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Differential Game
In game theory, differential games are a group of problems related to the modeling and analysis of conflict in the context of a dynamical system. More specifically, a state variable or variables evolve over time according to a differential equation. Early analyses reflected military interests, considering two actors—the pursuer and the evader—with diametrically opposed goals. More recent analyses have reflected engineering or economic considerations. Connection to optimal control Differential games are related closely with optimal control problems. In an optimal control problem there is single control u(t) and a single criterion to be optimized; differential game theory generalizes this to two controls u_(t),u_(t) and two criteria, one for each player. Each player attempts to control the state of the system so as to achieve its goal; the system responds to the inputs of all players. History In the study of competition, differential games have been employed since a 1925 art ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game 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 mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yuliy Sannikov
Yuliy Sannikov (born November 3, 1978) is a Ukrainian economist known for his contributions to mathematical economics, game theory, and corporate finance. He is an economics professor at the Stanford Graduate School of Business, and won both the 2015 Fischer Black Prize and 2016 John Bates Clark Medal. Sannikov is also one of the few participants to win three gold medals at the International Mathematical Olympiad. He received his A.B. in mathematics from Princeton in 2000, he then earned a Ph.D. in business administration from Stanford Graduate School of Business in 2004. Publications * with Markus K. Brunnermeier: ''The I Theory of Money''. NBER Working Paper 22533, 2016, . * with Markus K. Brunnermeier: ''International Credit Flows and Pecuniary Externalities''. In. '' American Economic Journal: Macroeconomics'' 7(1), January 2015, 297–338, . * with Markus K. Brunnermeier: ''A Macroeconomic Model with a Financial Sector''. ''The American Economic Review'' 104(2), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory Game Classes
A game is a structured form of play, usually undertaken for entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or games) or art (such as jigsaw puzzles or games involving an artistic layout such as Mahjong, solitaire, or some video games). Games are sometimes played purely for enjoyment, sometimes for achievement or reward as well. They can be played alone, in teams, or online; by amateurs or by professionals. The players may have an audience of non-players, such as when people are entertained by watching a chess championship. On the other hand, players in a game may constitute their own audience as they take their turn to play. Often, part of the entertainment for children playing a game is deciding who is part of their audience and who is a player. A toy and a game are not the same. Toys generally allow for unrestricted play whereas games come with present rules. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean-field Game Theory
Mean-field game theory is the study of strategic decision making by small interacting agents in very large populations. It lies at the intersection of game theory with stochastic analysis and control theory. The use of the term "mean field" is inspired by mean-field theory in physics, which considers the behavior of systems of large numbers of particles where individual particles have negligible impacts upon the system. In other words, each agent acts according to his minimization or maximization problem taking into account other agents’ decisions and because their population is large we can assume the number of agents goes to infinity and a representative agent exists. In traditional game theory, the subject of study is usually a game with two players and discrete time space, and extends the results to more complex situations by induction. However, for games in continuous time with continuous states (differential games or stochastic differential games) this strategy cannot be us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lotka–Volterra Equations
The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations: \begin \frac &= \alpha x - \beta x y, \\ \frac &= \delta x y - \gamma y, \end where * is the number of prey (for example, rabbits); * is the number of some predator (for example, foxes); *\tfrac and \tfrac represent the instantaneous growth rates of the two populations; * represents time; *, , , are positive real parameters describing the interaction of the two species. The Lotka–Volterra system of equations is an example of a Kolmogorov model, which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism. History The Lotka–Volterra pred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pursuit–evasion
Pursuit–evasion (variants of which are referred to as cops and robbers and graph searching) is a family of problems in mathematics and computer science in which one group attempts to track down members of another group in an environment. Early work on problems of this type modeled the environment geometrically. In 1976, Torrence Parsons introduced a formulation whereby movement is constrained by a graph. The geometric formulation is sometimes called continuous pursuit–evasion, and the graph formulation discrete pursuit–evasion (also called graph searching). Current research is typically limited to one of these two formulations. Discrete formulation In the discrete formulation of the pursuit–evasion problem, the environment is modeled as a graph. Problem definition There are innumerable possible variants of pursuit–evasion, though they tend to share many elements. A typical, basic example is as follows (cops and robber games): Pursuers and evaders occupy nodes of a g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autonomous Systems
