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This paper considers coverage games in which a group of agents are taskedwith identifying the highest-value subset of resources; in this context,game-theoretic approaches are known to yield Nash equilibria within a factor of2 of optimal. We consider the case that some of the agents suffer acommunication failure and cannot observe the actions of other agents; in thiscase, recent work has shown that if there are k>0 compromised agents, Nashequilibria 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; ina sense which we make precise, we show that if a problem instance has a verypoor worst-case guarantee, then it is necessarily very "close" to a probleminstance with an optimal Nash equilibrium. Conversely, an instance that is farfrom one with an optimal Nash equilibrium necessarily has relatively goodworst-case performance guarantees. To contextualize this fragility, we performsimulations using the log-linear learning algorithm and show that averageperformance on worst-case instances is considerably better even than ourimproved analytical guarantees. This suggests that the fragility of the priceof anarchy can be exploited algorithmically to compensate for onlinecommunication failures.

The Price of Anarchy is Fragile in Single-Selection Coverage Games