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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 ...
His investigation stemmed from classic pursuit–evasion type zero-sum dynamic two-player games such as the Princess and monster game. In 1942, he married Rose Bicov, and they had two daughters. His work in pure mathematics included working with monodiffric functions, fractional-order mappings, graph theory, analytic functions, and number theory.
John Forbes Nash Jr. (June 13, 1928 – May 23, 2015), known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations.
Game theory is the study of mathematical models of strategic interactions. [1] It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. [2]
Shannon's theorem (information theory) Shift theorem (differential operators) Siegel–Walfisz theorem (analytic number theory) Silverman–Toeplitz theorem (mathematical analysis) Simplicial approximation theorem (algebraic topology) Sinkhorn's theorem (matrix theory) Sion's minimax theorem (game theory)
John Harsanyi – equilibrium theory (Nobel Memorial Prize in Economic Sciences in 1994) Monika Henzinger – algorithmic game theory and information retrieval; John Hicks – general equilibrium theory (including Kaldor–Hicks efficiency) Naira Hovakimyan – differential games and adaptive control; Peter L. Hurd – evolution of aggressive ...
For this simple system, the Hamilton–Jacobi–Bellman partial differential equation is (,) + {(,) (,) + (,)} =subject to the terminal condition (,) = (),As before, the unknown scalar function (,) in the above partial differential equation is the Bellman value function, which represents the cost incurred from starting in state at time and controlling the system optimally from then until time .
Theory of Games and Economic Behavior, published in 1944 [1] by Princeton University Press, is a book by mathematician John von Neumann and economist Oskar Morgenstern which is considered the groundbreaking text that created the interdisciplinary research field of game theory.