1,721,030 research outputs found
Sharing Beliefs to Learn Nash Equilibria
Full text linkWe consider finite games where the agents only share their beliefs on the possible equilibrium configuration. Specifically, the agents experience the strategies of their opponents only as realized parameters, thereby updating and sharing beliefs on the possible configurations iteratively. We show that combining non-bayes updates with best-response dynamics allows the agents to learn the Nash equilibrium, i.e., the belief distribution over the set of parameters has a peak on the true configuration. Convergence results of the learning mechanism are provided in two cases: the agents learn the equilibrium configuration as a whole, or the agents learn those strategies of the opponents that constitute such an equilibrium
Generalized Nash equilibrium problems under partial-decision information with biased agents
Full text linkWe consider generalized Nash equilibrium (GNE) problems under a partial-decision information regime, in which each agent typically reconstructs the opponents' strategies through a linear averaging dynamics. In contrast, we consider a state-dependent, nonlinear susceptibility term within the communication mechanism, thereby modelling possible biases on the part of agents in processing information. By including such a term in a relaxed forward-backward iteration scheme, we design a distributed algorithm possessing convergence guarantees to a GNE. Simulation results illustrate how the susceptibility term affects the GNE computation
Actively Learning Equilibria in Nash Games With Misleading Information
Full text linkWe develop a scheme based on active learning to compute equilibria in a generalized Nash equilibrium problem (GNEP). Specifically, an external observer (or entity), with little knowledge on the multi-agent process at hand, collects sensible data by probing the agents’ best-response (BR) mappings, which are then used to recursively update local parametric estimates of these mappings. Unlike (Fabiani and Bemporad, 2024), we consider the realistic case in which the agents share corrupted information with the external entity for, e.g., protecting their privacy. Inspired by a popular approach in stochastic optimization, we endow the external observer with an inexact proximal scheme for updating the local BR proxies. This technique will prove key to establishing the convergence of our scheme under standard assumptions, thereby enabling the external observer to predict an equilibrium strategy even when relying on masked information
On Distributionally Robust Generalized Nash Games Defined over the Wasserstein Ball
Full text linkIn this paper we propose an exact, deterministic, and fully continuous reformulation of generalized Nash games characterized by the presence of soft coupling constraints in the form of distributionally robust (DR) joint chance-constraints (CCs). We first rewrite the underlying uncertain game introducing mixed-integer variables to cope with DR–CCs, where the integer restriction actually amounts to a binary decision vector only, and then extend it to an equivalent deterministic problem with one additional agent handling all those introduced variables. Successively we show that, by means of a careful choice of tailored penalty functions, the extended deterministic game with additional agent can be equivalently recast in a fully continuous setting
A Gauss-Seidel method for solving multi-leader-multi-follower games
No full textWe design a computational approach to find equilibria in a class of Nash games possessing a hierarchical structure. By using tools from mixed-integer optimization and the characterization of variational equilibria in terms of the Karush-Kuhn-Tucker conditions, we propose a mixed-integer game formulation for solving this challenging class of problems. Besides providing an equivalent reformulation, we design a proximal Gauss-Seidel method with global convergence guarantees in case the game enjoys a potential structure. We finally corroborate the numerical performance of the algorithm on a novel instance of the ride-hail market problem
A Distributed, Passivity-Based Control of Autonomous Mobile Sensors in an Underwater Acoustic Network
Full text linkThis paper presents a cooperative and distributed control law for multiple Autonomous Underwater Vehicles (AUVs) executing a mission while meeting mutual communication constraints. Virtual couplings define interaction control forces between neighbouring vehicles. Moreover, the couplings are designed to enforce a desired vehicle-vehicle and vehicle-target spacing. The whole network is modelled in the passive, energy-based, port-Hamiltonian framework. Such framework allows to prove closed-loop stability using the whole system kinetic and virtual potential energy by constructing a suitable Lyapunov function. Furthermore, the robustness to communication delays is also demonstrated. Simulation results are given to illustrate the effectiveness of the proposed approach
A stochastic generalized Nash equilibrium model for platforms competition in the ride-hail market
Full text linkThe inherent uncertainties in the ride-hailing market complicate the pricing strategies of on-demand platforms that compete each other to offer a mobility service while striving to maximize their profit. Looking at this problem as a stochastic generalized Nash equilibrium problem (SGNEP), we design a distributed, stochastic equilibrium seeking algorithm with Tikhonov regularization to find an optimal pricing strategy. The proposed iterative scheme does not require a potentially infinite number of samples of the random variable to perform the stochastic approximation, thus making it appealing from a practical perspective. Moreover, we show that the algorithm returns a Nash equilibrium under mere monotonicity assumptions and a careful choice of the step size sequence, obtained by exploiting the specific structure of the SGNEP at hand
A distributed passivity approach to AUV teams control in cooperating potential games
Full text linkThe paper proposes a general framework to manage a team of Autonomous Underwater Vehicles (AUVs), while keeping the communication constraints, during missions execution. Virtual spring-damper couplings (passive by definition) define the distributed interaction forces between neighbouring vehicles. In this way, through passivity theory, a suitable Lyapunov function for the closed loop system is built to ensure stable convergence of the network vehicles to an equilibrium point, also providing robustness in presence of communication fading and delays, very common in the marine environment. Simulations of typical missions show the effectiveness of the proposed approach. An equivalence between this typical port-Hamiltonian framework and a specific class of potential games, the Bilateral Symmetric Interaction (BSI) one, is also established. Hence, modelling the network with passive elements, it is possible to shape the transient behaviour of the players and the reached equilibria at the end of the game
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