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A refinement of undefeated equilibria avoids the problems posed by sequential equilibria that limit the usefulness of games of incomplete information, and an existence theorem on signalling games is provided. Difficulties in implementing the concept of forward induction are explained. The set of undefeated equilibria in continuous strategy set signalling games is shown to be non-empty, and proofs are presented.

Several conceptual points are made concerning communication in games of asymmetric information. Equilibrium refinements of Sender-Receiver cheap-talk games that are based on the concept of a putative equilibrium, and which rely on the presence of a rich language with literal meanings, are discussed. Three nested criteria are proposed: strong announcement-proofness, announcement-proofness, and weak announcement-proofness. Journal of Economic Literature Classification Number: 026.