Towards time-varying proximal dynamics in Multi-Agent Network Games

Distributed decision making in multi-agent networks has recently attracted significant research attention thanks to its wide applicability, e.g. in the management and optimization of computer networks, power systems, robotic teams, sensor networks and consumer markets. Distributed decision-making problems can be modeled as inter-dependent optimization problems, i.e., multi-agent game-equilibrium seeking problems, where noncooperative agents seek an equilibrium by communicating over a network. To achieve a network equilibrium, the agents may decide to update their decision variables via proximal dynamics, driven by the decision variables of the neighboring agents. In this paper, we provide an operator-theoretic characterization of convergence with a time-invariant communication network. For the time-varying case, we consider adjacency matrices that may switch subject to a dwell time. We illustrate our investigations using a distributed robotic exploration example.Comment: 6 pages, 3 figure

Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper)

Exploiting the efficiency and stability of Position-Based Dynamics (PBD), we introduce a novel crowd simulation method that runs at interactive rates for hundreds of thousands of agents. Our method enables the detailed modeling of per-agent behavior in a Lagrangian formulation. We model short-range and long-range collision avoidance to simulate both sparse and dense crowds. On the particles representing agents, we formulate a set of positional constraints that can be readily integrated into a standard PBD solver. We augment the tentative particle motions with planning velocities to determine the preferred velocities of agents, and project the positions onto the constraint manifold to eliminate colliding configurations. The local short-range interaction is represented with collision and frictional contact between agents, as in the discrete simulation of granular materials. We incorporate a cohesion model for modeling collective behaviors and propose a new constraint for dealing with potential future collisions. Our new method is suitable for use in interactive games.Comment: 9 page

Multi-agent network games with applications in smart electric mobility

The growing complexity and globalization of modern society brought to light novel problems and challenges for researchers that aim to model real-life phenomena. Nowadays communities and even single individuals cannot be considered as a closed system, since one's actions create a ripple effect that ends up influencing the action of others. Therefore, the study of decision-making processes over networks became a pivotal topic in the research community. The possible applications are virtually endless and span into many different fields. Two of the most relevant examples are smart mobility and energy management in highly populated cities, where a collection of (partially) noncooperative individuals interact over a network trying to reach an efficient equilibrium point, in the sense of Nash, and share limited resources due to the environment in which they operate. In this work, we approach these problems through the lens of game theory. We use different declinations of this powerful mathematical tool to study several aspects of these themes. We design decentralized iterative algorithms solving generalized network games that generate behavioral rules for the players that, if followed, ensure global convergence. Then, we question the classical assumption of perfect players’ rationality by introducing novel dynamics to model partial rationality and analyzing their properties. We conclude by focusing on the design of optimal policies to regulate smart mobility and energy management. In this case, we create a detailed and more realistic description of the problem and use a nudging mechanism, implemented by means of a semi-decentralized algorithm, to align the users' behavior with the one desired by the policymaker