Time-varying constrained proximal type dynamics in multi-agent network games

An asynchronous distributed and scalable generalized Nash equilibrium seeking algorithm for strongly monotone games

“…The choice of affine coupling constraints is widely spread in the literature of noncooperative games, see e.g., [7,18,19]. Moreover, in [3,Remark 3], it is highlighted that separable and convex coupling constraints can always be rewritten in an affine form.…”

“…Moreover, in [3,Remark 3], it is highlighted that separable and convex coupling constraints can always be rewritten in an affine form. Finally, we introduce some standard assumptions [7,19] on the sets just introduced.…”

“…An important property of these equilibria is that each agent faces the same penalty to fulfill the coupling constraints, which is particularly useful to represent a "fair" competition between agents [6]. Variational GNE can be seen as a particular case of the concept of normalized equilibrium points, firstly introduced by Rosen in [22] and further studied in [19,23].…”

“…Choose δ, ε i , τ i satisfying (19), while η ∈ (0, 1) and ρ ∈ (0, 1]. Iteration k: Communication: each i ∈ N gathers λ j (k) from the neighbors and updates the disagreement vector…”

“…For every i ∈ N, choose δ, ε i , τ i satisfying (19), η ∈ (0, 1) and set µ i = 0 m . Iteration k: Select the agent i k with probability P[ζ(k) = H i k ] = p i k Reading: Agent i k copies its public memory in the private one, i.e., the values x j , λ j , ∀ j ∈ N i k , and µ i .…”