Before revision: Consider a variation on the classic Weitzman search problem, in which  firms can choose how much information about their product to reveal to a consumer who decides to search them. In this zero-sum game, ex-ante identical firms commit to a signal distribution as a function of quality before they learn their (random) quality; a firm's goal is to maximize the chance that its product is the one selected by the searcher.
After revision: Consider a variation on the classic Weitzman search problem, in which firms can choose how much information about their product to reveal to a consumer .