The article introduces new ways to analyze how people communicate in games. It expands on the idea of Nash equilibrium, which is a key concept in game theory. The researchers suggest two new concepts: extensive form correlated equilibrium and communication equilibrium. These concepts allow players to observe signals and communicate during the game. The researchers found that the outcomes of these communication strategies can be represented as a convex polyhedron, which is a geometric shape with flat sides. They also created special games to show that the outcomes match the Nash equilibrium payoffs.