypothesis. The person delaying the payment of the current liability is compensating the person to whom he/she owes money for the lost revenue that could be earned from an investment during the time period covered by the delay in payment. Accordingly, it is the relevant "discount yield" that determines the "discount", not the other way around; as indicated, the rate of return is calculated in accordance to an annual return on investment. Since an investor earns a return on the original principal amount of the investment as well as on any prior period investment income, investment earnings are "compounded" as time advances. Therefore, considering the fact that the "discount" must match the benefits obtained from a similar investment asset, the "discount yield" must be used within the same compounding mechanism to negotiate an increase in the size of the "discount" whenever the time period of the payment is delayed or extended.
The "discount rate" is the rate at which the "discount" must grow as the delay in payment is extended. This fact is directly tied into the time value of its calculations; the "time value of money" indicates there is a difference between the "future value" of a payment and the "present value" of the same payment. The rate of return on investment should be the dominant factor in evaluating the market's assessment of the difference between the future value and the present value of a payment. Therefore, the "discount yield", predetermined by a related return on investment, found in the financial markets, is what is used within the time-value-of-money calculations to determine the "discount" required to delay payment of a financial liability for a given period of time. If we consider the value of the original payment presently due to be P, the debtor wants to delay the payment for t years an r market rate of return on a similar investment asset means the future value of P is P t, the discount would be calculated as Discount = P t − P where r is the discount yield.
If F is a payment that will be made t years in the future the "present value" of this payment called the "discounted value" of the payment, is P = F t To calculate the present value of a single cash flow, it is divided by one plus the interest rate for each period of time that will pass. This is expressed mathematically as raising the divisor to the power of the number of units of time. Consider the task to find the present value PV of $100 that will be received in five years, or equivalently, to find which amount of money today will grow to $100 in five years when subject to a constant discount rate. Assuming a 12% per year interest rate, it follows that P V = $100 5 = $56.74. The discount rate, used in financial calculations is chosen to be equal to the cost of capital; the cost of capital, in a financial market equilibrium, will be the same as the market rate of return on the financial asset mixture the firm uses to finance capital investment. Some adjustment may be made to the discount rate to take account of risks associated with uncertain cash flows, with other developments.
The discount rates applied to different types of companies show significant differences: Start-ups seeking money: 50–100% Early start-ups: 40–60% Late start-ups: 30–50% Mature companies: 10–25%The higher discount rate for start-ups reflects the various disadvantages they f
Robert Aumann
Robert John Aumann is an Israeli-American mathematician, a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem in Israel, he holds a visiting position at Stony Brook University, is one of the founding members of the Stony Brook Center for Game Theory. Aumann received the Nobel Memorial Prize in Economic Sciences in 2005 for his work on conflict and cooperation through game-theory analysis, he shared the prize with Thomas Schelling. Aumann was born in Frankfurt am Main and fled to the United States with his family in 1938, two weeks before the Kristallnacht pogrom, he attended a yeshiva high school in New York City. He graduated from the City College of New York in 1950 with a B. Sc. in Mathematics. He received his M. Sc. in 1952, his Ph. D. in Mathematics both from the Massachusetts Institute of Technology. His doctoral dissertation, Asphericity of Alternating Linkages, concerned knot theory, his advisor was Jr..
In 1956 he joined the Mathematics faculty of the Hebrew University of Jerusalem and has been a visiting professor at Stony Brook University since 1989. He has held visiting professorship at the University of California, Stanford University, Universite Catholique de Louvain. Aumann's greatest contribution was in the realm of repeated games, which are situations in which players encounter the same situation over and over again. Aumann was the first to define the concept of correlated equilibrium in game theory, a type of equilibrium in non-cooperative games, more flexible than the classical Nash equilibrium. Furthermore, Aumann has introduced the first purely formal account of the notion of common knowledge in game theory, he collaborated with Lloyd Shapley on the Aumann–Shapley value. He is known for his agreement theorem, in which he argues that under his given conditions, two Bayesian rationalists with common prior beliefs cannot agree to disagree. Aumann and Maschler used game theory to analyze Talmudic dilemmas.
