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The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory.From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.
Mean field game theory is the study of strategic decision making in very large populations of small interacting agents. This class of problems was considered in the economics literature by Boyan Jovanovic and Robert W. Rosenthal, in the engineering literature by Peter E. Caines, and by mathematicians Pierre-Louis Lions and Jean-Michel Lasry.
In game theory, a Bayesian game is a strategic decision-making model which assumes players have incomplete information. Players may hold private information relevant to the game, meaning that the payoffs are not common knowledge. [1] Bayesian games model the outcome of player interactions using aspects of Bayesian probability.
An important problem in the theory of cooperative dynamic games is the time-consistency of a given imputation function (in Russian literature it is termed dynamic stability of optimality principle). Let say that a number of players has made a cooperative agreement at the start of the game.
The Price of Anarchy (PoA) [1] is a concept in economics and game theory that measures how the efficiency of a system degrades due to selfish behavior of its agents. It is a general notion that can be extended to diverse systems and notions of efficiency.
Computational mathematics refers also to the use of computers for mathematics itself. This includes mathematical experimentation for establishing conjectures (particularly in number theory), the use of computers for proving theorems (for example the four color theorem), and the design and use of proof assistants.
In decision theory, a decision rule is a function which maps an observation to an appropriate action. Decision rules play an important role in the theory of statistics and economics, and are closely related to the concept of a strategy in game theory.
Statistical inference might be thought of as gambling theory applied to the world around us. The myriad applications for logarithmic information measures tell us precisely how to take the best guess in the face of partial information. [1] In that sense, information theory might be considered a formal expression of the theory of gambling. It is ...