Game Theory Is The Study Of Decision Making Under Competition

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Game Theory is the study of decision making under competition. More specially, Game Theory is the study of optimal decision making under competition when one individual 's decisions affect the outcome of a situation for all other individuals involved.

Game Theory can be broadly classified into four main sub-categories of study:
- Classical Game Theory
- Combinatorial Game Theory
- Dynamic Game Theory
- Other Topics in Game Theory

As a mathematical tool for the decision-maker the strength of game theory is the methodology it provides for structuring and analyzing problems of strategic choice. The process of formally modeling a situation as a game requires the decision-maker to enumerate explicitly the players and their preferred moves,
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• The techniques of solving games involving more than one strategies particularly in case of large pay-off matrix are very complicated.
• All the situations cannot be analyzed with the help of game theory.
Classical Game Theory
Game theorists consider the axiomatization of the utility function in the case of uncertainty a major contribution in von Neumann and Morgenstern. It paved the ground for the modeling of rational decision-making when a decision maker is faced by lotteries. Thereafter a utility function, ui(.), which satisfies the expected utility hypothesis, i.e.

(1) ui([A,p;B,1-p]) = pui(A) + (1-p)ui(B) is called a von Neumann-Morgenstern utility function. Here A and B are events p is the probability that event A occurs while 1-p is the probability of B occurring. Thus [A,p;B,1-p] is a lottery. It is a notational convention to write [A,p;B,1-p] = A if p = 1 and [A,p;B,1-p] = B if p =0.
The probability p can be related to a model of relative frequencies and are, in this sense, objective and thus represent risk; or they can be subjective and thus represent uncertainty.

The utility values which the function ui(.) assigns to events are called payoffs. Because of eq.1 we do not have to distinguish between payoff and expected payoffs: if player X is indifferent between the lottery [A,p;B,1-p] and the sure event C then ui([A,p;B,1-p]) = ui(C), i.e., the payoffs are identical. If ui(.)
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