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We study a networked economic system composed of $n$ producers supplying a single homogeneous good to a number of geographically separated markets and of a centralized authority, called the market maker. Producers compete \`a la Cournot, by choosing the quantities of good to supply to each market they have access to in order to maximize their profit. Every market is characterized by its inverse demand functions returning the unit price of the considered good as a function of the total available quantity. Markets are interconnected by a dispatch network through which quantities of the considered good can flow within finite capacity constraints. Such flows are determined by the market maker, who aims at maximizing a designated welfare function. We model such competition as a strategic game with $n+1$ players: the producers and the market game. For this game, we first establish the existence of Nash equilibria under standard concavity assumptions. We then identify sufficient conditions for the game to be potential with an essentially unique Nash equilibrium. Next, we present a general result that connects the optimal action of the market maker with the capacity constraints imposed on the network. For the commonly used Walrasian welfare, our finding proves a connection between capacity bottlenecks in the market network and the emergence of price differences between markets separated by saturated lines. This phenomenon is frequently observed in real-world scenarios, for instance in power networks. Finally, we validate the model with data from the Italian day-ahead electricity market., Comment: 15 pages, 11 figures

We study stochastic pairwise interaction network systems whereby a finite population of agents, identified with the nodes of a graph, update their states in response to both individual mutations and pairwise interactions with their neighbors. The considered class of systems include the main epidemic models -such as the SIS, SIR, and SIRS models-, certain social dynamics models -such as the voter and anti-voter models-, as well as evolutionary dynamics on graphs. Since these stochastic systems fall into the class of finite-state Markov chains, they always admit stationary distributions. We analyze the asymptotic behavior of these stationary distributions in the limit as the population size grows large while the interaction network maintains certain mixing properties. Our approach relies on the use of Lyapunov-type functions to obtain concentration results on these stationary distributions. Notably, our results are not limited to fully mixed population models, as they do apply to a much broader spectrum of interaction network structures, including, e.g., Erd\"oos-R\'enyi random graphs., Comment: 13 pages

Motivated by empirical research on bias and opinion formation, we formulate a multidimensional nonlinear opinion-dynamical model where agents have individual biases, which are fixed, as well as opinions, which evolve. The dimensions represent competing options, of which each agent has a relative opinion, and are coupled through normalization of the opinion vector. This can capture, for example, an individual's relative trust in different media. In special cases including where biases are uniform across agents our model achieves consensus, but in general, behaviors are richer and capture multipolar opinion distributions. We examine general fixed points of the system, as well as special cases such as zero biases toward certain options or partitioned decision sets. Lastly, we demonstrate that our model exhibits polarization when biases are spatially correlated across the network, while, as empirical research suggests, a mixed community can mediate biases.

This paper introduces a consensus-based generalized multi-population aggregative game coordination approach with application to electric vehicles charging under transmission line constraints. The algorithm enables agents to seek an equilibrium solution while considering the limited infrastructure capacities that impose coupling constraints among the users. The Nash-seeking algorithm consists of two interrelated iterations. In the upper layer, population coordinators collaborate for a distributed estimation of the coupling aggregate term in the agents' cost function and the associated Lagrange multiplier of the coupling constraint, transmitting the latest updated values to their population's agents. In the lower layer, each agent updates its best response based on the most recent information received and communicates it back to its population coordinator. For the case when the agents' best response mappings are non-expansive, we prove the algorithm's convergence to the generalized Nash equilibrium point of the game. Simulation results demonstrate the algorithm's effectiveness in achieving equilibrium in the presence of a coupling constraint., Comment: 8 pages, 5 figures, journal

