Competitive Information Design for Pandora's Box

Abstract: We study a natural competitive-information-design strategic variant for the celebrated 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. Our contributions are three-fold: (1) given the boxes' information policies, we characterize the agent's optimal search and stopping strategy; (2) we fully characterize the pure symmetric equilibrium for the game of boxes' competitive information revelation in a symmetric environment; and (3) we reveal various insights regarding information competition and the resultant agent payoff at equilibrium, and additionally, we study informational properties of Pandora's Box by establishing an intrinsic connection between informativeness of any box's value distribution and the utility order of the search agent.