Risk management in hierarchical games with random factors

A game-theoretic model of the Principal-agent type is considered, in which the result of an agent’s activity depends not only on his/her choice but also on some random factor. The Principal is assumed to choose the total probability of all negative events that he/she will exclude from consideration; in the other respects, he/she is cautious. The structure of the Principal’s optimal strategies is found. Two models differing by the Principal’s awareness of the partner’s actions are studied.