We study a susceptible-infected-recovered (SIR) epidemic model on a network of $n$ interacting subpopulations. We analyze the transient and asymptotic behavior of the infection dynamics in each node of the network. In contrast to the classical scalar epidemic SIR model, where the infection curve is known to be unimodal (either always decreasing over time, or initially increasing until reaching a peak and from then on monotonically decreasing and asymptotically vanishing), we show the possible occurrence of multimodal infection curves in the network SIR epidemic model with $n\ge2$ subpopulations. We then focus on the special case of rank-$1$ interaction matrices, modeling subpopulations of homogeneously mixing individuals with different activity rates, susceptibility to the disease, and infectivity levels. For this special case, we find $n$ invariants of motion and provide an explicit expression for the limit equilibrium point. We also determine necessary and sufficient conditions for stability of the equilibrium points. We then establish an upper bound on the number of changes of monotonicity of the infection curve at the single node level and provide sufficient conditions for its multimodality. Finally, we present some numerical results revealing that, in the case of interaction matrices with rank larger than $1$, the single nodes' infection curves may display multiple peaks.

We study optimal information provision in transportation networks when users are strategic and the network state is uncertain. An omniscient planner observes the network state and discloses information to the users with the goal of minimizing the expected travel time at the user equilibrium. Public signal policies, including full-information disclosure, are known to be inefficient in achieving optimality. For this reason, we focus on private signals and restrict without loss of generality the analysis to signals that coincide with path recommendations that satisfy obedience constraints, namely users have no incentive in deviating from the received recommendation according to their posterior belief. We first formulate the general problem and analyze its properties for arbitrary network topologies and delay functions. Then, we consider the case of two parallel links with affine delay functions, and provide sufficient conditions under which optimality can be achieved by information design. Interestingly, we observe that the system benefits from uncertainty, namely it is easier for the planner to achieve optimality when the variance of the uncertain parameters is large. We then provide an example where optimality can be achieved even if the sufficient conditions for optimality are not met., Comment: 8 pages, 3 figures. Full version of accepted paper for the 2023 62th IEEE Conference on Decision and Control (CDC)

Superconductivity often emerges as a dome around a quantum critical point (QCP) where long-range order is suppressed to zero temperature. So far, this has been mostly studied in magnetically ordered materials. By contrast, the interplay between charge order and superconductivity at a QCP is not fully understood. Here, we present resistance measurements proving that a dome of superconductivity surrounds the charge-density-wave (CDW) QCP in pristine samples of 1$T$-TiSe$_2$ tuned with hydrostatic pressure. Furthermore, we use quantum oscillation measurements to show that the superconductivity sets in at a Lifshitz transition in the electronic band structure. We use density functional theory to identify the Fermi pockets enabling superconductivity: large electron and hole pockets connected by the CDW wave vector $\vec{Q}$ which emerge upon partial suppression of the zero-pressure CDW gap. Hence, we conclude that superconductivity is of interband type enabled by the presence of hole and electron bands connected by the CDW $\vec{Q}$ vector. Earlier calculations show that interband interactions are repulsive, which suggests that unconventional s$_{\pm}$ superconductivity is realised in TiSe$_2$ - similar to the iron pnictides. These results highlight the importance of Lifshitz transitions in realising unconventional superconductivity and help understand its interaction with CDW order in numerous materials., Comment: 21 pages, 5 figures

We study the asymptotic stability of the logit evolutionary dynamics in population games, possibly with multiple heterogenous populations. For general population games, we prove that, on the one hand, strict Nash equilibria are asymptotically stable under the logit dynamics for low enough noise levels, on the other hand, a globally exponentially stable logit equilibrium exists for sufficiently large noise levels. This suggests the emergence of bifurcations in population games admitting multiple strict Nash equilibria, as observed in numerous examples. We then provide sufficient conditions on the population game structure for the existence of globally asymptotically stable logit equilibria for every noise level. The considered class of monotone separable games finds applications, e.g., in routing games on series compositions of networks with parallel routes when there are multiple populations of users that differ in the reward functions., Comment: 16 pages, 2 figures

