  In recent years, a significant research effort has been devoted to the design
of distributed protocols for the control of multi-agent systems, as the scale
and limited communication bandwidth characteristic of such systems render
centralized control impossible. Given the strict operating conditions, it is
unlikely that every agent in a multi-agent system will have local information
that is consistent with the true system state. Yet, the majority of works in
the literature assume that agents share perfect knowledge of their environment.
This paper focuses on understanding the impact that inconsistencies in agents'
local information can have on the performance of multi-agent systems. More
specifically, we consider the design of multi-agent operations under a game
theoretic lens where individual agents are assigned utilities that guide their
local decision making. We provide a tractable procedure for designing utilities
that optimize the efficiency of the resulting collective behavior (i.e., price
of anarchy) for classes of set covering games where the extent of the
information inconsistencies is known. In the setting where the extent of the
informational inconsistencies is not known, we show -- perhaps surprisingly --
that underestimating the level of uncertainty leads to better price of anarchy
than overestimating it.
