IJFANS International Journal of Food and Nutritional Sciences

ISSN PRINT 2319 1775 Online 2320-7876

FINANCIAL MATHEMATICS AND GAME THEORY APPLICATIONS

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MANI.S.M, Dr. N. RAMYA

Abstract

Over the past two decades, game theory has been applied to a growing variety of critical practical issues in economics, industrial organisation, corporate strategy, finance, accounting, market design, and marketing, such as antitrust analysis, monetary policy, and company restructuring. In this work, we discuss how game theory, especially the principal-agent model, is becoming more significant in the domains of finance and management accounting. Mathematical models of conflict and cooperation between utility optimizers whose actions affect each other's utility are studied in game theory, and mathematical approaches for assessing such scenarios are provided. Thus, it is similar to operations research and, in particular, mathematical programming in terms of optimization [Shubik (2002)], which are normally concerned with a single optimizer. In order to examine and solve the mathematical models that it analyses, game theory employs theoretical notions such as Karush-Kuhn-Tucker optimality requirements, as well as numerical tools from mathematical programming. Parallel to mathematical programming, such models are idealised representations of an imagined reality, since many features of the actual world cannot be expressed mathematically. This kind of approximation has sparked a lot of philosophical debate [Gintis (2000)]. The notions of strategies, Nash equilibrium and its offspring, such as Bayesian equilibrium, as well as game theory's vocabulary for studying information sets have made it possible to codify scenarios of conflict and cooperation that emerge in a number of domains under the same roof. Thus, game theory [Aumann (1985), Fudenberg and Tirole (1991)], which began as an elegant mathematical discipline [von Neumann and Morgenstern (1944), Owen (1982), Forgó et al. (1999)], has been applied to an ever increasing number of important practical problems [Tirole (1986), Milgrom and Roberts (1992), Shubik (2002)] in economics [Friedman (1990), Gibbons (1992), Besanko et

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