  Multiagent systems can use commitments as the core of a general coordination
infrastructure, supporting both cooperative and non-cooperative interactions.
Agents whose objectives are aligned, and where one agent can help another
achieve greater reward by sacrificing some of its own reward, should choose a
cooperative commitment to maximize their joint reward. We present a solution to
the problem of how cooperative agents can efficiently find an (approximately)
optimal commitment by querying about carefully-selected commitment choices. We
prove structural properties of the agents' values as functions of the
parameters of the commitment specification, and develop a greedy method for
composing a query with provable approximation bounds, which we empirically show
can find nearly optimal commitments in a fraction of the time methods that lack
our insights require.
