arXiv subjects

Dario Bauso

Publications and source records attributed to Dario Bauso.

At least 19 recordsLinked to original sources

arXiv2026

A Coalitional Game for Demand-Side Management in a Micro-Grid with Multiple Electricity Retailers

This paper develops a demand-side management framework for electricity networks with multiple competing retailers. The interaction among retailers is formulated as a coalitional game, yielding a family of coupled mixed-integer optimisation problems in which retail prices, consumer power demands, and the network partition are jointly optimised. To solve this problem, we propose a coalition-formation algorithm based on multi-objective optimisation principles. The algorithm seeks to identify coalition structures that balance retailer profit and consumer welfare. We prove that the proposed algorithm converges in a finite number of steps and recovers a subset of weakly Pareto-efficient solutions of the coupled optimisation problems. The framework is further extended to a risk-sharing formulation, in which the objective is defined using conditional value-at-risk. Numerical simulations on an academic example demonstrate the method's behaviour and show that the resulting equilibrium partition set contains several admissible trade-offs between the competing objectives. The results provide a tractable approach for analysing competition, coalition formation, and risk-aware pricing in multi-retailer demand-side management systems.

eess.SY↗

arXiv2025

Characterization of Invariance, Periodic Solutions and Optimization of Dynamic Financial Networks

Cascading failures, such as bankruptcies and defaults, pose a serious threat for the resilience of the global financial system. Indeed, because of the complex investment and cross-holding relations within the system, failures can occur as a result of the propagation of a financial collapse from one organization to another. While this problem has been studied in depth from a static angle, namely, when the system is at an equilibrium, we take a different perspective and study the corresponding dynamical system. The contribution of this paper is threefold. First, we carry out a systematic analysis of the regions of attraction and invariance of the system orthants, defined by the positive and negative values of the organizations' equity. Second, we investigate periodic solutions and show through a counterexample that there could exist periodic solutions of period greater than 2. Finally, we study the problem of finding the smallest cash injection that would bring the system to the maximal invariant region of the positive orthant.

eess.SY↗

arXiv2024

A Coalitional Game for Demand-Side Management in a Low-Voltage Resistive Micro-Grid with Multiple Electricity Retailers

An existing challenge in power systems is the implementation of optimal demand management through dynamic pricing. This paper encompasses the design, analysis and implementation of a novel on-line pricing scheme based on coalitional game theory. The setting consists of a network with multiple energy retailers competing to attract consumers by announcing a price in a hierarchical leader-follower structure. The process of coalition formation under such a pricing scheme can be viewed as a game for which we show that a Stackelberg equilibrium exists, \ie given a price, consumers will respond by conforming to a reciprocal power consumption quantity. We propose a coalition formation algorithm and perform a game-theoretic stability analysis on the resulting coalitions. We integrate the pricing setting with a resistive micro-grid dynamic model. In this context we analyse the behaviour of the integrated system, bridging the gap between market and physical layers of the problem. Simulations provide a comparison of profits generated by the proposed scheme against a more traditional single retailer scheme, while simultaneously showing convergence towards a steady-state equilibrium. Additionally, we shed light into the system's physical response when subject to our proposed pricing scheme.

math.OC↗

arXiv2023

Cascading Failures in the Global Financial System: A Dynamical Model

In this paper, we propose a dynamical model to capture cascading failures among interconnected organizations in the global financial system. Failures can take the form of bankruptcies, defaults, and other insolvencies. The network that underpins the financial interdependencies between different organizations constitutes the backbone of the financial system. A failure in one or more of these organizations can lead the propagation of the financial collapse onto other organizations in a domino effect. Paramount importance is therefore given to the mitigation of these failures. Motivated by the relevance of this problem and recent prominent events connected to it, we develop a framework that allows us to investigate under what conditions organizations remain healthy or are involved in the propagation of the failures in the network. The contribution of this paper is the following: i) we develop a dynamical model that describes the equity values of financial organizations and their evolution over time given an initial condition; ii) we characterize the equilibria for this model by proving the existence and uniqueness of these equilibria, and by providing an explicit expression for them; and iii) we provide a computational method via sign-space iteration to analyze the propagation of failures and the attractive equilibrium point.

math.OC↗

arXiv2023

Cascading failures: dynamics, stability and control

We develop a dynamic model of cascading failures in a financial network whereby cross-holdings are viewed as feedback, external assets investments as inputs and failure penalties as static nonlinearities. We provide sufficient milder and stronger conditions for the system to be a positive one, and study equilibrium points and stability. Stability implies absence of cascades and convergence of market values to constant values. We provide a constructive method for control design to obtain stabilizing market investments in the form of feedback-feedforward control inputs.

math.OC↗

arXiv2021

The Impact of Irrational Behaviours in the Optional Prisoner's Dilemma with Game-Environment Feedback