An autonomous robot is a robot that acts without recourse to human control. The first autonomous robots environment were known as Elmer and Elsie, which were constructed in the late 1940s by W. Grey Walter. They were the first robots in history that were programmed to "think" the way biological brains do and meant to have free will.Ingalis-Arkell, Esthe"The Very First Robot Brains Were Made of Old Alarm Clocks" 7 March 2012. Elmer and Elsie were often labeled as tortoises because of how they were shaped and the manner in which they moved. They were capable of phototaxis which is the movement that occurs in response to light stimulus. Historic examples include space probes. Modern examples include self-driving vacuums and cars. Industrial robot arms that work on assembly lines inside factories may also be considered autonomous robots, though their autonomy is restricted due to a highly structured environment and their inability to locomote. Components and criteria of robotic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Missile Guidance
Missile guidance refers to a variety of methods of guiding a missile or a guided bomb to its intended target. The missile's target accuracy is a critical factor for its effectiveness. Guidance systems improve missile accuracy by improving its Probability of Guidance (Pg). These guidance technologies can generally be divided up into a number of categories, with the broadest categories being "active", "passive", and "preset" guidance. Missiles and guided bombs generally use similar types of guidance system, the difference between the two being that missiles are powered by an onboard engine, whereas guided bombs rely on the speed and height of the launch aircraft for propulsion. History The concept of unmanned guidance originated at least as early as World War I, with the idea of remotely guiding an airplane bomb onto a target, such as the systems developed for the first powered drones by Archibald Low (The Father of Radio Guidance). In World War II, guided missiles were first d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Calculus
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. This field was created and started by the Japanese mathematician Kiyoshi Itô during World War II. The best-known stochastic process to which stochastic calculus is applied is the Wiener process (named in honor of Norbert Wiener), which is used for modeling Brownian motion as described by Louis Bachelier in 1900 and by Albert Einstein in 1905 and other physical diffusion processes in space of particles subject to random forces. Since the 1970s, the Wiener process has been widely applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates. The main flavours of stochastic calculus are the Itô calculus and its variational relative the Malliavin calculus. For technical reasons the Itô integral is the mos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Economic Association
The American Economic Association (AEA) is a learned society in the field of economics. It publishes several peer-reviewed journals acknowledged in business and academia. There are some 23,000 members. History and Constitution The AEA was established in 1885 in Saratoga Springs, New York by younger progressive economists trained in the German historical school, including Richard T. Ely, Edwin Robert Anderson Seligman and Katharine Coman, the only woman co-founder; since 1900 it has been under the control of academics. The purposes of the Association are: 1) The encouragement of economic research, especially the historical and statistical study of the actual conditions of industrial life; 2) The issue of publications on economic subjects; 3) The encouragement of perfect freedom of economic discussion. The Association as such will take no partisan attitude, nor will it commit its members to any position on practical economic questions. The Association publishes one of the most ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Bates Clark Medal
The John Bates Clark Medal is awarded by the American Economic Association to "that American economist under the age of forty who is adjudged to have made a significant contribution to economic thought and knowledge." The award is named after the American economist John Bates Clark (1847–1938). According to ''The Chronicle of Higher Education'', it "is widely regarded as one of the field's most prestigious awards... second only to the Nobel Memorial Prize in Economic Sciences." Many of the recipients went on to receive the Nobel Prizes in their later careers, including the inaugural recipient Paul Samuelson. The award was made biennially until 2007, but from 2009 is now awarded every year because of the growth of the field. Although the Clark medal is billed as a prize for American economists, it is sufficient that the candidates work in the US at the time of the award; US nationality is not necessary to be considered. Past recipients See also * List of economics awards ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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