  The assignment of tasks to multiple resources becomes an interesting game
theoretic problem, when both the task owner and the resources are strategic. In
the classical, nonstrategic setting, where the states of the tasks and
resources are observable by the controller, this problem is that of finding an
optimal policy for a Markov decision process (MDP). When the states are held by
strategic agents, the problem of an efficient task allocation extends beyond
that of solving an MDP and becomes that of designing a mechanism. Motivated by
this fact, we propose a general mechanism which decides on an allocation rule
for the tasks and resources and a payment rule to incentivize agents'
participation and truthful reports. In contrast to related dynamic strategic
control problems studied in recent literature, the problem studied here has
interdependent values: the benefit of an allocation to the task owner is not
simply a function of the characteristics of the task itself and the allocation,
but also of the state of the resources. We introduce a dynamic extension of
Mezzetti's two phase mechanism for interdependent valuations. In this changed
setting, the proposed dynamic mechanism is efficient, within period ex-post
incentive compatible, and within period ex-post individually rational.
