We address a class of Nash games with nonconvex coupling constraints for which we define a novel notion of local equilibrium, here named local generalized Nash equilibrium (LGNE). Our first technical contribution is to show the stability in the game theoretic sense of these equilibria on a specific local subset of the original feasible set. Remarkably, we show that the proposed notion of local equilibrium can be equivalently formulated as the solution of a quasi-variational inequality with equal Lagrange multipliers. Next, under the additional proximal smoothness assumption of the coupled feasible set, we define conditions for the existence and local uniqueness of a LGNE. To compute such an equilibrium, we propose two discrete-time dynamics, or fixed-point iterations implemented in a centralized fashion. Our third technical contribution is to prove convergence under (strongly) monotone assumptions on the pseudo- gradient mapping of the game and proximal smoothness of the coupled feasible set. Finally, we apply our theoretical results to a noncooperative version of the optimal power flow control problem.

We propose a data-driven, user-centric vehicle-to-grid (V2G) methodology based on multi-objective optimization to balance battery degradation and V2G revenue according to EV user preference. Given the lack of accurate and generalizable battery degradation models, we leverage input convex neural networks (ICNNs) to develop a data-driven degradation model trained on extensive experimental datasets. This approach enables our model to capture nonconvex dependencies on battery temperature and time while maintaining convexity with respect to the charging rate. Such a partial convexity property ensures that the second stage of our methodology remains computationally efficient. In the second stage, we integrate our data-driven degradation model into a multi-objective optimization framework to generate an optimal smart charging profile for each EV. This profile effectively balances the trade-off between financial benefits from V2G participation and battery degradation, controlled by a hyperparameter reflecting the user prioritization of battery health. Numerical simulations show the high accuracy of the ICNN model in predicting battery degradation for unseen data. Finally, we present a trade-off curve illustrating financial benefits from V2G versus losses from battery health degradation based on user preferences and showcase smart charging strategies under realistic scenarios.

We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov–Metzler inequalities and on a matrix S-lemma, we derive data-dependent bilinear programs, whose solution directly returns a provably stabilizing controller and ensures H₂ or H_∞ performance. We further present relaxations that considerably reduce the computational cost, still without requiring stabilizability of any of the switching modes. Finally, we showcase the flexibility of our approach on the constrained stabilization problem for an unknown perturbed linear system. We validate our theoretical findings numerically, demonstrating the favorable trade-off between conservatism and tractability achieved by the proposed relaxations.

We present a novel user-centric vehicle-to-grid (V2G) framework that enables electric vehicle (EV) users to balance the trade-off between financial benefits from V2G and battery health degradation based on individual preference signals. Specifically, we introduce a game-theoretic model that treats the conflicting objectives of maximizing revenue from V2G participation and minimizing battery health degradation as two self-interested players. Via an enhanced semi-empirical battery health degradation model, we propose a finite-horizon smart charging strategy based on a horizon-splitting approach. Our method determines an appropriate allocation of time slots to each player according to the user's preferences, allowing for a flexible, personalized trade-off between V2G revenue and battery longevity. We conduct a comparative study between our approach and a multi-objective optimization formulation by evaluating the robustness of the charging schedules under parameter uncertainty and providing empirical estimates of regret and sensitivity. We validate our approach using realistic datasets through extensive trade-off studies that explore the impact of factors such as ambient temperature, charger type, and battery capacity, offering key insights to guide EV users in making informed decisions about V2G participation.

We study coalitional games with exogenous uncertainty in the coalition value, in which each agent is allowed to have private samples of the uncertainty. As a consequence, the agents may have a different perception of stability of the grand coalition. In this context, we propose a novel methodology to study the out-of-sample coalitional rationality of allocations in the set of stable allocations (i.e., the core). Our analysis builds on the framework of probably approximately correct learning. Initially, we state a priori and a posteriori guarantees for the entire core. Furthermore, we provide a distributed algorithm to compute a compression set that determines the generalization properties of the a posteriori statements. We then refine our probabilistic robustness bounds by specialising the analysis to a single payoff allocation, taking, also in this case, both a priori and a posteriori approaches. Finally, we consider a relaxed ζ-core to include nearby allocations and also address the case of empty core. For this case, probabilistic statements are given on the eventual stability of allocations in the ζ-core.

In many areas of industry and society, including energy, healthcare, and logistics, agents collect vast amounts of data that are deemed proprietary. These data owners extract predictive information of varying quality and relevance from data depending on quantity, inherent information content, and their own technical expertise. Aggregating these data and heterogeneous predictive skills, which are distributed in terms of ownership, can result in a higher collective value for a prediction task. In this paper, a platform for improving predictions via the implicit pooling of private information in return for possible remuneration is envisioned. Specifically, a wagering-based forecast elicitation market platform has been designed, in which a buyer intending to improve their forecasts posts a prediction task, and sellers respond to it with their forecast reports and wagers. This market delivers an aggregated forecast to the buyer (pre-event) and allocates a payoff to the sellers (post-event) for their contribution. A payoff mechanism is proposed and it is proven that it satisfies several desirable economic properties, including those specific to electronic platforms. Furthermore, the properties of the forecast aggregation operator and scoring rules are discussed in order to emphasize their effect on the sellers’ payoff. Finally, numerical examples are provided in order to illustrate the structure and properties of the proposed market platform.

