Distributed Nash Equilibrium Seeking Strategy With Incomplete Information

The essence of the game lies in decision-making,and the index on which decision-making is based on optimization.This dissertation mainly consider-s the distributed Nash equilibrium problem under the theoretical framework of multi-player non-cooperative games.Generally speaking,a multi-player non-cooperative game system mainly includes the set of players,player systems,and profit functions of players.The profit function of each player is closely related to the state of other players.It is precise because of this correlation that multi-player interaction occurs.Three issues need to be considered when multiple players in-teract in a non-cooperative game system:one is to observe the state of the game and environmental information;the other is to estimate the expected effect,and the last is to update their strategies based on observations.In this dissertation,the leader-following protocol is used to enable each player to update the status information with other players,and the gradient method is used to optimize the profit function of each player.This dissertation mainly considers the following three issues:?In the process of multi-player non-cooperative games,each player changes his own control input to update his own state to maximize the profit function.However,in a distributed network,there is inevitably the problem of channel disturbance.To solve this problem,there is Gaussian white noise when each player interacts with his neighbors.In response to this problem,a distributed Nash equilibrium search algorithm is designed,and it is proved that the state of each player converges to the Nash equilibrium point in the sense of the mean.?In the framework of non-cooperative games,because each player is a com-petitor,the state of each player is private information,but it can be reflected by some functions.This dissertation assumes that the state of the player can be characterized by some linear random functions.In addition,during the player system control process,the system will also be disturbed by some process noise.This dissertation considers that each player's system is interfered with process noise and measurement noise,and designs a Nash equilibrium search strategy un-der privacy protection.The Kalman filter is used to estimate the player's state,and the consensus protocol is used to make each player in the network reach a consensus on the estimated value.Finally,this dissertation proves that in the sense of mean square,the state of each player converges to the Nash equilibrium point.?As the player's network gradually expands,network transmission resources will be limited,so this dissertation uses an event trigger mechanism to save chan-nel resources.On the foundation of the distributed Nash equilibrium search strategy based on privacy protection,in order to balance the solution quality and communication rate,an event-triggered Nash equilibrium search strategy is designed.The unitized output error function is used as the trigger function,while the trigger threshold is artificially set.When the trigger function is greater than the trigger threshold,the observation value is sent to the network,and the estimator uses the traditional Kalman filtering algorithm;otherwise,the obser-vation value is not transmitted,and the estimation is adopted a priori estimate.Different estimation algorithms are adopted for the remote estimator,and the game system becomes a switching system.By increasing the trigger threshold,the communication rate can be reduced,but at the same time it will also increase the estimation error;if the trigger threshold is 0,the mechanism degenerates into the problem ?.Finally,this dissertation gives the proof of the stability of the algorithm.