Flows and Decompositions of Games: Harmonic and Potential Games

Understand

In this paper we introduce a novel flow representation for finite games in strategic form.

• This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components.
• We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component.
• We show that the first class corresponds to the well-known potential games.