Optimal guarantee strategy

A strategy whose efficiency in a given situation is equal to the best guaranteed result (see Principle of the largest sure result). If, for example, in a situation with efficiency criterion the undefined factor takes values from a set , then the optimal guarantee strategy satisfies the equality

If the last upper bound over is not attained, then the concept of an -optimal guarantee strategy arises, for which

where . Dependent on the set of strategies and the information on the undefined factor (the conditions under which the operation is carried out), the optimal guarantee strategy is concretely defined (see [1]). So, if the set of strategies comprises all functions and the operation contains complete information on , then the optimal guarantee strategy is called the absolutely optimal strategy and is defined by the condition

Optimal strategies corresponding to other principles of optimality are also studied (see, for example, [2] and [4]).

References

[1]	Yu.B. Germeier, "Introduction to the theory of operations research" , Moscow (1971) (In Russian)
[2]	Yu.B. Germeier, "Non-antagonistic games" , Reidel (1986) (Translated from Russian)
[3]	J.-P. Aubin, "L'analyse non-linéaire et ses motivations économiques" , Masson (1984)
[4]	N.N. Borob'ev, "Game theory. Lectures for economists and cyberneticists" , Leningrad (1974) (In Russian)

Comments

The phrase "worst case strategyworst case strategy" is also used for "optimal guarantee strategy" . It provides a security level for the outcome of the efficiency criterion. Worst case designs naturally show up in two-person zero-sum games in which uncertainties of unknowns (the -variable) are replaced by the worst possible. This idea is age old and universal in engineering and military analysis.

References

[a1]	Y.C. Ho, G.J. Olsder, "Differential games: concepts and applications" M. Shubik (ed.) , Mathematics of Conflict , Elsevier & North-Holland (1983) pp. 127–186