Competitive Information Design for Pandora's Box

We study a natural competitive-information-design variant for the Pandora's Box problem (Weitzman, 1979), where each box is associated with a strategic information sender who can design what information about the box's prize value to be revealed to the agent when she inspects the box. This variant with strategic boxes is motivated by a wide range of real-world economic applications for Pandora's box. For example, to encourage buyers to purchase, sellers for goods such as TVs or houses may strategically conceal some information about their products in order to influence buyer's valuations of the products. The main contributions of this article are two-fold: (1) we study informational properties of Pandora's Box by analyzing how a box's partial information revelation affects the agent's optimal decisions; and (2) we fully characterize the pure symmetric equilibrium for the boxes' competitive information revelation, and reveals various insights regarding information competition and the resultant agent utility at equilibrium.