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This paper focuses on a time-varying Nash equilibrium trajectory trackingproblem, that is applicable to a wide range of non-cooperative gameapplications arising in dynamic environments. To solve this problem, we proposea distributed prediction correction algorithm, termed DPCA, in which eachplayer predicts future strategies based on previous observations and thenexploits predictions to effectively track the NE trajectory by using one ormultiple distributed gradient descent steps across a network. We rigorouslydemonstrate that the tracking sequence produced by the proposed algorithm isable to track the time-varying NE with a bounded error. We also show that thetracking error can be arbitrarily close to zero when the sampling period issmall enough. Furthermore, we achieve linear convergence for the time-invariantNash equilibrium seeking problem as a special case of our results. Finally, anumerical simulation of a multi-robot surveillance scenario verifies thetracking performance and the prediction necessary for the proposed algorithm.

Distributed Prediction-Correction Algorithms for Time-Varying Nash Equilibrium Tracking