Abstract
A popular formalism for multiagent control applies tools from game theory, casting a multiagent decision problem as a cooperation-style game in which individual agents make local choices to optimize their own local utility functions in response to the observable choices made by other agents. When the system-level objective is submodular maximization, it is known that if every agent can observe the action choice of all other agents, then all Nash equilibria of a large class of resulting games are within a factor of 2 of optimal; that is, the price of anarchy is 1/2. However, little is known if agents cannot observe the action choices of other relevant agents. To study this, we extend the standard game-theoretic model to one in which a subset of agents either become \emph{blind} (unable to observe others' choices) or \emph{isolated} (blind, and also invisible to other agents), and we prove exact expressions for the price of anarchy as a function of the number of compromised agents. When k agents are compromised (in any combination of blind or isolated), we show that the price of anarchy for a large class of utility functions is exactly 1/(2+k). We then show that if agents use marginal-cost utility functions and at least 1 of the compromised agents is blind (rather than isolated), the price of anarchy improves to 1/(1+k). We also provide simulation results demonstrating the effects of these observation denials in a dynamic setting.