  In this paper, we study the distributed generalized Nash equilibrium seeking
problem of non-cooperative games in dynamic environments. Each player in the
game aims to minimize its own time-varying cost function subject to a local
action set. The action sets of all players are coupled through a shared convex
inequality constraint. Each player can only have access to its own cost
function, its own set constraint and a local block of the inequality
constraint, and can only communicate with its neighbours via a connected graph.
Moreover, players do not have prior knowledge of their future cost functions.
To address this problem, an online distributed algorithm is proposed based on
consensus algorithms and a primal-dual strategy. Performance of the algorithm
is measured by using dynamic regrets. Under mild assumptions on graphs and cost
functions, we prove that if the deviation of variational generalized Nash
equilibrium sequence increases within a certain rate, then the regrets, as well
as the violation of inequality constraint, grow sublinearly. A simulation is
presented to demonstrate the effectiveness of our theoretical results.
