  Promoting behavioural diversity is critical for solving games with
non-transitive dynamics where strategic cycles exist, and there is no
consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous
treatment for defining diversity and constructing diversity-aware learning
dynamics. In this work, we offer a geometric interpretation of behavioural
diversity in games and introduce a novel diversity metric based on
\emph{determinantal point processes} (DPP). By incorporating the diversity
metric into best-response dynamics, we develop \emph{diverse fictitious play}
and \emph{diverse policy-space response oracle} for solving normal-form games
and open-ended games. We prove the uniqueness of the diverse best response and
the convergence of our algorithms on two-player games. Importantly, we show
that maximising the DPP-based diversity metric guarantees to enlarge the
\emph{gamescape} -- convex polytopes spanned by agents' mixtures of strategies.
To validate our diversity-aware solvers, we test on tens of games that show
strong non-transitivity. Results suggest that our methods achieve much lower
exploitability than state-of-the-art solvers by finding effective and diverse
strategies.
