  The paper studies the convergence properties of (continuous) best-response
dynamics from game theory. Despite their fundamental role in game theory,
best-response dynamics are poorly understood in many games of interest due to
the discontinuous, set-valued nature of the best-response map. The paper
focuses on elucidating several important properties of best-response dynamics
in the class of multi-agent games known as potential games---a class of games
with fundamental importance in multi-agent systems and distributed control. It
is shown that in almost every potential game and for almost every initial
condition, the best-response dynamics (i) have a unique solution, (ii) converge
to pure-strategy Nash equilibria, and (iii) converge at an exponential rate.
