  The use of game theoretic methods for control in multiagent systems has been
an important topic in recent research. Valid utility games in particular have
been used to model real-world problems; such games have the convenient property
that the value of any decision set which is a Nash equilibrium of the game is
guaranteed to be within 1/2 of the value of the optimal decision set. However,
an implicit assumption in this guarantee is that each agent is aware of the
decisions of all other agents. In this work, we first describe how this
guarantee degrades as agents are only aware of a subset of the decisions of
other agents. We then show that this loss can be mitigated by restriction to a
relevant subclass of games.
