Directed Search and the Bertrand Paradox

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. I study a directed search model of oligopolistic competition, extended to incorporate general capacity constraints, congestion effects, and pricing based on ex-post realized demand. I show that as long as any one of these ingredients is present, the Bertrand paradox will fail to hold. Hence, I argue that, despite the emphasis that has been placed by the literature on sellers' capacity constraints as a resolution to the paradox, the existence of such constraints is only a subcase of a general class of environments where the paradox fails. More precisely, Bertrand's paradox will not arise whenever the buyers' expected utility from visiting a specific seller is decreasing in that seller's realized demand. Abstract I study a directed search model of oligopolistic competition, extended to incorporate general capacity constraints, congestion effects, and pricing based on ex-post realized demand. I show that as long as any one of these ingredients is present, the Bertrand paradox will fail to hold. Hence, I argue that, despite the emphasis that has been placed by the literature on sellers' capacity constraints as a resolution to the paradox, the existence of such constraints is only a subcase of a general class of environments where the paradox fails. More precisely, Bertrand's paradox will not arise whenever the buyers' expected utility from visiting a specific seller is decreasing in that seller's realized demand. Terms of use: Documents in

Pricing, Signalling, and Sorting with Frictions

“…3 As an alternative to capacity constraints the trade-off can be modelled by introducing congestion effects directly in the utility function of the buyers or by letting the price increase in demand. See Geromichalos (2014) and Lester (2011) for more on congestion effects and directed search. 4 In principle this exposes the sellers to the hold-up problem.…”

Instability of endogenous price dispersion equilibria: A simulation

“…The number of firms is modelled either as finite N < ∞ or as a continuum in 1 This approach is often termed random search because the probability that a buyer meets (or more appropriately in this context, observes) a particular seller is independent of seller characteristics, such as price, capacity or queue length. Using the main alternative paradigm, directed search, Geromichalos (2014) studies the Bertrand paradox and a general class of resolutions of the paradox.…”

Conditional loyalty and its implications for pricing

“…In Camera and Selcuk (2009), the profile of prices posted by the sellers determines the probability distribution of the buyers across the sellers; imperfect commitment to the posted price may leave room to renegotiating the price in light of actual demand. In Geromichalos (2014), each seller specifies how his own price will depend on his forthcoming demand; based on these price schedules, a mixed strategy equilibrium obtains. In either case, differences in prices at equilibrium are derived in terms of different pressure of demand over capacity at the various sellers.…”