Message Complexity on a Binary Type Space

We study a sender-receiver game in which the sender privately observes his type — either good or bad — and strategically chooses the complexity of a message. Upon observing this complexity, the receiver selects an analysis level that determines both the cost of processing the message and the informativeness of a binary signal about the sender’s type. The receiver then decides whether to accept or reject the sender. We focus on pure-strategy Perfect Bayesian Equilibria that maximize the good-type sender’s expected payoff, which we term Good-type Optimal Equilibria (GOE). We show that, under reasonable conditions, a forward-induction-based refinement uniquely selects a GOE. The good-type sender’s expected payoff may increase when the receiver becomes less capable of interpreting the message, as the sender strategically simplifies the message to facilitate interpretation and reduce misclassification risk — while still deterring imitation by the bad-type. The sender’s payoff may also increase or decrease with the receiver’s prior, depending on how she weighs potential gains and losses. Our results highlight how strategic complexity and limited cognition jointly shape communication outcomes.