They were able to solve the mystery about the "division problem", a long-standing dilemma of explaining the Talmudic rationale in dividing the heritage of a late husband to his three wives depending on the worth of the heritage compared to its original worth. The article in that matter was dedicated to a son of Aumann, killed during the 1982 Lebanon War, while serving as a tank gunner in the Israel Defense Forces's armored corps; these are some of the themes of Aumann's Nobel lecture, named "War and Peace": War is not irrational, but must be scientifically studied in order to be understood, conquered. Aumann is a member in the Professors for a right-wing political group. Aumann opposed the disengagement from Gaza in 2005 claiming it is a crime against Gush Katif settlers and a serious threat to the security of Israel. Aumann draws on a case in game theory called the Blackmailer Paradox to argue that giving land to the Arabs is strategically foolish based on the mathematical theory. By presenting an unyielding demand, the Arab states force Israel to "yield to blackmail due to the perception that it will leave the negotiating room with nothing if it is inflexible".
As a result of his political views, his use of his research to justify them, the decision to give him the Nobel prize was criticized in the European press. A petition to cancel his prize garnered signatures from 1,000 academics worldwide. In a speech to a religious Zionist youth movement, Bnei Akiva, Aumann claimed that Israel is in "deep trouble", he revealed his belief that the anti-Zionist Satmar Jews might have been right in their condemnation of the original Zionist movement. "I fear the Satmars were right", he said, quoted a verse from Psalm 127: "Unless the Lord builds a house, its builders toil on it in vain." Aumann feels that the historical Zionist establishment failed to transmit its message to its successors, because it was secular. The only way that Zionism can survive, according to Aumann, is. In 2008, Aumann joined the new political party Ahi led by Yitzhak Levy. Aumann has entered the controversy of Bible codes research. In his position as both a religious Jew and a man of science, the codes research holds special interest to him.
He has vouched for the validity of the "Great Rabbis Experiment" by Doron Witztum, Eliyahu Rips, Yoav Rosenberg, published in Statistical Science. Aumann not only arranged for Rips to give a lecture on Torah codes in the Israel Academy of Sciences and Humanities, but sponsored the Witztum-Rips-Rosenberg paper for publication in the Proceedings of the National Academy of Sciences; the Academy requires a member to sponsor any publication in its Proceedings. In 1996, a committee consisting of Robert J. Aumann, Dror Bar-Natan, Hillel Furstenberg, Isaak Lapides, Rips, was formed to examine the results, reported by H. J. Gans regarding the existence of "encoded" text in the bible foretelling events that took place many years after the Bible was written; the committee performed two additional tests in the spirit of the Gans experiments. Both tests failed to confirm the existence of the putative code. After a long analysis of the experiment and the dynamics of the controversy, stating for example that "almost everybody included made up thei
Game theory
Game theory is the study of mathematical models of strategic interaction between rational decision-makers. It has applications in all fields of social science, as well as in computer science, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, is now an umbrella term for the science of logical decision making in humans and computers. Modern game theory began with the idea regarding the existence of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics, his paper was followed by the 1944 book Theory of Games and Economic Behavior, co-written with Oskar Morgenstern, which considered cooperative games of several players. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.
Game theory was developed extensively in the 1950s by many scholars. It was explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been recognized as an important tool in many fields; as of 2014, with the Nobel Memorial Prize in Economic Sciences going to game theorist Jean Tirole, eleven game theorists have won the economics Nobel Prize. John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology. 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, uncle to James Waldegrave, a British diplomat, in 1713. In this letter, Waldegrave provides a minimax mixed strategy solution to a two-person version of the card game le Her, the problem is now known as Waldegrave problem. In his 1838 Recherches sur les principes mathématiques de la théorie des richesses, Antoine Augustin Cournot considered a duopoly and presents a solution, a restricted version of the Nash equilibrium.
In 1913, Ernst Zermelo published Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels. It proved that the optimal chess strategy is determined; this paved the way for more general theorems. In 1938, the Danish mathematical economist Frederik Zeuthen proved that the mathematical model had a winning strategy by using Brouwer's fixed point theorem. In his 1938 book Applications aux Jeux de Hasard and earlier notes, Émile Borel proved a minimax theorem for two-person zero-sum matrix games only when the pay-off matrix was symmetric. Borel conjectured that non-existence of mixed-strategy equilibria in two-person zero-sum games would occur, a conjecture, proved false. Game theory did not exist as a unique field until John von Neumann published the paper On the Theory of Games of Strategy in 1928. Von Neumann's original proof used Brouwer's fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics, his paper was followed by his 1944 book Theory of Games and Economic Behavior co-authored with Oskar Morgenstern.
