arXiv subjects

Martina Vanelli

Publications and source records attributed to Martina Vanelli.

12 recordsLinked to original sources

arXiv2026

Local Identifiability of Networks with Nonlinear Node Dynamics

We study the identifiability of nonlinear network systems with partial excitation and partial measurement when the network dynamics is linear on the edges and nonlinear on the nodes. We assume that the graph topology and the nonlinear functions at the node level are known, and we aim to identify the weight matrix of the graph. Our main result is that, for almost all static analytic nonlinearities that cross the origin, directed graphs are generically locally identifiable if and only if at least one node is excited in every source component of the condensation graph and at least one node is measured in every sink component. This holds even when all other nodes remain unexcited and unmeasured and stands in sharp contrast to most findings on network identifiability requiring measurement and/or excitation of each node. The result applies to homogeneous feed-forward and recurrent artificial neural networks and generalizes previous literature by considering a broader class of activations and architectures.

math.OC↗

arXiv2026

Interpolation Conditions for Instant Data Consistency with Port-Hamiltonian Structure

We develop a data-driven framework for nonlinear port-Hamiltonian (pH) systems based on interpolation conditions to characterize consistency between observed data and structured dynamical models. Specifically, we derive necessary and sufficient conditions for the existence of a pH system with a smooth (convex) Hamiltonian instantly consistent with a given dataset, without requiring explicit parametrization. We further provide a semidefinite programming formulation to verify consistency with non-degenerate interconnection and dissipation structures. Our results provide a principled approach to assess instant data consistency with physical structure and pave the way for control design directly from data.

math.OC↗

arXiv2026

Equilibria in Network Constrained Markets with System Operator

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 à 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 and possibly satisfying additional linear physical constraints. Such flows are determined by the action of a system operator, who aims at maximizing a designated welfare function. We model such competition as a strategic game with $n+1$ players: the producers and the system operator. For this game, we first establish the existence of pure-strategy Nash equilibria under standard concavity assumptions. We then identify sufficient conditions for the game to be exact potential with an essentially unique Nash equilibrium. Next, we present a general result that connects the optimal action of the system operator 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.

cs.GT↗

arXiv2026

On Signed Network Games with Binary Actions

We study binary-action pairwise-separable graphical games that encompass both coordination and anti-coordination network games. Our model is grounded in an underlying directed signed graph, where each link is associated with a signed weight that describes both nature and the strength of the strategic pairwise interaction. Specifically, positive link weight corresponds to a strategic complement type interaction, whereas negative link weight corresponds to strategic substitute type interaction. The utility for each player is then an aggregation of pairwise terms determined by the weights of the signed graph in addition to an individual bias term. We consider a scenario that assumes the presence of a prominent cohesive subset of players, who are either connected exclusively by positive weights, or form a structurally balanced subset that can be bipartitioned into two adversarial subcommunities with positive intra-community and negative inter-community edges. Under suitable properties of the game restricted to the remaining players, our results guarantee the existence of Nash equilibria characterized by either consensus or polarization within the first group, as well as their stability under best response transitions. Our results can be interpreted as robustness results, building on the super-modular properties of network coordination games and on a novel use of the concept of graph cohesiveness.

cs.GT↗

arXiv2026

Data Poisoning Attacks Can Systematically Destabilize Data-Driven Control Synthesis

Data-driven control has emerged as a powerful paradigm for synthesizing controllers directly from data, bypassing explicit model identification. However, this reliance on data introduces new and largely unexplored vulnerabilities. In this paper, we show that an attacker can systematically poison the data used for control synthesis, causing any linear state-feedback controller synthesized by the planner to destabilize the physical system. Concerningly, we show that the attacker can achieve this objective without knowledge of the system model or the controller synthesis procedure. To this end, we develop a recursive data-poisoning mechanism that generates falsified state trajectories, inducing a precise geometric shift in the apparent system dynamics. More broadly, our results establish that data-driven control pipelines can be deterministically destabilized by model-agnostic attacks operating solely at the data level. Numerical simulations corroborate these findings for both noise-free and noisy data.

math.OC↗

arXiv2025

Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems

We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all trajectories consistent with the measured data and these prior bounds in a purely data-driven manner. This characterization enables data-consistency verification, inference, and one-step ahead prediction, which can be leveraged for safety verification and cost minimization. Ultimately, this work represents a preliminary step toward exploiting interpolation conditions in data-driven control, offering a systematic way to characterize trajectories consistent with a dynamical system within a given class and enabling their use in control design.

eess.SY↗

arXiv2025

How competitive are pay-as-bid auction games?

We study the pay-as-bid auction game, a supply function model with discriminatory pricing and asymmetric firms. In this game, strategies are non-decreasing supply functions relating pric to quantity and the exact choice of the strategy space turns out to be a crucial issue: when it includes all non-decreasing continuous functions, pure-strategy Nash equilibria often fail to exist. To overcome this, we restrict the strategy space to the set of Lipschitz-continuous functions and we prove that Nash equilibria always exist (under standard concavity assumptions) and consist of functions that are affine on their own support and have slope equal to the maximum allowed Lipschitz constant. We further show that the Nash equilibrium is unique up to the market-clearing price when the demand is affine and the asymmetric marginal production costs are homogeneous in zero. For quadratic production costs, we derive a closed-form expression and we compute the limit as the allowed Lipschitz constant grows to infinity. Our results show that in the limit the pay-as-bid auction game achieves perfect competition with efficient allocation and induces a lower market-clearing price compared to supply function models based on uniform price auctions.

math.OC↗

arXiv2023

Nash equilibria of the pay-as-bid auction with K-Lipschitz supply functions

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.

eess.SY↗

arXiv2023

Robust Coordination of Linear Threshold Dynamics on Directed Weighted Networks

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.

cs.GT↗

arXiv2021

Equilibria and learning dynamics in mixed network coordination/anti-coordination games

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.

cs.GT↗

arXiv2021

On games with coordinating and anti-coordinating agents

This work studies Nash equilibria for games where a mixture of coordinating and anti-coordinating agents, with possibly heterogeneous thresholds, coexist and interact through an all-to-all network. Whilst games with only coordinating or only anti-coordinating agents are potential, also in the presence of heterogeneities, this does not hold when both type of agents are simultaneously present. This makes their analysis more difficult and existence of Nash equilibria not guaranteed. Our main result is a checkable condition on the threshold distributions that characterizes the existence of Nash equilibria in such mixed games. When this condition is satisfied an explicit algorithm allows to determine the complete set of such equilibria. Moreover, for the special case when only one type of agents is present (either coordinating or anti-coordinating), our results allow an explicit computation of the cardinality of Nash equilibria.

cs.GT↗

arXiv2020

Robustness of Nash Equilibria in Network Games

We analyze the robustness of (pure strategy) Nash equilibria for network games against perturbations of the players' utility functions. We first derive a simple characterization of the margin of robustness, defined as the minimum magnitude of a perturbation that makes a Nash equilibrium of the original game stop being so in the perturbed game. Then, we investigate what the maximally robust equilibria are in some standard network games such as the coordination and the anti-coordination game. Finally, as an application, we provide some sufficient conditions for the existence of Nash equilibria in network games with a mixture of coordinating and anticoordinating games.

cs.GT↗