13 research outputs found
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
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