The second edition of this book provided an axiomatic theory of utility, which reincarnated Daniel Bernoulli's old theory of utility as an independent discipline. Von Neumann's work in game theory culminated in this 1944 book; this foundational work contains the method for finding mutually consistent solutions for two-person zero-sum games. During the following time period, work on game theory was 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 mathematical discussion of the prisoner's dilemma appeared, an experiment was undertaken by notable mathematicians Merrill M. Flood and Melvin Dresher, as part of the RAND Corporation's investigations into game theory. RAND pursued the studies because of possible applications to global nuclear strategy. Around this same time, John Nash developed a criterion for mutual consistency of players' strategies, known as Nash equilibrium, applicable to a wider variety of games than the criterion proposed by von Neumann and Morgenstern.
Nash proved that every n-player, non-zero-sum non-cooperative game has what is now known as a Nash equilibrium. Game theory experienced a flurry of activity in the 1950s, during which time the concepts of the core, the extensive form game, fictitious play, repeated games, the Shapley value were developed. In addition, the first applications of game theory to philosophy and political science occurred during this time. In 1979 Robert Axelrod tried setting up computer programs as players and found that in tournaments between them the winner was a simple "tit-for-tat" program that cooperates on the first step on subsequent steps just does whatever its opponent did on the previous step; the same winner was often obtained by natural selection. In 1965, Reinhard Selten introduced his solution concept of subgame perfect equilibria, which further refined the Nash equilibrium. In 1994 Nash and Harsanyi became Economics Nobel Laureates for their contributi
Jean-François Mertens
Jean-François Mertens was a Belgian game theorist and mathematical economist. Mertens contributed to economic theory in regards to order-book of market games, cooperative games, noncooperative games, repeated games, epistemic models of strategic behavior, refinements of Nash equilibrium. In cooperative game theory he contributed to the solution concepts called the core and the Shapley value. Regarding repeated games and stochastic games, Mertens 1982 and 1986 survey articles, his 1994 survey co-authored with Sylvain Sorin and Shmuel Zamir, are compendiums of results on this topic, including his own contributions. Mertens made contributions to probability theory and published articles on elementary topology. Mertens and Zamir implemented John Harsanyi's proposal to model games with incomplete information by supposing that each player is characterized by a known type that describes his feasible strategies and payoffs as well as a probability distribution over other players' types, they constructed a universal space of types in which, subject to specified consistency conditions, each type corresponds to the infinite hierarchy of his probabilistic beliefs about others' probabilistic beliefs.
They showed that any subspace can be approximated arbitrarily by a finite subspace, the usual tactic in applications. Repeated games with incomplete information, were pioneered by Maschler. Two of Jean-François Mertens's contributions to the field are the extensions of repeated two person zero-sum games with incomplete information on both sides for both the type of information available to players and the signalling structure. Information: Mertens extended the theory from the independent case where the private information of the players is generated by independent random variables, to the dependent case where correlation is allowed. Signalling structures: the standard signalling theory where after each stage both players are informed of the previous moves played, was extended to deal with general signalling structure where after each stage each player gets a private signal that may depend on the moves and on the state. In those set-ups Jean-François Mertens provided an extension of the characterization of the minmax and maxmin value for the infinite game in the dependent case with state independent signals.
Additionally with Shmuel Zamir, Jean-François Mertens showed the existence of a limiting value. Such a value can be thought either as the limit of the values v n of the n stage games, as n goes to infinity, or the limit of the values v λ of the λ -discounted games, as agents become more patient and λ → 1. A building block of Mertens and Zamir's approach is the construction of an operator, now referred to as the MZ operator in the field in their honor. In continuous time, the MZ operator becomes an infinitesimal operator at the core of the theory of such games. Unique solution of a pair of functional equations and Zamir showed that the limit value may be a transcendental function unlike the maxmin or the minmax. Mertens found the exact rate of convergence in the case of game with incomplete information on one side and general signalling structure. A detailed analysis of the speed of convergence of the n-stage game value to its limit has profound links to the central limit theorem and the normal law, as well as the maximal variation of bounded martingales.
Attacking the study of the difficult case of games with state dependent signals and without recursive structure and Zamir introduced new tools on the introduction based on an auxiliary game, reducing down the set of strategies to a core that is'statistically sufficient.'Collectively Jean-François Mertens's contributions with Zamir provide the foundation for a general theory for two person zero sum repeated games that encompasses stochastic and incomplete information aspects and where concepts of wide relevance are deployed as for example reputation, bounds on rational levels for the payoffs, but tools like splitting lemma and approachability. While in many ways Mertens's work here goes back to the von Neumann original roots of game theory with a zero-sum two person set up, vitality and innovations with wider application have been pervasive. Stochastic games were introduced by Lloyd Shapley in 1953; the first paper studied the discounted two-person zero-sum stochastic game with finitely many states and actions and demonstrates the existence of a value and stationary optimal strategies.
