  In a multi-agent system, an agent's optimal policy will typically depend on
the policies chosen by others. Therefore, a key issue in multi-agent systems
research is that of predicting the behaviours of others, and responding
promptly to changes in such behaviours. One obvious possibility is for each
agent to broadcast their current intention, for example, the currently executed
option in a hierarchical reinforcement learning framework. However, this
approach results in inflexibility of agents if options have an extended
duration and are dynamic. While adjusting the executed option at each step
improves flexibility from a single-agent perspective, frequent changes in
options can induce inconsistency between an agent's actual behaviour and its
broadcast intention. In order to balance flexibility and predictability, we
propose a dynamic termination Bellman equation that allows the agents to
flexibly terminate their options. We evaluate our model empirically on a set of
multi-agent pursuit and taxi tasks, and show that our agents learn to adapt
flexibly across scenarios that require different termination behaviours.