We model a system of n asymmetric firms selling a homogeneous good in a common market through a pay-as-bid auction. Every producer chooses as its strategy a supply function returning the quantity S(p) that it is willing to sell at a minimum unit price p. The market clears at the price at which the aggregate demand intersects the total supply and firms are paid the bid prices. We study a game theoretic model of competition among such firms and focus on its equilibria (Supply function equilibrium). The game we consider is a generalization of both models where firms can either set a fixed quantity (Cournot model) or set a fixed price (Bertrand model). Our main result is to prove existence and provide a characterization of (pure strategy) Nash equilibria in the space of K-Lipschitz supply functions., Comment: 6 pages, 5 figures, to appear Proc. of the 22nd International Federation of Automatic Control World Congress (IFAC 2023)

Road traffic scene reconstruction from videos has been desirable by road safety regulators, city planners, researchers, and autonomous driving technology developers. However, it is expensive and unnecessary to cover every mile of the road with cameras mounted on the road infrastructure. This paper presents a method that can process aerial videos to vehicle trajectory data so that a traffic scene can be automatically reconstructed and accurately re-simulated using computers. On average, the vehicle localization error is about 0.1 m to 0.3 m using a consumer-grade drone flying at 120 meters. This project also compiles a dataset of 50 reconstructed road traffic scenes from about 100 hours of aerial videos to enable various downstream traffic analysis applications and facilitate further road traffic related research. The dataset is available at https://github.com/duolu/CAROM., Comment: Accepted to IEEE ICRA 2023

1$T$-TaSe$_2$ is widely believed to host a Mott metal-insulator transition in the charge density wave (CDW) phase according to the spectroscopic observation of a band gap that extends across all momentum space. Previous investigations inferred that the occurrence of the Mott phase is limited to the surface only of bulk specimens, but recent analysis on thin samples revealed that the Mott-like behavior, observed in the monolayer, is rapidly suppressed with increasing thickness. Here, we report combined time- and angle-resolved photoemission spectroscopy and theoretical investigations of the electronic structure of 1$T$-TaSe$_2$. Our experimental results confirm the existence of a state above $E_F$, previously ascribed to the upper Hubbard band, and an overall band gap of $\sim 0.7$ eV at $\overline{\Gamma}$. However, supported by density functional theory calculations, we demonstrate that the origin of this state and the gap rests on band structure modifications induced by the CDW phase alone, without the need for Mott correlation effects., Comment: Accepted by PRL

We study a network formation game where $n$ players, identified with the nodes of a directed graph to be formed, choose where to wire their outgoing links in order to maximize their PageRank centrality. Specifically, the action of every player $i$ consists in the wiring of a predetermined number $d_i$ of directed out-links, and her utility is her own PageRank centrality in the network resulting from the actions of all players. We show that this is a potential game and that the best response correspondence always exhibits a local structure in that it is never convenient for a node $i$ to link to other nodes that are at incoming distance more than $d_i $ from her. We then study the equilibria of this game determining necessary conditions for a graph to be a (strict, recurrent) Nash equilibrium. Moreover, in the homogeneous case, where players all have the same number $d$ of out-links, we characterize the structure of the potential maximizing equilibria and, in the special cases $ d=1 $ and $ d=2 $, we provide a complete classification of the set of (strict, recurrent) Nash equilibria. Our analysis shows in particular that the considered formation mechanism leads to the emergence of undirected and disconnected or loosely connected networks., Comment: 42 pages, 11 figures

A critical aspect in strategic modeling of transportation systems is user heterogeneity. In many real-world scenarios, e.g., when tolls are charged and drivers have different trade-offs between time and money, or when they get informed about current congestion by different routing apps, modeling users as rational decision makers with homogeneous utility functions becomes too restrictive. While global asymptotic stability of user equilibria in homogeneous routing games is known to hold for a broad class of evolutionary dynamics, the stability analysis of user equilibria in heterogeneous routing games is a largely open problem. In this work we study the logit dynamics in heterogeneous routing games on arbitrary network topologies. We show that the dynamics may exhibit bifurcations as the noise level of the dynamics varies, and provide sufficient conditions for asymptotic stability of user equilibria., Comment: 8 pages, 5 figures. Full version of accepted paper for the 2022 61th IEEE Conference on Decision and Control (CDC)

