1,415 research outputs found
Geometric Convergence of Distributed Heavy-Ball Nash Equilibrium Algorithm over Time-Varying Digraphs with Unconstrained Actions
We propose a new distributed algorithm that combines heavy-ball momentum and
a consensus-based gradient method to find a Nash equilibrium (NE) in a class of
non-cooperative convex games with unconstrained action sets. In this approach,
each agent in the game has access to its own smooth local cost function and can
exchange information with its neighbors over a communication network. The
proposed method is designed to work on a general sequence of time-varying
directed graphs and allows for non-identical step-sizes and momentum
parameters. Our work is the first to incorporate heavy-ball momentum in the
context of non-cooperative games, and we provide a rigorous proof of its
geometric convergence to the NE under the common assumptions of strong
convexity and Lipschitz continuity of the agents' cost functions. Moreover, we
establish explicit bounds for the step-size values and momentum parameters
based on the characteristics of the cost functions, mixing matrices, and graph
connectivity structures. To showcase the efficacy of our proposed method, we
perform numerical simulations on a Nash-Cournot game to demonstrate its
accelerated convergence compared to existing methods
Accelerating Distributed Nash Equilibrium Seeking
This work proposes a novel distributed approach for computing a Nash
equilibrium in convex games with restricted strongly monotone pseudo-gradients.
By leveraging the idea of the centralized operator extrapolation method
presented in [4] to solve variational inequalities, we develop the algorithm
converging to Nash equilibria in games, where players have no access to the
full information but are able to communicate with neighbors over some
communication graph. The convergence rate is demonstrated to be geometric and
improves the rates obtained by the previously presented procedures seeking Nash
equilibria in the class of games under consideration
Nash Equilibrium Seeking in N-Coalition Games via a Gradient-Free Method
This paper studies an -coalition non-cooperative game problem, where the
players in the same coalition cooperatively minimize the sum of their local
cost functions under a directed communication graph, while collectively acting
as a virtual player to play a non-cooperative game with other coalitions.
Moreover, it is assumed that the players have no access to the explicit
functional form but only the function value of their local costs. To solve the
problem, a discrete-time gradient-free Nash equilibrium seeking strategy, based
on the gradient tracking method, is proposed. Specifically, a gradient
estimator is developed locally based on Gaussian smoothing to estimate the
partial gradients, and a gradient tracker is constructed locally to trace the
average sum of the partial gradients among the players within the coalition.
With a sufficiently small constant step-size, we show that all players' actions
approximately converge to the Nash equilibrium at a geometric rate under a
strongly monotone game mapping condition. Numerical simulations are conducted
to verify the effectiveness of the proposed algorithm
Distributed Nash Equilibrium Seeking with Limited Cost Function Knowledge via A Consensus-Based Gradient-Free Method
This paper considers a distributed Nash equilibrium seeking problem, where
the players only have partial access to other players' actions, such as their
neighbors' actions. Thus, the players are supposed to communicate with each
other to estimate other players' actions. To solve the problem, a
leader-following consensus gradient-free distributed Nash equilibrium seeking
algorithm is proposed. This algorithm utilizes only the measurements of the
player's local cost function without the knowledge of its explicit expression
or the requirement on its smoothness. Hence, the algorithm is gradient-free
during the entire updating process. Moreover, the analysis on the convergence
of the Nash equilibrium is studied for the algorithm with both diminishing and
constant step-sizes, respectively. Specifically, in the case of diminishing
step-size, it is shown that the players' actions converge to the Nash
equilibrium almost surely, while in the case of fixed step-size, the
convergence to the neighborhood of the Nash equilibrium is achieved. The
performance of the proposed algorithm is verified through numerical
simulations
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