[Paper Review] Comparison Shopping: Learning Before Buying From Duopolists

Brian C. Albrecht, Mark Whitmeyer|arXiv (Cornell University)|Feb 13, 2023

Merger and Competition Analysis4 citations

TL;DR

This paper studies a duopoly model where consumers learn about product fit before purchasing, showing that in equilibrium, consumers engage in 'comparison shopping'—learning only relative product values. As information costs vanish, competition restores ex post efficiency, reversing the inefficiency found in RRS's monopoly model, with welfare effects flipping from negative to positive when information becomes cheap.

ABSTRACT

We explore a model of duopolistic competition in which consumers learn about the fit of each competitor's product. In equilibrium, consumers comparison shop: they learn only about the relative values of the products. When information is cheap, increasing the cost of information decreases consumer welfare; but when information is expensive, this relationship flips. As information frictions vanish, there is a limiting equilibrium that is ex post efficient.

Motivation & Objective

• To analyze how consumer learning about product fit affects equilibrium outcomes in a duopolistic market.
• To investigate whether competition can reverse the ex post inefficiency found in RRS's monopoly model with learning before trading.
• To characterize the optimal learning strategy and its impact on pricing and consumer welfare.
• To examine the comparative statics of information costs on consumer surplus under duopoly competition.

Proposed method

• Models a two-seller duopoly with horizontally differentiated products and binary valuations for the consumer.
• Assumes consumers can acquire any signal about valuations at a smooth, increasing cost, with signals being privately observed.
• Solves a sequential game: consumer chooses learning strategy first, then firms set prices non-sequentially, unaware of the consumer’s signal.
• Uses a Bayesian framework where the consumer updates beliefs along the line y = 1 - x, reflecting relative value comparison.
• Characterizes equilibrium via a multidimensional information design problem coupled with a random pricing game.
• Employs comparative statics to analyze how changes in information cost κ affect consumer welfare and firm pricing.

Experimental results

Research questions

• RQ1 Does competition between duopolists eliminate the ex post inefficiency that arises in RRS's monopoly model with learning before trading?
• RQ2 What learning strategy does the consumer optimally choose in equilibrium, and does it reveal absolute or relative valuations?
• RQ3 How does the cost of information affect consumer welfare in a duopoly setting?
• RQ4 What happens to equilibrium outcomes as information frictions vanish?
• RQ5 How does the outcome change if firms observe the consumer’s learning, compared to private learning?

Key findings

• In equilibrium, consumers learn only the relative value of the two products, restricting their posterior beliefs to the line y = 1 - x, a phenomenon termed 'comparison shopping'.
• As information costs vanish, the limiting equilibrium becomes ex post efficient: the consumer always purchases the higher-value product.
• When information is expensive (κ ≥ κ̄), consumer welfare decreases with lower information costs; when information is cheap (κ ≤ κ̄), welfare increases with lower costs—reversing the relationship.
• For intermediate information costs (κ ∈ [κ̄, κ̄]), consumer welfare is strictly decreasing in the cost of information.
• If firms observe the consumer’s learning, the consumer strictly prefers not to learn at all, as it leads to Bertrand-style competition and full surplus extraction.
• The model’s key result is that competition restores efficiency in the limit of perfect information, countering the inefficiency found in the monopoly benchmark.