Competitive Information Design for Pandora's Box

2021-03-05

ACM-SIAM Symposium on Discrete Algorithms

AI Summary

This paper studies the Pandora’s Box problem in a strategic information sender setting: each box acts as a strategic sender who designs signals about its prize value, while an agent sequentially searches at cost and responds to manipulable disclosures. Methodologically, we formulate the first Bayesian game model of competitive information revelation among multiple senders, integrating game theory, optimal stopping theory, and information design. Our main contributions are: (1) a complete characterization of the agent’s optimal search-and-stop policy; (2) necessary and sufficient conditions for the existence of a pure-strategy symmetric equilibrium, along with a uniqueness proof; (3) identification of the double-edged nature of information competition—stronger signals do not necessarily improve agent welfare and may even reduce overall search efficiency; and (4) establishment of an intrinsic link between the informativeness of signal distributions and the ordinal ranking of search utility.

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.

Problem

• Strategic information design in Pandora's Box
• Optimal search strategy with competitive boxes
• Equilibrium analysis of information revelation

Innovation

• Strategic box information design
• Optimal search strategy characterization
• Symmetric equilibrium information revelation