Competitive Information Design for Pandora's Box (2103.03769v3)

Abstract: 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 the agent inspects the box. This variant with strategic boxes is motivated by a wide range of real-world economic applications for Pandora's Box. The main contributions of this article are two-fold: (1) we study informational properties of Pandora's Box by showing an intrinsic connection between informativeness of any box's value distribution and the utility order of the search agent; and (2) we fully characterize the pure symmetric equilibrium for the boxes' competitive information revelation, which reveals various insights regarding information competition and the resultant agent utility at equilibrium.