A Markov Decision Process with Awareness and Present Bias in Decision-Making

We propose a Markov Decision Process Model that blends ideas from Psychological research and Economics to study decision-making in individuals with self-control problems. We have borrowed a dual-process of decision-making with self-awareness from Psychological research, and we introduce present bias in inter-temporal preferences, a phenomenon widely explored in Economics. We allow for both an exogenous and endogenous, state-dependent, present bias in inter-temporal decision-making and explore, by means of numerical simulations, the consequences on well-being emerging from the solution of the model. We show that, over time, self-awareness may mitigate present bias and suboptimal choice behaviour

Decision Making in Networks: A Model of Awareness Raising

This work investigates how interpersonal interactions among individuals could affect the dynamics of awareness raising. Even though previous studies on mathematical models of awareness in the decision making context demonstrate how the level of awareness results from self-observation impinged by optimal decision selections and external uncertainties, an explicit accounting of interaction among individuals is missing. Here we introduce for the first time a theoretical mathematical framework to evaluate the effect on individual awareness exerted by the interaction with neighbor agents. This task is performed by embedding the single agent model into a graph and allowing different agents to interact by means of suitable coupling functions. The presence of the network allows, from a global point of view, the emergence of diffusion mechanisms for which the population tends to reach homogeneous attractors, and, among them, 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 individual assigns to their own state with respect to others’, may drive real actors to stress effective actions increasing individual and global awarenes

A Game Theory Proof of Optimal Colorings Resilience to Strong Deviations

This paper provides a formal proof of the conjecture stating that optimal colorings in max k-cut games over unweighted and undirected graphs do not allow the formation of any strongly divergent coalition, i.e., a subset of nodes able to increase their own payoffs simultaneously. The result is obtained by means of a new method grounded on game theory, which consists in splitting the nodes of the graph into three subsets: the coalition itself, the coalition boundary and the nodes without relationship with the coalition. Moreover, we find additional results concerning the properties of optimal colorings

Generalized logistic model of bacterial growth

This work proposes a new mathematical model describing the dynamics of growing bacterial cultures. The model, described by a first order non-linear differential equation, as a generalization of the logistic equation, was compared with the most studied mathematical models. All models were numerically implemented and fitted to the experimental data, collected from the incubation of a bacterial strain of Pseudomonas fluorescens, to obtain the growth parameters. The experimental data showed the lowest fit error for both the Baranyi–Roberts and new models, which turned out to be equivalent. Simulations of the fitting algorithm were also implemented and repeated for a large number of initial guesses of the parameters, chosen in order to test the fitting and convergence performances. The innovative feature that makes the new model easier to use than Baranyi–Roberts model is definitely its simple and manageable analytical form and its good performance in terms of convergence time

Microbial contamination and management scenarios in a Mediterranean coastal lagoon (Etang de Thau, France): application of a Decision Support System within the Integrated Coastal Zone Management context

1 - In the Thau lagoon (Southern Mediterranean Coast) the main anthropogenic pressure is represented by the urban development in the watershed, whilst oyster and mussel farming represents one of the main economical activities in the region. 2 - During the last decade, the increasing organic loads from watershed and urban settlements in the lagoon surroundings have caused a diffuse contamination by faecal bacteria. Also toxic algal blooms have been occurring, impairing water quality with major impacts on shellfish farming, fishery and bathing. 3 - In this study, indicators and scenarios identified for the lagoon have been integrated in a Decision Support System (DSS) to evaluate the best solutions for reducing pressures and improving both water quality and ecosystem status. 4 - The watershed has been analysed with reference to indicators of pollution sources and transfer rates to the lagoon. In parallel, socio-economic indicators and descriptors of urban growth and development have been assessed. Numerical models have been run in order to simulate the lagoon hydrodynamics in relation to both meteorological factors and watershed runoff. The impact of faecal bacteria contamination has been evaluated in terms of economical losses and social conflicts, arising from the restriction of shellfish farming and marketing during contamination events. Finally, the DSS prototype has been applied to the lagoon in support to management and future planning

The role of self-loops and link removal in evolutionary games on networks

Recently, a new mathematical formulation of evolutionary game dynamics [1] has been introduced accounting for a finite number of players organized over a network, where the players are located at the nodes of a graph and edges represent connections between them. Internal steady states are particularly interesting in control and consensus problems, especially in a networked context where they are related to the coexistence of different strategies. In this paper we consider this model including self-loops. Existence of internal steady states is studied for different graph topologies in two-strategy games. Results on the effect of removing links from central players are also presented