Martina Vanelli

Martina Vanelli, Laura Arditti, Giacomo Como et al.

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.

Giacomo Como, Fabio Fagnani, Leonardo Massai et al.

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.

Martina Vanelli, Nima Monshizadeh, Julien M. Hendrickx

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.