• awareness
• complex systems
• decision support systems
• dynamic systems
• game and network dynamics
• Markov decision processes
• mathematical modelling
• optimal control

This work is focused on the investigation of a mathematical framework regarding the study of individuals’ awareness-increasing phenomenon in the context of decision-making processes, which can integrate different behavioral facets to analyze their influence and interplay in the decision-making process. There is an always increasing interest in these multifaced concepts by a theoretical point of view, in different field of research, however a mathematical formalization still lacks, and this is the gap this work tries to fill, trying to define, beyond a conceptual and descriptive perspective, a mathematical formalism of the main mechanisms involved.
The focus of this work is on providing a mathematical an engineering view, and it necessarily requires an attempt to synthetize and schematize the main concept involved which are so complex and wide that deserve a whole thesis for their effective explanation, definition, and treatment. This work represents a very initial and perhaps risky step in the study of the mechanisms underlying the process of human awareness-increasing in decision-making.
There is now a consistent body of research into the nature of decision considering a rich conception of the decision-maker: besides the well-known dual-process which describe two different ways of information processing – that we call ‘analytical’ and ‘intuitive’ – there were gradually included other subjective aspects like emotions, tacit knowledge, and intuition. From the specific fields of inquiry ranging from a philosophical to logic, from economics to behavioral sciences, some characteristics and properties are extrapolated in order to translated them into a quantitative and mathematical simplified formalism which permits to elaborate a first raw and internally consistent model, always maintaining a focus on the context of decision-making process.

The model proposed is based on the framework of Sequential Decision-Making models, and in particular in the Markovian class. It embeds an attempt to extrapolate and synthetize the main descriptive characteristics of the involved phenomena and translating them into a formal and quantitative language. This effort enables to create a setting in which is also possible to perform simulation. Different settings have been analyzed embodying different individual characteristics: a different trade-off between analytical and intuitive approach, the presence or absence of a self-awareness mechanism, the influence of other external factors. They have conducted some simulations using these structures highlighting the improvement guaranteed by the presence of the self-awareness part and how awareness emerges from a mechanism of self-observation when the individual has the specific focus on it.
These considerations hold for the case of a single individual acting independently, a condition which is unrealistic in our world where the interaction with others, and consequently their influence on our personal behaviors and internal dynamics, is a relevant and essential component. Then, the “single agent” perspective, which until now considers the behavior of a single individual taken in isolation, has been extended by adding a first basic presence of an interaction among different decision-makers through the implementation of the single agent model on a network structure. In the wider application these nodes could be humans but not necessarily, it is enough that they perform some kind of choice. Each node has its reasoning modality, and their interconnections can be applied to investigate the reciprocal influences in a network system. In this way, we can introduce the explicit dependence of decisions on the action of others. Simulation have been performed and the results highlights the possibility of overcoming stopping condition to the growth of awareness, incurred in some situation of the single individual decision, by this addition of an interconnected component with different individuals. The presence of the networks allows, from a global point of view, the emergence of diffusive mechanisms for which the population tends to reach homogeneous attractors, and particularly the one with the highest level of awareness. The structural and behavioral patterns, such as the initial levels of awareness and the relative importance the individuals assign to their own state with respect to neighbors’ ones, may drive to stress effective actions to increase individuals’ awareness.
The proposed framework is broad enough to be declined, with some appropriate adjustments and modifications, to different study of the individual’s behavior and groups. Exactly for its general and abstract formulation it can range from the study of aspect related, for example, to the problems of addictions to the analysis of flow of information and misinformation inside a population.
Although limited and imperfect by nature, also due to the difficulties in modeling extremely wide and complex phenomena – as human behaviors and awareness are – the hope is that this study could contribute to introducing new aspects which can expand research in the field.