Mathematical models of decision making under risk with ordered outcomes

Viktor V. Rozen

Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 8 (2016) no. 3, pp. 20-33

Résumé

We consider mathematical models of decision making under risk as follows. Realization structure of the model consists of a set of strategies $X$, a set of states of an environment $Y,$ set of outcomes $A$, realization function $F:X\times Y\to A$ and some distribution of probabilities on set $Y$. Goal structure of the model by partial order relation $\omega $ on the set of outcomes $A$ is given. Fix a strategy $x\in X$ we can consider some probabilistic vector of standard simplex $S(A)$ and the order relation $\omega $ may be extended on $S(A)$. An optimal solution we mean as a strategy $x^* \in X$ that the corresponding probabilistic vector is a maximal element under extension of the order $\omega $. The main problem of the article is development of method for finding of optimal solutions in considered model. In the case the sets $X$, $Y$, $A$ are finite, we propose some algorithm for solving of this problem. Every step of the algorithm is based on the check of solvability some finite system of linear inequalities.

Détail

Keywords: decision making under risk, extension of order relation, ordinal core.