The study of the undiscounted case evolved in the following three decades, with solutions of special cases by Blackwell and Ferguson in 1968 and Kohlberg in 1974. The existence of an undiscounted value in a strong sense, both a uniform value and a limiting average value, was proved in 1981 by Jean-François Mertens and Abraham Neyman; the study of the non-zero-sum with a general state and action spaces attracted much attention, Mertens and Parthasarathy proved a general existence result under the condition that the transitions, as a function of the state and actions, are norm continuous in the actions. Mertens had the idea to use linear competitive economies as an order book to model limit orders and generalize double auctions to a multivariate set up. Acceptable relative prices of players are conveyed by their linear preferences, money can be one of the goods
Public goods game
The public goods game is a standard of experimental economics. In the basic game, subjects secretly choose how many of their private tokens to put into a public pot; the tokens in this pot are multiplied by a factor and this "public good" payoff is evenly divided among players. Each subject keeps the tokens they do not contribute; the group's total payoff is maximized when everyone contributes all of their tokens to the public pool. However, the Nash equilibrium in this game is zero contributions by all; this only holds if the multiplication factor is less than the number of players, otherwise the nash equilibrium is for all players to contribute all of their tokens to the public pool. In fact, the Nash equilibrium is seen in experiments; the actual levels of contribution found. The average contribution depends on the multiplication factor. Capraro has proposed a new solution concept for social dilemmas, based on the idea that players forecast if it is worth to act cooperatively and they act cooperatively in a rate depending on the forecast.
His model indeed predicts increasing level of cooperation as the multiplication factor increases. Depending on the experiment's design, those who contribute below average or nothing are called "defectors" or "free riders", as opposed to the contributors or above average contributors who are called "cooperators". "Repeat-play" public goods games involve the same group of subjects playing the basic game over a series of rounds. The typical result is a declining proportion of public contribution, from the simple game; when trusting contributors see that not everyone is giving up as much as they do they tend to reduce the amount they share in the next round. If this is again repeated the same thing happens but from a lower base, so that the amount contributed to the pot is reduced again. However, the amount contributed to the pool drops to zero when rounds of the game are iterated, because there tend to remain a hard core of ‘givers’. One explanation for the dropping level of contribution is inequity aversion.
During repeated games players learn their co-player's inequality aversion in previous rounds on which future beliefs can be based. If players receive a bigger share for a smaller contribution the sharing members react against the perceived injustice; those who contribute nothing in one round contribute something in rounds after discovering that others are. Transparency about past choices and payoffs of group members affects future choices. Studies show individuals in groups can be influenced by the group leaders, whether formal or informal, to conform or defect. Players signal their intentions through transparency which allows “conditional operators” to follow the lead. If players are informed of individual payoffs of each member of the group it can lead to a dynamic of players adopting the strategy of the player who benefited the most in the group; this can lead a drop in cooperation through subsequent iterations of the game. However, if the amount contributed by each group member is not hidden, the amount contributed tends to be higher.
The finding is robust in different experiment designs: Whether in "pairwise iterations" with only two players or in nominations after the end of the experiment. The option to punish non-contributors and to reward the highest contributions after a round of the public goods game has been the issue of many experiments. Findings suggest that non-rewarding is not seen as sanction, while rewards don't substitute punishment. Rather they are used differently as a means to enforce cooperation and higher payoffs. Punishing is exercised at a cost, in most experiments it leads to greater group cooperation. However, since punishment is costly, it tends to lead to lower payoffs, at least initially. On the other hand, a 2007 study found. Many studies therefore emphasize the combination of punishment and rewards; the combination seems to yield both a higher level of cooperation and of payoffs. This holds for iterated games in changing groups as well as in identical groups. Asymmetric cost and or benefit functions have direct influence in the contribution behaviour of agents.
