This paper by Jeffrey S. Banks and Joel Sobel explores the concept of equilibrium selection in signaling games, introducing a new solution concept called "divine equilibrium." Divine equilibria refine the set of sequential equilibria by imposing additional restrictions on off-the-equilibrium-path beliefs. The authors demonstrate that divine equilibria exist and are more restrictive than stable equilibria, which are defined in terms of stability. They show that every stable component contains a divine equilibrium but not vice versa. The paper also provides a characterization of stable equilibria in generic signaling games, showing that an equilibrium is stable if and only if it can be supported as a sequential equilibrium with restricted off-the-equilibrium-path beliefs. The results are illustrated through examples and compared with other equilibrium concepts, such as rationalizable equilibria and perfect equilibria.This paper by Jeffrey S. Banks and Joel Sobel explores the concept of equilibrium selection in signaling games, introducing a new solution concept called "divine equilibrium." Divine equilibria refine the set of sequential equilibria by imposing additional restrictions on off-the-equilibrium-path beliefs. The authors demonstrate that divine equilibria exist and are more restrictive than stable equilibria, which are defined in terms of stability. They show that every stable component contains a divine equilibrium but not vice versa. The paper also provides a characterization of stable equilibria in generic signaling games, showing that an equilibrium is stable if and only if it can be supported as a sequential equilibrium with restricted off-the-equilibrium-path beliefs. The results are illustrated through examples and compared with other equilibrium concepts, such as rationalizable equilibria and perfect equilibria.