  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
determinantal point processes (DPP). By incorporating the diversity metric into
best-response dynamics, we develop diverse fictitious play and 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 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 at least the same,
and in most games, lower exploitability than PSRO solvers by finding effective
and diverse strategies.
