Competition, Persuasion, and Search

An agent engages in sequential search and learns about the quality of sampled goods through signals purchased from profit-maximizing information broker(s). We study how the market structure–the number of competing brokers–shapes the pricing and design of information, as well as the resulting welfare outcomes. We characterize the equilibrium payoff set, and show that when the agent’s search cost falls below a threshold, market structure affects neither how much surplus is generated in equilibrium nor how it is divided. Above this threshold, however, competition yields equilibrium outcomes that raise the agent’s payoff but reduce total surplus relative to any monopoly equilibrium outcome. Methodologically, we extend the classic theory of repeated games to stopping problems, such as sequential search.

💡 Research Summary

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The paper develops a formal model of sequential search in which a decision‑making agent repeatedly samples a good of unknown quality and must purchase a signal from profit‑maximizing information brokers in order to learn about that quality. The agent faces a per‑period search cost (c) and decides after observing the broker’s signal whether to stop and accept the current good or to continue searching in the next period. Brokers can design any signaling scheme and set a price for the signal; they earn revenue only while the agent continues to search, giving them a clear incentive to make the signal as informative as possible.

Two market structures are examined: a monopoly broker and a competitive market with (n\ge 2) brokers. The analysis characterizes the subgame‑perfect equilibrium (SPE) of the repeated stopping game for both structures. A key contribution is the identification of a threshold search cost (c^{}). When (c<c^{}) (low‑cost search), the equilibrium payoff set is identical under monopoly and competition. In this regime the broker’s optimal strategy is to provide a signal that makes the agent indifferent between stopping and continuing, and the price extracts exactly the surplus generated by the search process. Consequently, total surplus (the sum of agent and broker profits) and its division are invariant to the number of brokers.

When (c>c^{*}) (high‑cost search), the situation reverses. Competition forces brokers to lower prices and to increase signal precision in order to keep the agent searching. The agent’s expected payoff rises relative to the monopoly case because the more accurate signal reduces the probability of stopping at a low‑quality good. However, the total surplus falls: the competition‑induced price cut reduces broker revenue, and the higher signal precision raises the cost of information provision. Thus, while competition benefits the consumer, it harms overall efficiency—a result that contrasts with the classic intuition that competition always improves welfare.

The paper also shows that a simple binary “pass‑fail” signal is sufficient to implement any equilibrium outcome; more elaborate multi‑level signals are unnecessary. The value of a signal to the agent depends on two distinct factors: (i) its ability to distinguish whether the current good meets the agent’s reservation quality, and (ii) its impact on the agent’s continuation value (the expected future surplus from further search). Because the continuation value is endogenous to the stopping rule, the broker’s optimal pricing problem intertwines with the agent’s stopping decision.

Methodologically, the authors extend repeated‑game theory to stopping problems. Each period consists of a signaling stage followed by a continuation decision, and the equilibrium is derived by backward induction on the stopping rule. This approach yields a complete characterization of the equilibrium payoff set and the critical cost threshold.

Policy implications follow directly. In markets where search costs are low—such as many online platforms—regulating broker competition or imposing price caps will have little effect on welfare, and excessive competition may even reduce total surplus. In contrast, in high‑cost search markets (used‑car, real‑estate, pre‑employment screening) encouraging broker competition can substantially raise consumer surplus, albeit at the expense of total efficiency. The finding that binary signals suffice suggests that simple certification schemes (e.g., “approved” vs “rejected”) can be welfare‑optimal, avoiding the need for costly, detailed disclosures.

In summary, the paper provides a rigorous theoretical framework linking information design, market structure, and sequential search. It demonstrates that the welfare impact of broker competition hinges critically on the magnitude of search costs, offering clear guidance for both economists and policymakers dealing with information‑mediated markets.