Social influence is largely recognized as a key factor in opinion formation processes. Recently, the role of external forces in inducing opinion displacement and polarization in social networks has attracted significant attention. This is in particular motivated by the necessity to understand and possibly prevent interference phenomena during political campaigns and elections. In this paper, we formulate and solve a targeted intervention problem for opinion displacement minimization on a social network. Specifically, we consider a min-max problem whereby a social planner (the defender) aims at selecting the optimal network intervention within her given budget constraint in order to minimize the opinion displacement in the system that an adversary (the attacker) is instead trying to maximize. Our results show that the optimal intervention of the defender has two regimes. For large enough budget, the optimal intervention of the social planner acts on all nodes proportionally to a new notion of network centrality. For lower budget values, such optimal intervention has a more delicate structure and is rather concentrated on a few target individuals.

Consider discrete-time linear distributed averaging dynamics, whereby agents in a network start with uncorrelated and unbiased noisy measurements of a common underlying parameter (state of the world) and iteratively update their estimates following a non-Bayesian rule. Specifically, let every agent update her estimate to a convex combination of her own current estimate and those of her neighbors in the network. As a result of this iterative averaging, each agent obtains an asymptotic estimate of the state of the world, and the variance of this individual estimate depends on the matrix of weights the agents assign to self and to the others. We study a game-theoretic multi-objective optimization problem whereby every agent seeks to choose her self-weight in such a convex combination in a way to minimize the variance of her asymptotic estimate of the state of the unknown parameters. Assuming that the relative influence weights assigned by the agents to their neighbors in the network remain fixed and form an irreducible and aperiodic relative influence matrix, we characterize the Pareto frontier of the problem, as well as the set of Nash equilibria in the resulting game., Comment: Accepted as a regular paper by MTNS 2022 conference

We investigate a novel approach to resilient distributed optimization with quadratic costs in a multi-agent system prone to unexpected events that make some agents misbehave. In contrast to commonly adopted filtering strategies, we draw inspiration from phenomena modeled through the Friedkin-Johnsen dynamics and argue that adding competition to the mix can improve resilience in the presence of misbehaving agents. Our intuition is corroborated by analytical and numerical results showing that (i) there exists a nontrivial trade-off between full collaboration and full competition and (ii) our competition-based approach can outperform state-of-the-art algorithms based on Weighted Mean Subsequence Reduced. We also study impact of communication topology and connectivity on resilience, pointing out insights to robust network design., Comment: Accepted in IEEE TAC; 17 pages, 44 figures

We study an energy market composed of producers who compete to supply energy to different markets and want to maximize their profits. The energy market is modeled by a graph representing a constrained power network where nodes represent the markets and links are the physical lines with a finite capacity connecting them. Producers play a networked Cournot game on such a network together with a centralized authority, called market maker, that facilitates the trade between geographically separate markets via the constrained power network and aims to maximize a certain welfare function. We first prove a general result that links the optimal action of the market maker with the capacity constraint enforced on the power network. Under mild assumptions, we study the existence and uniqueness of Nash equilibria and exploit our general result to prove a connection between capacity bottlenecks in the power network and the emergence of price differences between different markets that are separated by saturated lines, a phenomenon that is often observed in real power networks.

