Except for special classes of games, there is no systematic framework for
analyzing the dynamical properties of multi-agent strategic interactions.
Potential games are one such special but restrictive class of games that allow
for tractable dynamic analysis. Intuitively, games that are "close" to a
potential game should share similar properties. In this paper, we formalize and
develop this idea by quantifying to what extent the dynamic features of
potential games extend to "near-potential" games.
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.