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Jean-François Mertens
Jean-François Mertens (11 March 1946 – 17 July 2012) 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, and refinements of Nash equilibrium (see solution concept). 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, and his 1994 survey co-authored with Sylvain Sorin and Shmuel Zamir, are compendiums of results on this topic, including his own contributions. Mertens also made contributions to probability theory and published articles on elementary topology. Epistemic models Mertens and Zamir implemented John Harsanyi's proposal to model games with incomplete information by supposing that each player is characterized by a privately known type that describes h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Université Catholique De Louvain
UCLouvain (or Université catholique de Louvain , French for Catholic University of Louvain, officially in English the University of Louvain) is Belgium's largest French-speaking university and one of the oldest in Europe (originally established in 1425). It is located in Louvain-la-Neuve, which was expressly built to house the university, and has smaller campuses in Brussels, Charleroi, Mons, Belgium, Mons, Tournai and Namur. Since September 2018, the university uses the branding UCLouvain, replacing the acronym UCL, following a merger with Saint-Louis University, Brussels. The original Old University of Louvain, University of Louvain (''Universitas Lovaniensis'') was founded at the centre of the historic town of Leuven (or ''Louvain'') in 1425, making it the List of universities in Belgium, first university in Belgium and the Low Countries, and abolished by law in 1797. This university was the centre of Baianism, Jansenism and Febronianism in Europe. A new university, the Stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Harsanyi
John Charles Harsanyi (; May 29, 1920 and August 9, 2000) was a Hungarian-American economist who spent most of his career at the University of California, Berkeley. He was the recipient of the Nobel Memorial Prize in Economic Sciences in 1994. Harsanyi is best known for his contributions to the study of game theory and its application to economics, specifically for his developing the highly innovative analysis of games of incomplete information, so-called Bayesian games. He also made important contributions to the use of game theory and economic reasoning in political and moral philosophy (specifically utilitarian ethics) as well as contributing to the study of equilibrium selection. For his work, he was a co-recipient along with John Nash and Reinhard Selten of the 1994 Nobel Memorial Prize in Economic Sciences. He moved to the United States in 1956, and spent most of his life there. According to György Marx, he was one of The Martians. Early life Harsanyi was born on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Book (trading)
An order book is the list of orders (manual or electronic) that a trading venue (in particular stock exchanges) uses to record the interest of buyers and sellers in a particular financial instrument. A matching engine uses the book to determine which orders can be fully or partially executed. In securities trading In securities trading, an order book contains the list of buy orders and the list of sell orders. For each entry it must keep among others, some means of identifying the party (even if this identification is obscured, as in a dark pool), the number of securities and the price that the buyer or seller are bidding/asking for the particular security. Price levels When several orders contain the same price, they are referred as a price level, meaning that if, say, a bid comes at that price level, all the sell orders on that price level could potentially fulfill that. Crossed book When the order book is part of a matching engine, orders are matched as the interest of buy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The National Academy Of Sciences
''Proceedings of the National Academy of Sciences of the United States of America'' (often abbreviated ''PNAS'' or ''PNAS USA'') is a peer-reviewed multidisciplinary scientific journal. It is the official journal of the National Academy of Sciences, published since 1915, and publishes original research, scientific reviews, commentaries, and letters. According to ''Journal Citation Reports'', the journal has a 2022 impact factor of 9.4. ''PNAS'' is the second most cited scientific journal, with more than 1.9 million cumulative citations from 2008 to 2018. In the past, ''PNAS'' has been described variously as "prestigious", "sedate", "renowned" and "high impact". ''PNAS'' is a delayed open-access journal, with an embargo period of six months that can be bypassed for an author fee ( hybrid open access). Since September 2017, open access articles are published under a Creative Commons license. Since January 2019, ''PNAS'' has been online-only, although print issues are available ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lloyd Shapley
Lloyd Stowell Shapley (; June 2, 1923 – March 12, 2016) was an American mathematician and Nobel Memorial Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally considered one of the most important contributors to the development of game theory since the work of von Neumann and Morgenstern. With Alvin E. Roth, Shapley won the 2012 Nobel Memorial Prize in Economic Sciences "for the theory of stable allocations and the practice of market design." Life and career Lloyd Shapley was born on June 2, 1923, in Cambridge, Massachusetts, one of the sons of astronomers Harlow Shapley and Martha Betz Shapley, both from Missouri. He attended Phillips Exeter Academy and was a student at Harvard when he was drafted in 1943. He served in the United States Army Air Corps in Chengdu, China and received the Bronze Star decoration for breaking the Soviet weather code. After the war, Shapley returned to Harvard and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martingale (probability Theory)