In the optional prisoner's dilemma (OPD), players can choose to cooperate and defect as usual, but can also abstain as a third possible strategy. This strategy models the players' participation in the game and is a relevant aspect in many settings, e.g. social networks or opinion dynamics where abstention is an option during an election. In this paper, we provide a formulation of the OPD where we consider irrational behaviours in the population inspired by prospect theory. Prospect theory has gained increasing popularity in recent times thanks to its ability to capture aspects such as reference dependence or loss aversion which are common in human behaviour. This element is original in our formulation of the game and is incorporated in our framework through pairwise comparison dynamics. Recently, the impact of the environment has been studied in the form of feedback on the population dynamics. Another element of novelty in our work is the extension of the game-environment feedback to the OPD in two forms of dynamics, the replicator and the pairwise comparison. The contribution of this paper is threefold. First, we propose a modelling framework where prospect theory is used to capture irrational behaviours in an evolutionary game with game-environment feedback. Second, we carry out the stability analysis of the system equilibria and discuss the oscillating behaviours arising from the game-environment feedback. Finally, we extend our previous results to the OPD and we discuss the main differences between the model resulting from the replicator dynamics and the one resulting from the pairwise comparison dynamics.

cs.GT↗

arXiv2020

Evolutionary Dynamics on a Regular Networked Structured and Unstructured Multi-population

In this paper we study collective decision making on a multi-population, represented by a regular network of groups of individuals. Each group consists of a collection of players and every player can choose between two options. A group is characterised by variables denoting the fractions of individuals committed to each respective option, and they are influenced by the state of neighboring groups. First, we study its steady-state and show that the equilibrium is a consensus equilibrium. We also derive a sufficient condition for local asymptotic stability. Then, we study a structured model where every population is now assumed to represent a structured complex network. We conclude the paper with simulations, corroborating the obtained theoretical findings.

math.OC↗

arXiv2020

Stochastic Programming with Primal-Dual Dynamics: A Mean-Field Game Approach

This study addresses primal-dual dynamics for a stochastic programming problem for capacity network design. It is proven that consensus can be achieved on the \textit{here and now} variables which represent the capacity of the network. The main contribution is a heuristic approach which involves the formulation of the problem as a mean-field game. Every agent in the mean-field game has control over its own primal-dual dynamics and seeks consensus with neighboring agents according to a communication topology. We obtain theoretical results concerning the existence of a mean-field equilibrium. Moreover, we prove that the consensus dynamics converge such that the agents agree on the capacity of their respective micro-networks. Lastly, we emphasize how penalties on control and state influence the dynamics of agents in the mean-field game.

math.OC↗

arXiv2020

The Role of Asymptomatic Individuals in the COVID-19 Pandemic via Complex Networks

Recent seroprevalence studies have tried to estimate the real number of asymptomatic cases affected by COVID-19. It is of paramount importance to understand the impact of these infections in order to prevent a second wave. This study aims to model the interactions in the population by means of a complex network and to shed some light on the effectiveness of localised control measures in Italy in relation to the school opening in mid-September. The formulation of an epidemiological predictive model is given: the advantage of using this model lies in that it discriminates between asymptomatic and symptomatic cases of COVID-19 as the interactions with these two categories of infected individuals are captured separately, allowing for a study on the impact of asymptomatic cases. This model is then extended to a structured nonhomogeneous version by means of the Watts-Strogatz complex network, which is adopted widely to model societal interactions as it holds the small world property. Finally, a case study on the situation in Italy is given: first the homogeneous model is used to compare the official data with the data of the recent seroprevalence study from Istat; second, in view of the return to school in mid-September, a study at regional level is conducted. The results of this study highlight the importance of coordinating the deployment of appropriate control measures that take into account the role of asymptomatic infections, especially in younger individuals, and inter-regional connectivity in Italy.

physics.soc-ph↗

arXiv2018

Mean-field Games for Bio-inspired Collective Decision-making in Dynamical Networks

Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are based on the players' knowledge of their current state and of the distribution of all the other players, and this introduces mean-field terms in the running and the terminal cost. The first contribution involves a mean-field game model that brings together macroscopic and microscopic dynamics. We obtain the mean-field equilibrium associated with this model, by solving the corresponding initial-terminal value problem. We perform an asymptotic analysis to obtain a stationary equilibrium for the system. The second contribution involves the study of the microscopic dynamics of the system for a finite number of players that interact in a structured environment modeled by an interaction topology. The third contribution is the specialization of the model to describe honeybee swarms, virus propagation, and cascading failures in interconnected smart-grids. A numerical analysis is conducted which involves two types of cyber-attacks. We simulate in which ways failures propagate across the interconnected smart grids and the impact on the grids frequencies. We reframe our analysis within the context of Lyapunov's linearisation method and stability theory of nonlinear systems and Kuramoto coupled oscillators model.

eess.SY↗

arXiv2017

Nonlinear network dynamics for interconnected micro-grids

This paper deals with transient stability in interconnected micro-grids. The main contribution involves i) robust classification of transient dynamics for different intervals of the micro-grid parameters (synchronization, inertia, and damping); ii) exploration of the analogies with consensus dynamics and bounds on the damping coefficient separating underdamped and overdamped dynamics iii) the extension to the case of disturbed measurements due to hackering or parameter uncertainties.