The excitation and detection of coherent phonons has given unique insights into condensed matter, in particular for materials with strong electron-phonon coupling. We report a study of coherent phonons in the layered charge density wave (CDW) compound 1$T$-TaSe$_2$ performed using transient broadband reflectivity spectroscopy, in the photon energy range 1.75-2.65 eV. Several intense and long lasting (> 20 ps) oscillations, arising from the CDW superlattice reconstruction, are observed allowing for detailed analysis of the spectral dependence of their amplitude and phase. We find that for energies above 2.4 eV, where transitions involve Ta d-bands, the CDW amplitude mode at 2.19 THz dominates the coherent response. At lower energies, instead, beating arises between additional frequencies, with a particularly intense mode at 2.95 THz. Interestingly, our spectral analysis reveals a $\pi$ phase shift at 2.4 eV. Results are discussed considering the selective coupling of specific modes to energy bands involved in the optical transitions seen in steady-state reflectivity. The work demonstrates how coherent phonon spectroscopy can distinguish and resolve optical states strongly coupled to the CDW order and provide additional information normally hidden in conventional steady-state experiments., Comment: 20 pages, 4 figures

This paper proposes a novel approach to resilient distributed optimization with quadratic costs in a networked control system (e.g., wireless sensor network, power grid, robotic team) prone to external attacks (e.g., hacking, power outage) that cause agents to misbehave. Departing from classical filtering strategies proposed in literature, we draw inspiration from a game-theoretic formulation of the consensus problem and argue that adding competition to the mix can enhance resilience in the presence of malicious agents. Our intuition is corroborated by analytical and numerical results showing that i) our strategy highlights the presence of a nontrivial tradeoff between blind collaboration and full competition, and ii) such competition-based approach can outperform state-of-the-art algorithms based on Mean Subsequence Reduced., Comment: 7 pages, 8 figures; accepted for CDC 2022

The recent COVID-19 pandemic highlighted the need of non-pharmaceutical interventions in the first stages of a pandemic. Among these, lockdown policies proved unavoidable yet extremely costly from an economic perspective. To better understand the tradeoffs between economic and epidemic costs of lockdown interventions, we here focus on a simple SIR epidemic model and study lockdowns as solutions to an optimal control problem. We first show numerically that the optimal lockdown policy exhibits a phase transition from suppression to mitigation as the time horizon grows, i.e., if the horizon is short the optimal strategy is to impose severe lockdown to avoid diffusion of the infection, whereas if the horizon is long the optimal control steers the system to herd immunity to reduce economic loss. We then consider two alternative policies, motivated by government responses to the COVID-19 pandemic, where lockdown levels are selected to either stabilize the reproduction number (i.e., "flatten the curve") or the fraction of infected (i.e., containing the number of hospitalizations). We compute analytically the performance of these two feedback policies and compare them to the optimal control. Interestingly, we show that in the limit of infinite horizon stabilizing the number of infected is preferable to controlling the reproduction number, and in fact yields close to optimal performance., Comment: 9 pages, 10 figures. Full version of accepted paper for the 2021 60th IEEE Conference on Decision and Control (CDC)

Whilst network coordination games and network anti-coordination games have received a considerable amount of attention in the literature, network games with coexisting coordinating and anti-coordinating players are known to exhibit more complex behaviors. In fact, depending on the network structure, such games may even fail to have pure-strategy Nash equilibria. An example is represented by the well-known matching pennies (discoordination) game. In this work, we first provide graph-theoretic conditions for the existence of pure-strategy Nash equilibria in mixed network coordination/anti-coordination games of arbitrary size. For the case where such conditions are met, we then study the asymptotic behavior of best-response dynamics and provide sufficient conditions for finite-time convergence to the set of Nash equilibria. Our results build on an extension and refinement of the notion of network cohesiveness and on the formulation of the new concept of network indecomposibility.