In probability theory, a martingale is a stochastic process in which the expected value of the next observation, given all prior observations, is equal to the most recent value. In other words, the conditional expectation of the next value, given the past, is equal to the present value. Martingales are used to model fair games, where future expected winnings are equal to the current amount regardless of past outcomes. History Originally, ''martingale (betting system), martingale'' referred to a class of betting strategy, betting strategies that was popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins their stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double their bet after every loss so that the first win would recover all previous losses plus win a profit equal to the original stake. As the gambler's wealth and available time jointly approach infinity, their pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Limit Theorem
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the Probability distribution, distribution of a normalized version of the sample mean converges to a Normal distribution#Standard normal distribution, standard normal distribution. This holds even if the original variables themselves are not Normal distribution, normally distributed. There are several versions of the CLT, each applying in the context of different conditions. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern form it was only precisely stated as late as 1920. In statistics, the CLT can be stated as: let X_1, X_2, \dots, X_n denote a Sampling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcendental Function
In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the independent variable that can be written using only the basic operations of addition, subtraction, multiplication, and division (without the need of taking limits). This is in contrast to an algebraic function. Examples of transcendental functions include the exponential function, the logarithm function, the hyperbolic functions, and the trigonometric functions. Equations over these expressions are called transcendental equations. Definition Formally, an analytic function f of one real or complex variable is transcendental if it is algebraically independent of that variable. This means the function does not satisfy any polynomial equation. For example, the function f given by :f(x)=\frac for all x is not transcendental, but algebraic, because it satisfies the polynomial equation :(ax+b)-(cx+d)f(x)=0. Similarly, the functio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Of Operations Research
''Mathematics of Operations Research'' is a quarterly peer-reviewed scientific journal established in February 1976. It focuses on areas of mathematics relevant to the field of operations research such as continuous optimization, discrete optimization, game theory, machine learning, simulation methodology, and stochastic models. The journal is published by INFORMS (Institute for Operations Research and the Management Sciences). the journal has a 2017 impact factor of 1.078. History The journal was established in 1976. The founding editor-in-chief was Arthur F. Veinott Jr. (Stanford University). He served until 1980, when the position was taken over by Stephen M. Robinson, who held the position until 1986. Erhan Cinlar served from 1987 to 1992, and was followed by Jan Karel Lenstra (1993-1998). Next was Gérard Cornuéjols (1999-2003) and Nimrod Megiddo (2004-2009). Finally came Uri Rothblum (2009-2012), Jim Dai (2012-2018), and the current editor-in-chief Katya Scheinberg (20 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Game
In game theory, differential games are dynamic games that unfold in continuous time, meaning players’ actions and outcomes evolve smoothly rather than in discrete steps, and for which the rate of change of each state variable—like position, speed, or resource level—is governed by a differential equation. This distinguishes them from turn-based games (Sequential game, sequential games) like chess, focusing instead on real-time strategic conflicts. Differential games are sometimes called continuous-time games, a broader term that includes them. While the two overlap significantly, continuous-time games also encompass models not governed by differential equations, such as those with stochastic Jump process, jump processes, where abrupt, unpredictable events introduce discontinuities Early differential games, often inspired by military scenarios, modeled situations like a pursuer chasing an evader, such as a missile targeting an aircraft. Today, they also apply to fields like ec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxmin
Minimax (sometimes Minmax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for ''minimizing'' the possible loss for a worst case (''max''imum loss) scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain. Originally formulated for several-player zero-sum game theory, covering both the cases where players take alternate moves and those where they make simultaneous moves, it has also been extended to more complex games and to general decision-making in the presence of uncertainty. Game theory In general games The maximin value is the highest value that the player can be sure to get without knowing the actions of the other players; equivalently, it is the lowest value the other players can force the player to receive when they know the player's action. Its formal definition is: :\underline = \max_ \min_ Where: * is the index of the play ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
