  In this work, we extend the convex bodies chasing problem (CBC) to an
adversarial setting, where an agent (the Player) is tasked with chasing a
sequence of convex bodies generated adversarially by another agent (the
Opponent). The Player aims to minimize the total cost associated with its own
movements, while the Opponent tries to maximize the same cost. The set of
feasible convex bodies is finite and known to both agents, which allows us to
provide performance guarantees with max-min optimality. Under certain
assumptions, we show the continuity of the optimal value function, and propose
an algorithm to numerically approximate the optimal policies for both the
Player and the Opponent within a guaranteed tolerance. Finally, the theoretical
results are verified through numerical examples.