We study asynchronous dynamics in a network of interacting agents updating their binary states according to a time-varying threshold rule. Specifically, agents revise their state asynchronously by comparing the weighted average of the current states of their neighbors in the interaction network with possibly heterogeneous time-varying threshold values. Such thresholds are determined by an exogenous signal representing an external influence field modeling the different agents' biases towards one state with respect to the other one. We prove necessary and sufficient conditions for global stability of consensus equilibria, i.e., equilibria where all agents have the same state, robustly with respect to the (constant or time-varying) external field. Our results apply to general weighted directed interaction networks and build on super-modularity properties of certain network coordination games whose best response dynamics coincide with the linear threshold dynamics. In particular, we introduce a novel notion of robust improvement paths for such games and characterize conditions for their existence., Comment: 16 pages, 7 figures

We study extensions of the classical SIR model of epidemic spread. First, we consider a single population modified SIR epidemics model in which the contact rate is allowed to be an arbitrary function of the fraction of susceptible and infected individuals. This allows one to model either the reaction of individuals to the information about the spread of the disease or the result of government restriction measures, imposed to limit social interactions and contain contagion. We study the effect of both smooth dependancies of the contact rate for which we prove the existence of a threshold phenomenon that generalizes the well-known dichotomy associated to the reproduction rate parameter in the classical SIR model, and discontinuous feedback terms, which can be studied using tools from sliding mode control. Finally, we consider network SIR models involving different subpopulations that interact on a contact graph and present some preliminary simulations of modified versions of the classic SIR network., Comment: 6 pages. 4 figures. Accepted to the 2021 60th IEEE Conference on Decision and Control (CDC)

Traffic monitoring cameras are powerful tools for traffic management and essential components of intelligent road infrastructure systems. In this paper, we present a vehicle localization and traffic scene reconstruction framework using these cameras, dubbed as CAROM, i.e., "CARs On the Map". CAROM processes traffic monitoring videos and converts them to anonymous data structures of vehicle type, 3D shape, position, and velocity for traffic scene reconstruction and replay. Through collaborating with a local department of transportation in the United States, we constructed a benchmarking dataset containing GPS data, roadside camera videos, and drone videos to validate the vehicle tracking results. On average, the localization error is approximately 0.8 m and 1.7 m within the range of 50 m and 120 m from the cameras, respectively., Comment: Accepted to IEEE ICRA 2021

We study a network design problem (NDP) where the planner aims at selecting the optimal single-link intervention on a transportation network to minimize the travel time under Wardrop equilibrium flows. Our first result is that, if the delay functions are affine and the support of the equilibrium is not modified with interventions, the NDP may be formulated in terms of electrical quantities computed on a related resistor network. In particular, we show that the travel time variation corresponding to an intervention on a given link depends on the effective resistance between the endpoints of the link. We suggest an approach to approximate such an effective resistance by performing only local computation, and exploit it to design an efficient algorithm to solve the NDP. We discuss the optimality of this procedure in the limit of infinitely large networks, and provide a sufficient condition for its optimality. We then provide numerical simulations, showing that our algorithm achieves good performance even if the equilibrium support varies and the delay functions are non-linear., Comment: 40 pages, 12 figures

We analyze a class of stochastic processes, referred to as asynchronous and semi-anonymous dynamics (ASD), over directed labeled random networks. These processes are a natural tool to describe general best-response and noisy best-response dynamics in network games where each agent, at random times governed by independent Poisson clocks, can choose among a finite set of actions. The payoff is determined by the relative popularity of different actions among neighbors, while being independent of the specific identities of neighbors. Using a mean-field approach, we prove that, under certain conditions on the network and initial node configuration, the evolution of ASD can be approximated, in the limit of large network sizes, by the solution of a system of non-linear ordinary differential equations. Our framework is very general and applies to a large class of graph ensembles for which the typical random graph locally behaves like a tree. In particular, we will focus on labeled configuration-model random graphs, a generalization of the traditional configuration model which allows different classes of nodes to be mixed together in the network, permitting us, for example, to incorporate a community structure in the system. Our analysis also applies to configuration-model graphs having a power-law degree distribution, an essential feature of many real systems. To demonstrate the power and flexibility of our framework, we consider several examples of dynamics belonging to our class of stochastic processes. Moreover, we illustrate by simulation the applicability of our analysis to realistic scenarios by running our example dynamics over a real social network graph., Comment: 64 pages, 15 figures, submitted