155 research outputs found
Nash and Wardrop equilibria in aggregative games with coupling constraints
We consider the framework of aggregative games, in which the cost function of
each agent depends on his own strategy and on the average population strategy.
As first contribution, we investigate the relations between the concepts of
Nash and Wardrop equilibrium. By exploiting a characterization of the two
equilibria as solutions of variational inequalities, we bound their distance
with a decreasing function of the population size. As second contribution, we
propose two decentralized algorithms that converge to such equilibria and are
capable of coping with constraints coupling the strategies of different agents.
Finally, we study the applications of charging of electric vehicles and of
route choice on a road network.Comment: IEEE Trans. on Automatic Control (Accepted without changes). The
first three authors contributed equall
Probably Approximately Correct Nash Equilibrium Learning
We consider a multi-agent noncooperative game with agents' objective
functions being affected by uncertainty. Following a data driven paradigm, we
represent uncertainty by means of scenarios and seek a robust Nash equilibrium
solution. We treat the Nash equilibrium computation problem within the realm of
probably approximately correct (PAC) learning. Building upon recent
developments in scenario-based optimization, we accompany the computed Nash
equilibrium with a priori and a posteriori probabilistic robustness
certificates, providing confidence that the computed equilibrium remains
unaffected (in probabilistic terms) when a new uncertainty realization is
encountered. For a wide class of games, we also show that the computation of
the so called compression set - a key concept in scenario-based optimization -
can be directly obtained as a byproduct of the proposed solution methodology.
Finally, we illustrate how to overcome differentiability issues, arising due to
the introduction of scenarios, and compute a Nash equilibrium solution in a
decentralized manner. We demonstrate the efficacy of the proposed approach on
an electric vehicle charging control problem.Comment: Preprint submitted to IEEE Transactions on Automatic Contro
Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control
This paper considers decentralized control and optimization methodologies for
large populations of systems, consisting of several agents with different
individual behaviors, constraints and interests, and affected by the aggregate
behavior of the overall population. For such large-scale systems, the theory of
aggregative and mean field games has been established and successfully applied
in various scientific disciplines. While the existing literature addresses the
case of unconstrained agents, we formulate deterministic mean field control
problems in the presence of heterogeneous convex constraints for the individual
agents, for instance arising from agents with linear dynamics subject to convex
state and control constraints. We propose several model-free feedback
iterations to compute in a decentralized fashion a mean field Nash equilibrium
in the limit of infinite population size. We apply our methods to the
constrained linear quadratic deterministic mean field control problem and to
the constrained mean field charging control problem for large populations of
plug-in electric vehicles.Comment: IEEE Trans. on Automatic Control (cond. accepted
Autonomous Demand Side Management Based on Energy Consumption Scheduling and Instantaneous Load Billing: An Aggregative Game Approach
In this paper, we investigate a practical demand side management scenario
where the selfish consumers compete to minimize their individual energy cost
through scheduling their future energy consumption profiles. We propose an
instantaneous load billing scheme to effectively convince the consumers to
shift their peak-time consumption and to fairly charge the consumers for their
energy consumption. For the considered DSM scenario, an aggregative game is
first formulated to model the strategic behaviors of the selfish consumers. By
resorting to the variational inequality theory, we analyze the conditions for
the existence and uniqueness of the Nash equilibrium (NE) of the formulated
game. Subsequently, for the scenario where there is a central unit calculating
and sending the real-time aggregated load to all consumers, we develop a one
timescale distributed iterative proximal-point algorithm with provable
convergence to achieve the NE of the formulated game. Finally, considering the
alternative situation where the central unit does not exist, but the consumers
are connected and they would like to share their estimated information with
others, we present a distributed agreement-based algorithm, by which the
consumers can achieve the NE of the formulated game through exchanging
information with their immediate neighbors.Comment: 11 pages, 7 figure
Getting noncooperative agents to cooperate:nudging and dynamic interventions
Due to the strong interconnection between modern engineering systems and their users, performance of these systems heavily rely on the user behavior. Therefore, uncoordinated user behavior can deteriorate the overall performance and entail undesired outcomes. To address this problem, this thesis studies the problem of designing suitable interventions that provide coordination among noncooperative agents/players. We investigate the development of suitable interventions in several setups and propose mechanisms that achieve a desired outcome. The first part of the thesis focuses on altering the aggregative behavior of noncooperative price-taking agents towards a desired stationary or temporal behavior. We address this problem by introducing a nudge framework, where a system regulator modifies the behavior of the agents by providing a price prediction signal. In the second part of the thesis, we focus on designing intervention mechanisms that steer the actions of noncooperative players in network games to the social optimum. We investigate different cases based on the knowledge of the system regulator on the game as well as constraints on the actions and interventions. The third part of the thesis deals with the problem of Nash equilibrium seeking in aggregative games. We develop a distributed algorithm where the players communicate to their neighboring players. The robustness and privacy preserving properties of the algorithm are also analyzed
Mean-Field-Type Games in Engineering
A mean-field-type game is a game in which the instantaneous payoffs and/or
the state dynamics functions involve not only the state and the action profile
but also the joint distributions of state-action pairs. This article presents
some engineering applications of mean-field-type games including road traffic
networks, multi-level building evacuation, millimeter wave wireless
communications, distributed power networks, virus spread over networks, virtual
machine resource management in cloud networks, synchronization of oscillators,
energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201
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