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Distributed inertial online game algorithm for tracking generalized Nash equilibria.

Haomin Bai1, Wenying Xu1, Shaofu Yang2

  • 1School of Mathematics, Southeast University, Nanjing 211189, China.

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|October 13, 2023
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Summary
This summary is machine-generated.

This study introduces a distributed inertial online game (D-IOG) algorithm to track generalized Nash equilibrium (GNE) in dynamic noncooperative games. The algorithm effectively manages time-varying costs and constraints, achieving sublinear regret bounds.

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Area of Science:

  • Distributed Optimization
  • Game Theory
  • Noncooperative Games
  • Dynamic Systems

Background:

  • Challenges in tracking generalized Nash equilibrium (GNE) in dynamic environments with time-varying functions.
  • Need for distributed algorithms that can handle agents revealing information after decisions.
  • Limitations of existing methods in addressing coupled constraints and time-varying communication.

Purpose of the Study:

  • To develop a distributed algorithm for tracking GNE in noncooperative games with dynamic cost and coupled constraint functions.
  • To analyze the performance of the proposed algorithm in terms of regret and constraint violation.
  • To investigate the impact of inertia and information transmission modes on algorithm efficiency.

Main Methods:

  • Proposal of a distributed inertial online game (D-IOG) algorithm based on mirror descent for GNE tracking without coupled constraints.
  • Modification of the D-IOG algorithm using primal-dual and mirror descent methods to incorporate time-varying coupled constraints.
  • Derivation of upper bounds for regrets and constraint violations.

Main Results:

  • The D-IOG algorithm successfully tracks Nash equilibrium (NE) over time-varying communication graphs.
  • Sublinear growth of regrets is achieved under specific conditions on stepsize and inertial parameters.
  • The modified D-IOG algorithm demonstrates effectiveness in tracking GNE with coupled constraints, supported by derived bounds.

Conclusions:

  • The proposed D-IOG algorithms are effective for distributed GNE tracking in dynamic noncooperative games.
  • The algorithms offer potential for low average regret and manageable constraint violation.
  • Simulation examples validate the practical applicability and performance of the developed algorithms.