When confronted with different payoff returns to their contributions, agents behave differently though they still contribute more than in Nash equilibrium. A public goods games variant suggested as an improvement for researching the free rider problem is one in which endowment are earned as income; the standard game allows no work effort variation and cannot capture the marginal substitutions among three factors: private goods, public goods, leisure. Researchers have found that in an experiment where an agent’s wealth at the end of period t serves as her endowment in t+1, the amounts contributed increase over time in the absences of punishment strategies. A different framing of the original neutral experiment setting induces players to act differently because they associate different real-life situations. For example, a public good experiment could be presented as a climate negotiation or as contributions to private parties; the effect of associations (l
Jean Tirole
Jean Tirole is a French professor of economics. He focuses on industrial organization, game theory and finance, economics and psychology. In 2014 he was awarded the Nobel Memorial Prize in Economic Sciences for his analysis of market power and regulation. Tirole received engineering degrees from the École Polytechnique in Paris in 1976, from the École nationale des ponts et chaussées in 1978, he graduated as a member of the elite Corps of Bridges and Forests. Tirole pursued graduate studies at the Paris Dauphine University and was awarded a DEA degree in 1976 and a Doctorat de troisième cycle in decision mathematics in 1978. In 1981, he received a Ph. D. in economics from the Massachusetts Institute of Technology for his thesis titled Essays in economic theory, under the supervision of Eric Maskin. Tirole is chairman of the board of the Jean-Jacques Laffont Foundation at the Toulouse School of Economics, scientific director of the Industrial Economics Institute at Toulouse 1 University Capitole.
After receiving his doctorate from MIT in 1981, he worked as a researcher at the École nationale des ponts et chaussées until 1984. From 1984–1991, he worked as Professor of Economics at MIT, his work by 1988 helped to define modern industrial organization theory by organising and synthesising the main results of the game-theory revolution vis-à-vis understanding of non-competitive markets. From 1994 to 1996 he was a Professor of Economics at the École Polytechnique. Tirole was involved with Jean-Jacques Laffont in the project of creating a new School of Economics in Toulouse, he is Engineer General of the Corps of Bridges and Forest, serving as Chair of the Board of the Toulouse School of Economics, Visiting Professor at MIT and Professor "cumulant" at the École des hautes études en sciences sociales since 1995. He was president of the Econometric Society in 1998 and of the European Economic Association in 2001. Around this time, he was able to determine a way to calculate the optimal prices for the regulation of natural monopolies and wrote a number of articles about the regulation of capital markets—with a focus on the differential of control between decentralised lenders and the centralised control of bank management.
Tirole has been a member of the Académie des Sciences morales et politiques since 2011, the Conseil d'analyse économique since 2008 and the Conseil stratégique de la recherché since 2013. In the early 2010s, he showed that banks tend to take short-term risks and recommended a change in quantitative easing towards a more quality-based market stimulation policy. Tirole authored the famous textbook The Theory of Industrial Organization, which synthesised modern models of oligopolistic competition, analysing various cases where industries consist of a small number of firms, with significant market power, he and Oliver Hart published a paper showing the conditions in which a vertical merger can result in foreclosure. Rochet and Tirole analysed the implications of 2-sided markets for competition policy. Fundenberg and Tirole created a taxonomy of strategic effects in oligopolistic competition models. Tirole was awarded the Nobel Memorial Prize in Economic Sciences in 2014 for his analysis of market power and the regulation of natural monopolies.
Tirole received doctorates honoris causa from the Université libre de Bruxelles in 1989, the London Business School and the University of Montreal in 2007, the University of Mannheim in 2011, the Athens University of Economics and Business and the University of Rome Tor Vergata in 2012 as well as the University of Lausanne in 2013. Tirole received the inaugural BBVA Foundation Frontiers of Knowledge Award in the Economics and Management category in 2008, the Public Utility Research Center Distinguished Service Award in 1997, the Yrjö Jahnsson Award of the Yrjö Jahnsson Foundation and the European Economic Association in 1993, he is a foreign honorary member of the American Academy of Arts and Sciences and of the American Economic Association. He has been a Sloan Fellow and a Guggenheim Fellow, he was a fellow of the Econometric Society in 1986 and an Economic Theory Fellow in 2011. In 2013 Tirole was elected an Honorary Fellow of the Royal Society of Edinburgh. In 2007 he was awarded the highest award of the French CNRS.
In 2008, he received the Prix du Cercle d'Oc. He is among the most influential economists in the world according to IDEAS/RePEc. Besides his numerous academic distinctions, he was the recipient of the Gold Medal of the city of Toulouse in 2007, a Chevalier de la Légion d'honneur since 2007 and an Officer in the Ordre national du Mérite since 2010. Tirole has published about 200 professional articles in economics and finance, as well as 10 books, including The Theory of Industrial Organization, Game Theory, A Theory of Incentives in Procurement and Regulation, The Prudential Regulation of Banks, Competition in Telecommunications, Financial Crises and the International Monetary System, The Theory of Corporate Finance, his research covers industrial organization, game theory, public economics and finance, psychology and economics, international finance and macroeconomics. Dy