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The HoneyComb Paradigm for Research on Collective Human Behavior
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Distributed Nash equilibrium seeking strategy with incomplete information.

Cheng Yuwen1, Xiaowen Wang1, Shuai Liu1

  • 1School of Control Science and Engineering, Shandong University, Jinan 250012, China.

ISA Transactions
|February 7, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces two Kalman filter-based strategies for distributed Nash equilibrium seeking in non-cooperative games with incomplete information, enhancing player decision-making under uncertainty.

Keywords:
Event-based schedulerIncomplete informationKalman filterNash equilibriumNon-cooperative game

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Area of Science:

  • Control Theory
  • Game Theory
  • Networked Systems

Background:

  • Distributed systems often involve non-cooperative games where players act selfishly.
  • Incomplete information and network noise complicate achieving optimal outcomes like Nash equilibrium.
  • Estimating player states is crucial for decentralized decision-making.

Purpose of the Study:

  • To develop novel distributed strategies for seeking Nash equilibrium in non-cooperative games.
  • To address challenges posed by incomplete information, system noise, and communication constraints.
  • To analyze the convergence and stability of the proposed equilibrium-seeking methods.

Main Methods:

  • Utilizing gradient-based methods for individual player profit maximization.
  • Employing Kalman filters for state estimation in noisy discrete-time systems.
  • Implementing leader-following consensus algorithms for distributed state information sharing.
  • Introducing an event-based scheduler to balance strategy precision and communication efficiency.

Main Results:

  • Two distinct distributed Nash equilibrium seeking strategies were proposed and analyzed.
  • The convergence of both strategies was rigorously proven using Lyapunov stability methods.
  • Both strategies demonstrated bounded performance in the mean square sense, even with noise.
  • Simulation examples confirmed the practical efficiency of the developed methods.

Conclusions:

  • The proposed Kalman filter-based strategies effectively facilitate Nash equilibrium seeking in complex networked games.
  • The event-based approach offers a viable method to optimize communication rates without significantly compromising equilibrium-seeking precision.
  • The findings provide a robust framework for decentralized decision-making in systems with incomplete information and noise.