Noisy signalling over time

Many signalling situations feature noisy observation of the sender’s effort and multiple opportunities to signal. Information release could be gradual or discrete. Gradual information revelation is modelled as the sender controlling the drift of a Brownian motion signal process, discrete information release as controlling the intensity of a Poisson process. If the intensity increases (decreases) in the effort, then the signal is called good (bad) news. The receivers observe the signals, but not the sender’s effort or type. Under bad news, there are Markov stationary perfect Bayesian equilibria in which the bad type exerts strictly higher effort than the good type. In these equilibria, if no signal occurs, then the types eventually pool on zero effort. If a signal occurs, then the play transitions irreversibly to a regime in which a single bad signal reveals the bad type. In that regime, the bad type takes no effort and the good type takes maximal effort. The payoff is lower for the bad than the good type, which provides the incentive for the bad type to take higher effort initially. Under good news, the bad type prefers pooling to all informative equilibria, even when the payoff is convex in the receivers’ posterior. In ∗Department of Economics, Yale University. 28 Hillhouse Ave., New Haven, CT 06511, USA. Email: [email protected], website: http://sanderheinsalu.com/ The author is greatly indebted to Johannes Hörner for many enlightening discussions about this research. Numerous conversations with Larry Samuelson have helped improve the paper. The author is grateful to Eduardo Faingold, Dirk Bergemann, Juuso Välimäki, Philipp Strack, Willemien Kets, Tadashi Sekiguchi, Flavio Toxvaerd, Françoise Forges, Jack Stecher, Daniel Barron, Benjamin Golub, Florian Ederer, Vijay Krishna, Sambuddha Ghosh, Sergiu Hart and participants of the 24th International Conference on Game Theory at Stony Brook University, EconCon 2013, the Yale micro theory breakfast and lunch and the Yale Graduate Summer Workshop for comments and suggestions. Any remaining errors are the author’s.