Event‐triggered distributed algorithm for searching general Nash equilibrium with general step‐size

In this article, searching the general Nash equilibrium in the noncooperation game is discussed under the general constraints of containing bounded constraint, coupled equality constraint, and private inequality constraint. Meanwhile, the continuous-time event-triggered distributed subgradient projective algorithm (C-ETDSP algorithm), to greatly cut down the number of communication flows, is designed. In the C-ETDSP algorithm, the demand for step-size is weakened to a general step-size of square nonsummable. Then it is proved that the Zeno behavior did not exist in the continuous-time event-triggered mechanism. In addition, the convergence of different types of step-sizes is further compared. Finally, the effectiveness of the design algorithm and the correctness of the theoretical results are verified by a simulation example.