The role of common “context” in signaling

In order to signal effectively, is it sufficient for decentralized agents to share a signaling protocol, a common language? In this paper, we argue that the agents also need a common signaling “context” that can depend on the environment. Paralleling traditional communication, where mapping of information-sequence to codewords can be thought of as a “language”, the meaning attached to points in the state-space defines a signaling-language. In this framework, the coordinate-axes of an agent can be viewed as its signaling-context. By investigating the impact of context-misalignment in the minimalist signaling problem, the Witsenhausen counterexample, we show that significant context-misalignment can lead to lack of coordination despite agreement on the signaling-language. While Witsenhausen's counterexample is a single-shot problem, decentralized agents often act for longer time-horizons. By formulating a multi-shot extension of Witsenhausen's counterexample, we show that the agents can arrive at a common context by observing the costs arising due to their actions at previous time-steps, and are then able to use their common language to coordinate effectively.