[Paper Review] Lemonade from Lemons: Information Design and Adverse Selection

Navin Kartik, Weijie Zhong|arXiv (Cornell University)|May 4, 2023

Auction Theory and Applications17 citations

TL;DR

The paper characterizes the set of equilibrium payoffs across all information structures in a single-object market with interdependent values, showing that feasible and individually rational payoffs can be implemented and that the buyer can capture the entire surplus under certain structures.

ABSTRACT

A seller posts a price for a single object. The seller's and buyer's values may be interdependent. We characterize the set of payoff vectors across all information structures. Simple feasibility and individual-rationality constraints identify the payoff set. The buyer can obtain the entire surplus; often, other mechanisms cannot enlarge the payoff set. We also study payoffs when the buyer is more informed than the seller, and when the buyer is fully informed. All three payoff sets coincide (only) in notable special cases -- in particular, when there is complete breakdown in a ``lemons market'' with an uninformed seller and fully-informed buyer.

Motivation & Objective

• Motivate study of how information asymmetry shapes market outcomes in a simple trade setting.
• Characterize the set of ex-ante equilibrium payoffs across all information structures.
• Identify how payoff sets tighten under different information structures (uninformed seller, fully informed buyer, etc.).
• Show that simple feasibility and individual-rationality constraints identify the feasible payoff set.

Proposed method

• Model a seller posting a price for a single object and a buyer with interdependent value v and seller cost c(v).
• Define information structures as joint signal distributions conditional on v and analyze equilibrium via weak Perfect Bayesian Equilibrium (wPBE).
• Derive three main theorems outlining implementable payoff sets under arbitrary information, when the buyer is more informed than the seller, and when the buyer is fully informed.
• Use Bayes plausibility and sequential rationality to construct incentive compatible distributions that implement payoff points.
• Present canonical information structures (uninformed seller, fully informed buyer, more informed buyer) and impose price-independent beliefs where appropriate.

Experimental results

Research questions

• RQ1 What payoff vectors are implementable in equilibrium across all possible information structures for interdependent values?
• RQ2 How do information structure restrictions (un-informed seller, buyer more informed, buyer fully informed) constrain the feasible payoff set?
• RQ3 Under what conditions can the buyer capture the entire surplus, despite the seller’s position?
• RQ4 How do price-dependent beliefs and sequential equilibrium refinements affect implementability of payoff points?
• RQ5 What is the relationship between the Akerlof-like fully-informed buyer scenario and other information regimes?

Key findings

• The set of implementable payoffs equals the set of feasible and individually rational payoffs with Buyer’s payoff nonnegative and Seller’s payoff bounded below by her IR constraint and by the total surplus S(Γ).
• Under arbitrary information structures, any feasible and IR payoff pair within the surplus S(Γ) can be implemented (Theorem 1).
• When the Buyer is better informed than the Seller, the achievable payoffs lie in a specific triangle (ADE) and any point in that triangle is implementable by adjusting Buyer’s information (Theorem 2).
• When the Buyer is fully informed, the achievable payoffs form the triangle ABC, with trade-offs determined by the Seller’s IR constraint and the Akerlof benchmark; the buyer can, in some environments, capture the entire surplus.
• The three payoff sets are nested, with Theorem 1’s set largest, Theorem 2’s intermediate, and Theorem 3’s smallest; richer information can enlarge or shrink the Buyer’s or Seller’s ex-ante utilities depending on the environment.