math.OC↗

arXiv2017

Distributionally Robust Games: f-Divergence and Learning

In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each player's payoff depends on the other players' decisions and on the decision of a virtual player (nature) who selects an adversarial distribution of scenarios. This paper provides three main contributions. Firstly, the distributionally robust game is formulated using the statistical notions of $f$-divergence between two distributions, here represented by the adversarial distribution, and the exact distribution. Secondly, the complexity of the problem is significantly reduced by means of triality theory. Thirdly, stochastic Bregman learning algorithms are proposed to speedup the computation of robust equilibria. Finally, the theoretical findings are illustrated in a convex setting and its limitations are tested with a non-convex non-concave function.

math.OC↗

arXiv2017

Bio-inspired Evolutionary Game Dynamics on Complex Networks under Uncertain Cross-inhibitory Signals

Given a large population of players, each player has three possible choices between option 1 or 2 or no option. The two options are equally favorable and the population has to reach consensus on one of the two options quickly and in a distributed way. The more popular an option is, the more likely it is to be chosen by uncommitted players. Uncommitted players can be attracted by those committed to any of the other two options through a cross-inhibitory signal. This model originates in the context of honeybees swarms, and we generalize it to duopolistic competition and opinion dynamics. The contributions of this work include (1) the formulation of an evolutionary game model to explain the behavioral traits of the honeybees, (2) the study of the individuals and collective behavior including equilibrium points and stability, (3) the extension of the results to the case of structured environment via complex network theory, (4) the analysis of the impact of the connectivity on consensus, and (5) the study of absolute stability for the collective system under time-varying and uncertain cross-inhibitory parameter.

eess.SY↗

arXiv2014

A game-theoretic approach to dynamic demand response management

Within the realm of dynamic of \emph{smart buildings} and \emph{smart cities}, dynamic response management is playing an ever-increasing role thus attracting the attention of scientists from different disciplines. Dynamic demand response management involves a set of operations aiming at decentralizing the control of loads in large and complex power networks. Each single appliance if fully responsive and readjusts its energy demand to the overall network load. A main issue is related to mains frequency oscillations resulting from an unbalance between supply and demand. In a nutshell, this paper contributes to the topic by equipping each signal consumer with strategic insight. In particular, we highlight three main contributions and a few other minor contributions. First, we design a mean-field game for the TCLs application, study the mean-field equilibrium for the deterministic mean-field game and investigate on asymptotic stability for the microscopic dynamics. Second, we extend the analysis and design to imperfect models which involve both stochastic or deterministic disturbances. This leads to robust mean-field equilibrium strategies guaranteeing stochastic and worst-case stability, respectively. Minor contributions involve the use of stochastic control strategies rather than deterministic, and some numerical studies illustrating the efficacy of the proposed strategies.

math.OC↗

arXiv2014

Approachability in Population Games

This paper reframes approachability theory within the context of population games. Thus, whilst one player aims at driving her average payoff to a predefined set, her opponent is not malevolent but rather extracted randomly from a population of individuals with given distribution on actions. First, convergence conditions are revisited based on the common prior on the population distribution, and we define the notion of \emph{1st-moment approachability}. Second, we develop a model of two coupled partial differential equations (PDEs) in the spirit of mean-field game theory: one describing the best-response of every player given the population distribution (this is a \emph{Hamilton-Jacobi-Bellman equation}), the other capturing the macroscopic evolution of average payoffs if every player plays its best response (this is an \emph{advection equation}). Third, we provide a detailed analysis of existence, nonuniqueness, and stability of equilibria (fixed points of the two PDEs). Fourth, we apply the model to regret-based dynamics, and use it to establish convergence to Bayesian equilibrium under incomplete information.

math.OC↗

arXiv2014

Mean-Field Games for Marriage

This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being.

math.OC↗

arXiv2014

Attainability in Repeated Games with Vector Payoffs

We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called {\em attainable} if player 1 can ensure that there is a finite horizon $T$ such that after time $T$ the distance between the set and the cumulative payoff is arbitrarily small, regardless of what strategy player 2 is using. This paper focuses on the case where the attainable set consists of one payoff vector. In this case the vector is called an attainable vector. We study properties of the set of attainable vectors, and characterize when a specific vector is attainable and when every vector is attainable.

math.OC↗

arXiv2013

Finite Alphabet Control of Logistic Networks with Discrete Uncertainty

We consider logistic networks in which the control and disturbance inputs take values in finite sets. We derive a necessary and sufficient condition for the existence of robustly control invariant (hyperbox) sets. We show that a stronger version of this condition is sufficient to guarantee robust global attractivity, and we construct a counterexample demonstrating that it is not necessary. Being constructive, our proofs of sufficiency allow us to extract the corresponding robust control laws and to establish the invariance of certain sets. Finally, we highlight parallels between our results and existing results in the literature, and we conclude our study with two simple illustrative examples.

math.OC↗