Core Concepts
Generalized weakly acyclic games (GenWAGs) are crucial for multi-agent learning and Nash equilibrium seeking algorithms.
Abstract
The content introduces GenWAGs as a generalization of weakly acyclic games, focusing on satisficing paths and their importance in game theory. It discusses the structure of games, best response paths, and the concept of Nash equilibrium. The paper presents theorems and proofs related to GenWAGs, including sufficiency conditions for two-player and n-player games. It concludes with an open question regarding the uniqueness of Nash equilibria in generalized weak acyclicity.
Stats
Weakly acyclic games generalize potential games.
GenWAGs are defined using a game's satisficing graph.
The paper provides sufficient conditions for GenWAGs.
Quotes
"Weakly acyclic games are fundamental to the study of game theoretic control."
"Our generalization of weakly acyclic games is closely related to the theory of satisficing paths."