Risk measures on networks and expected utility

In reliability theory projects are usually evaluated in terms of their riskiness, and often decision under risk is intended as the one-shot-type binary choice of accepting or not accepting the risk. In this paper we elaborate on the concept of risk acceptance, and propose a theoretical framework based on network theory. In doing this, we deal with system reliability, where the interconnections among the random quantities involved in the decision process are explicitly taken into account. Furthermore, we explore the conditions to be satisfied for risk-acceptance criteria to be consistent with the axiomatization of standard expected utility theory within the network framework. In accordance with existing literature, we show that a risk evaluation criterion can be meaningful even if it is not consistent with the standard axiomatization of expected utility, once this is suitably reinterpreted in the light of networks. Finally, we provide some illustrative examples.