When undertaking cybersecurity risk assessments, it is important to be able to assign numeric values to metrics to compute the final expected loss that represents the risk that an organization is exposed to due to cyber threats. Even if risk assessment is motivated by real-world observations and data, there is always a high chance of assigning inaccurate values due to different uncertainties involved (e.g., evolving threat landscape, human errors) and the natural difficulty of quantifying risk. Existing models empower organizations to compute optimal cybersecurity strategies given their financial constraints, i.e., available cybersecurity budget. Further, a general game-theoretic model with uncertain payoffs (probability-distribution-valued payoffs) shows that such uncertainty can be incorporated in the game-theoretic model by allowing payoffs to be random. This paper extends previous work in the field to tackle uncertainties in risk assessment that affect cybersecurity investments. The findings from simulated examples indicate that although uncertainties in cybersecurity risk assessment lead, on average, to different cybersecurity strategies, they do not play a significant role in the final expected loss of the organization when utilising a game-theoretic model and methodology to derive these strategies. The model determines robust defending strategies even when knowledge regarding risk assessment values is not accurate. As a result, it is possible to show that the cybersecurity investments’ tool is capable of providing effective decision support.

Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action can be modeled by a random variable, then the decision problem boils down to comparing different effects (random variables) by comparing their distribution functions. Although the full space of probability distributions cannot be ordered, a properly restricted subset of distributions can be totally ordered in a practically meaningful way. We call these loss-distributions, since they provide a substitute for the concept of loss-functions in decision theory. This article introduces the theory behind the necessary restrictions and the hereby constructible total ordering on random loss variables, which enables decisions under uncertainty of consequences. Using data obtained from simulations, we demonstrate the practical applicability of our approach.