The decision theory is a theory of Mathématiques applied having for object the Decision making in risky universe.

Risky universe

What the theory of the Decision?

An example utilizing it is the problem of the gangster penguin. -->

Limits of the theory of probability

In presences of choice, the theory of probability proposes to calculate the expectations of profit and to choose the choice which maximizes this hope of profit. However this process has several limits. The theory of the Décision aims at bringing an answer to these borderline cases.

Concept of risk

Let us consider the choice to take part in a play or the player has a chance on ten to gain hundred times his setting. The hope of profit is very positive and any player would be ready with miser 1 euro; but which would make the choice play if the obligatory setting were all the fortune of the player?

This example shows that a reasonable behavior is not compatible with the " rationalisme" probability theory. The normal behavior is certain a aversion with the risk and the decision theory tries to model this behavior to deduce the choices from them from the player.

Nonquantifiable profit

In addition, in many cases, the profits are not quantifiable (see the example of the bet of Pascal, or the insurance life), not easily measurable (like the catastrophes) or not easily comparable. There still, the decision theory seeks to bring answers, to establish preferences.

Theory of the utility of Von Neumann - Morgenstern

Optimization and maximalisation are the two key words defining the theories of decision making based on the rationalization, i.e. the theories defining the logical and rational standards that all the decision makers are supposed to follow so that the choice is that which " rapporte" more.

A decision which complies with the 6 following rules should be the best.

; Principle of the ordinance of the alternatives

a decision maker must be able to compare two results of an alternative and to prefer one with the other of them or then not to take account of this alternative.

; Principle of predominance

the maker decision will have to never take a strategy of answer dominated by another, i.e. whose whole of the results includes/understands results weaker or equal to those of another strategy. It will have on the contrary to choose the dominant strategy.

; Principle of cancellation (or the unquestionable setting)

If two risky choices involve results of which some are identical and of the same probabilities then the utility of these results should not be taken into account by the decision maker.

; Principle of transitivity

If a decision maker prefers has to B and B with C then it must prefer has with C.

; Principle of continuity

a maker decision must prefer a risky option going from a maximum result to a minimum result, with a sure intermediate choice in so far as the chances to gain are sufficient.

; Principle of invariance

a decision maker should not be influenced by the way in which the proposals are formulated.

Non-linearity of probability -->

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