Can price dispersion be supported solely by information frictions?
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Can price dispersion be supported solely by information frictions? José Tudón1 Received: 6 August 2020 / Accepted: 29 October 2020 © Society for the Advancement of Economic Theory 2020
Abstract Even with identical consumers and identical firms, if firms set prices in a first stage, and if consumers search sequentially in a second stage, price dispersion arises in the form of a mixed-strategy Nash equilibrium. One only needs to assume consumers know the realized price distribution and that they do not know which firm has what price. In contrast to Burdett and Judd (1983), price quotes are not required to be “noisy.” Moreover, actual search is predicted to be nontrivial. Keywords Price dispersion · Information frictions · Sequential search JEL L13 · D83 · D21
1 Introduction In his economics-of-information article, Stigler (1961) wrote that “it would be metaphysical, and fruitless, to assert that all [price] dispersion is due to heterogeneity.” Since then, several studies have confirmed the empirical significance of price dispersion.1 However, after Stigler’s seminal paper, Diamond (1971) presented a challenge: if firms and consumers are identical, and if consumers pay to sequentially search for prices, the only Nash equilibrium is the monopoly price. Intuitively, if all firms set the monopoly price, the consumer will not search, but if the consumer will not search, all firms set the monopoly price. As Reinganum (1979) said, the Diamond paradox seemed to imply “imperfect information alone is insufficient to support price dispersion.” 1 See, for example, Kaplan and Menzio (2015), Hortaçsu and Syverson (2004), or Sorensen (2000).
Thanks to Alex Frankel, Ali Hortaçsu, Philip Reny, Enrique Seira, Chad Syverson, Balázs Szentes, Gábor Virág, and workshop participants at the University of Chicago.
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José Tudón [email protected] ITAM, Río Hondo 1, Ciudad de México 01080, Mexico
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This paper adds to recent efforts by showing with minimal assumptions that imperfect information alone is indeed sufficient to support price dispersion. I assume firms fix their prices before consumers search, and that consumers know the distribution of actual prices being charged in the market, but do not know which firm is charging which price. This paper shows this information structure is sufficient to generate price dispersion, even with homogeneous firms and homogeneous consumers. The informational assumption that drives the result is that the consumer knows the realized price distribution when she starts searching the market. As Menzio and Trachter (2015) explain, “This is the same assumption made in the vast majority of search models where the price distribution is exogenously given (e.g., Stigler 1961; McCall 1970). Indeed, only a few papers model the buyer’s problem of learning about the price distribution while searching (see, e.g., Rothschild 1974; Burdett and Vishwanath 1988). The assumption is also common in models where prices are endogenous (see, e.g., Pratt 1979; Rob 1985; Stiglitz 1987). Other models, such a
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