Revisiting Common Randomness, No-signaling and Information Structure in Decentralized Control

Abstract

This work revisits the no-signaling condition for decentralized information structures. We produce examples to show that within the no-signaling polytope exist strategies that cannot be achieved by passive common randomness but instead require agents to either share their observations with a mediator or communicate directly with each other. This poses a question mark on whether the no-signaling condition truly captures the decentralized information structure in the strictest sense.