On Distributed Nash Equilibrium Computation: Hybrid Games and a Novel Consensus-Tracking Perspective

Area of Science:

• Game Theory
• Networked Systems
• Computational Mathematics

Background:

• Nash equilibrium computation is crucial for networked games.
• Existing methods primarily focus on discrete-time or continuous-time players separately.
• Hybrid games with mixed player types present unique computational challenges.

Purpose of the Study:

• To develop methods for computing Nash equilibria in hybrid networked games.
• To explore alternative perspectives for solving continuous-time networked games beyond existing algorithms.
• To address the limitations of current approaches in accommodating diverse player dynamics.

Main Methods:

• Proposed a hybrid gradient search algorithm for hybrid games.
• Developed a consensus-based hybrid gradient-like algorithm for hybrid games.
• Reformulated continuous-time games using consensus tracking for Nash equilibrium learning.
• Introduced two new computation strategies based on consensus tracking.

Main Results:

• The proposed hybrid algorithms demonstrate convergence for mixed-time players.
• Continuous-time players use continuous-time algorithms; discrete-time players update at sampling instants.
• New strategies effectively solve Nash equilibrium learning problems in continuous-time games.
• Numerical validation confirmed the efficacy of the developed strategies.

Conclusions:

• The study successfully addresses Nash equilibrium computation for hybrid and continuous-time networked games.
• Novel algorithms offer effective solutions for complex game dynamics.
• The findings expand the scope of solvable networked game problems.