  This paper considers coverage games in which a group of agents are tasked
with identifying the highest-value subset of resources; in this context,
game-theoretic approaches are known to yield Nash equilibria within a factor of
2 of optimal. We consider the case that some of the agents suffer a
communication failure and cannot observe the actions of other agents; in this
case, recent work has shown that if there are k>0 compromised agents, Nash
equilibria are only guaranteed to be within a factor of k+1 of optimal.
However, the present paper shows that this worst-case guarantee is fragile; in
a sense which we make precise, we show that if a problem instance has a very
poor worst-case guarantee, then it is necessarily very "close" to a problem
instance with an optimal Nash equilibrium. Conversely, an instance that is far
from one with an optimal Nash equilibrium necessarily has relatively good
worst-case performance guarantees. To contextualize this fragility, we perform
simulations using the log-linear learning algorithm and show that average
performance on worst-case instances is considerably better even than our
improved analytical guarantees. This suggests that the fragility of the price
of anarchy can be exploited algorithmically to compensate for online
communication failures.