We formulate for the first time the economic dispatch problem among prosumers in an integrated electrical and gas distribution system (IEGDS) as a game equilibrium problem. Specifically, by approximating the nonlinear gas-flow equations either with a mixed-integer second-order cone (MISOC) or a piecewise affine (PWA) model and by assuming that electricity and gas prices depend linearly on the total consumption, we obtain a potential mixed-integer game. To compute an approximate generalized Nash equilibrium (GNE), we propose an iterative two-stage method that exploits a problem convexification and the gas-flow models. We quantify the quality of the computed solution and perform a numerical study to evaluate the performance of our method.

We study the data-driven finite-horizon linear quadratic regularization (LQR) problem reformulated as a semidefinite program (SDP). Our contribution is to propose two novel accelerated first-order methods for solving the resulting SDP. Our methods enjoy adaptive stepsize and adaptive smoothing parameters that speed up convergence and in turn, enhance scalability. Finally, we compare our accelerated first-order methods and show their benefits via numerical simulations on a benchmark LQR example.

We examine the routing problem for self-interested vehicles using stochastic decision strategies. By approximating the road latency functions and a non-linear variable transformation, we frame the problem as an aggregative game. We characterize the approximation error and we derive a new monotonicity condition for a broad category of games that encompasses the problem under consideration. Next, we propose a semi-decentralized algorithm to calculate the routing as a variational generalized Nash equilibrium and demonstrate the solution's benefits with numerical simulations. In the particular case of potential games, which emerges for linear latency functions, we explore a receding-horizon formulation of the routing problem, showing asymptotic convergence to destinations and analysing closed-loop performance dependence on horizon length through numerical simulations.

Multiagent decision problems are typically solved via distributed iterative algorithms, where the agents only communicate among themselves on a peer-to-peer network. Each agent usually maintains a copy of each decision variable, while agreement among the local copies is enforced via consensus protocols. Yet, each agent is often directly influenced by a small portion of the decision variables only: neglecting this sparsity results in redundancy, poor scalability with the network size, and communication and memory overhead. To address these challenges, we develop Estimation Network Design (END), a framework for the design and analysis of distributed algorithms. END algorithms can be tuned to exploit problem-specific sparsity structures, by optimally allocating copies of each variable only to a subset of agents, to improve efficiency and minimize redundancy. We illustrate the END's potential on generalized Nash equilibrium seeking under partial-decision information by designing new algorithms that can leverage the sparsity in cost functions, constraints, and aggregation values, and by relaxing the assumptions on the (directed) communication network postulated in the literature. Finally, we numerically test our methods on a unicast rate allocation problem, revealing greatly reduced communication and memory costs.

In this paper, we solve the problem of learning a generalized Nash equilibrium (GNE) in merely monotone games. First, we propose a novel continuous semi-decentralized solution algorithm without projections that uses first-order information to compute a GNE with a central coordinator. As the second main contribution, we design a gain adaptation scheme for the previous algorithm in order to alleviate the problem of improper scaling of the cost functions versus the constraints. Third, we propose a data-driven variant of the former algorithm, where each agent estimates their individual pseudogradient via zeroth-order information, namely, measurements of their individual cost function values. Finally, we apply our method to a perturbation amplitude optimization problem in oil extraction engineering.

Generative adversarial networks (GANs) are a class of generative models with two antagonistic neural networks: a generator and a discriminator. These two neural networks compete against each other through an adversarial process that can be modeled as a stochastic Nash equilibrium problem. Since the associated training process is challenging, it is fundamental to design reliable algorithms to compute an equilibrium. In this article, we propose a stochastic relaxed forward-backward (SRFB) algorithm for GANs, and we show convergence to an exact solution when an increasing number of data is available. We also show convergence of an averaged variant of the SRFB algorithm to a neighborhood of the solution when only a few samples are available. In both cases, convergence is guaranteed when the pseudogradient mapping of the game is monotone. This assumption is among the weakest known in the literature. Moreover, we apply our algorithm to the image generation problem.

We study generalized games with full row rank equality coupling constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.

In this article, we propose a bilateral peer-to-peer (P2P) energy trading scheme under single-contract and multi-contract market setups, both as an assignment game, a special class of coalitional games. The proposed market formulation allows for efficient computation of a market equilibrium while keeping the desired economic properties offered by the coalitional games. Furthermore, our market model allows buyers to have heterogeneous preferences (product differentiation) over the energy sellers, which can be economic, social, or environmental. To address the problem of scalability in coalitional games, we design a novel distributed negotiation mechanism that utilizes the geometric structure of the equilibrium solution to improve the convergence speed. Our algorithm enables market participants (prosumers) to reach a consensus on a set of 'stable' and 'fair' bilateral contracts which encourages prosumer participation. The negotiation process is executed with virtually minimal information requirements on a time-varying communication network that in turn preserves privacy. We use operator-theoretic tools to rigorously prove its convergence. Numerical simulations illustrate the benefits of our negotiation protocol and show that the average execution time of a negotiation step is much faster than the benchmark.

We study predictive control for blood glucose regulation in patients with type 1 diabetes mellitus. We determine optimal control actions for insulin and glucagon infusion via linear time-varying model predictive control (LTV MPC) and dynamic linerization around the state trajectory predicted. Through in silico implementation of a comprehensive nonlinear model, we show that our proposed controller is able to reject meal disturbances, retain normoglycemia afterwards and significantly outperform standard linearized MPC.

We consider a large population of decision makers that choose their evolutionary strategies based on simple pairwise imitation rules. We describe such a dynamic process by the replicator dynamics. Differently from the available literature, where the payoffs signals are assumed to be updated continuously, we consider a more realistic scenario where they are updated occasionally. Our main technical contribution is to devise two event-triggered communication schemes with asymptotic convergence guarantees to a Nash equilibrium. Finally, we show how our proposed approach is applicable as an efficient distributed demand response mechanism.