## 1 Introduction and Objectives
In the applied economics literature, there are several studies addressing the topic of ICT implementation in agriculture and water management [4, 5, 16]. The most important works in applied economics estimate the benefits of ICT implementation by defining the circumstances in which information has a value for a DM [17]. Although scholars agree on the theoretical settings in which ICT-information is valuable, empirical applications show discordances and ICT-benefits are still unclear. Further, there are gaps in the modelling of decision on ICT implementation to account for the uncertainty settings which affect DM's behavior and might impede ICT uptake. Accordingly, there are different sources of uncertainty around the decision for ICT implementation. These can be caused by the following issues: (i) the ICT provides imperfect information (information is not 100% reliable) and (ii) the DM does not know ICT's reliability (the ICT is new to the DM). However, uncertainty is often modeled not distinguishing between its different sources and issues generated by a lack of knowledge on ICT reliability are overlooked. This does not allow to understand how perceptions on ICT reliability affect the farmer's or Water Authority's (WA) behavior and, in turn, the decision on ICT implementation. In this paper, we reviewed the economic literature on decision making under uncertainty to seek for the theoretical basis for better modelling ICT uptake decisions in irrigated agriculture. Between theories, we found the one of ambiguity developed by [PERSON] (1961) to be suited to help modelling the uncertainty settings affecting ICT uptake for irrigation management. In particular, we represent ambiguity as the share of uncertainty generated by not knowing ICT's reliability and risk as the error in ICT-information. This distinction will yield a deeper understanding of decision processes when the reliability of ICT is not known. Further, it allows to model the process of familiarity which occurs as the DM gains experience on the ICT. As familiarity can be a powerful tool to ease ICT-uptake we will also consider policy implications to favor the achievement of the digital irrigated agriculture  
The novelty of this research is in the application of economic literature's theories to provide the basis needed to model the uncertainty settings around ICT adoption for irrigation management. In most of applied studies on ICT adoption in agriculture risk is modeled in the decision process to be the only element which shapes uncertainty. Contrarily to these studies, we introduce the concept of ambiguity explaining the share of uncertainty rising when the reliability of a new ICT is unknown. The remainder of this paper is organized as follows: in the next section we will frame the problems and gaps by reviewing literature on ICT implementation and water management. In Section 2, we will analyze the most relevant theories and applications of decision making under uncertainty. In Section 3, we will focus on the theory developed by [PERSON] [18] and apply it to the context of our research; finally, in Sections 4 and 5 we respectively discuss what we have learned from this review and draw conclusions and policy implications.