Our focus will be on problems in which two or more agents confront (as in non-cooperative game theory) and the consequences that they receive are random (as in risk analysis) depending on the actions of all participants (as in game theory at large). In this context, it is typical to address just two types of uncertain phenomena: aleatory uncertainty, referring to the randomness of the outcomes the agents receive; and epistemic uncertainty, referring to the strategic choices of intelligent adversaries. However, a number of issues have arisen prominently in several application areas. To wit, high-pro file terrorist attacks are demanding signi ficant investments in protective responses which are in doubt of being sufficiently effective; key business sectors have become more mathematically sophisticated and use this expertise to shape strategies in competitive decisions; and the on-going arms race in cyber-security implies that fi nancial penalties for myopic protection are random and may be remarkably high. These have entailed the need to consider a third type of uncertainty, concept uncertainty, referring to beliefs about how opponents frame the problem. Most authors would focus on game theoretical methods based on variants of Nash equilibria, but this is not satisfactory in many of the above applications since beliefs and preferences of adversaries will not be readily available, frequently violating game theoretic common knowledge assumptions. In contrast, we shall turn to Adversarial Risk Analysis (ARA), an emergent paradigm for the type of problems we consider. ARA provides one-sided prescriptive support to a decision maker, maximising her subjective expected utility, treating the adversaries' decisions as random variables. To do so, ARA models the adversaries' decision-making problems and, under assumptions about their rationality, tries to assess their probabilities and utilities to predict their optimal actions, with the uncertainty in the assessments leading to probability distributions over them. We shall stress this idea of concept uncertainty with a qualitative security example, showing its relevance in what we call Adversarial Statistical Decision Theory, which extends the standard Statistical Decision Theory framework with the presence of several decision makers, focusing on point estimation.