Signalling Rivalry and Quality Uncertainty in a Duopoly

Abstract

This paper considers price competition in a duopoly with quality uncertainty. The established firm (the 'incumbent') offers a quality that is publicly known; the other firm (the 'entrant') offers a new good whose quality is not known by some consumers. The incumbent is fully informed about the entrant's quality. This leads to price signalling rivalry because the incumbent gains and the entrant loses if observed prices make the uninformed consumers more pessimistic about the entrant's quality. When the uninformed consumers' beliefs satisfy the 'intuitive criterion' and the 'unprejudiced belief refinement', prices signal the entrant's quality only in a two-sided separating equilibrium and are identical to the full information outcome.

Entry and Quality Signaling When the Incumbent Is Informed of the Entrant's Quality

“…This implies that consumers can learn the entrant's 10 bðU H À P E Þ þ ð1 À bÞðU L À P E Þ ¼ bU H þ ð1 À bÞU L À P E ¼ U b À P E . 11 In a similar model with horizontal differentiation, Wu (2009) and Bester and Demuth (2011) found a unique equilibrium in which both firms choose different prices. 12 Otherwise, it is possible that H could profitably deviate to a price P E , where P E 2 ðc H , P Ã I ðHÞÞ with the purpose of mimicking a low quality entrant, and win all consumers.…”

“…Most recently, Wu (2009) and Bester and Demuth (2011) also considered a duopoly model of competition with horizontal product differentiation, in addition to the possible vertical differentiation. The information structure in our model is similar to theirs.…”

Strategic stability of equilibria in multi-sender signaling games

“…For any unsent, out-of-equilibrium signal m ∈ (0, 4/3), the firm believes that the worker is of low type with high enough probability. 3 This is necessary for maintaining the equilibrium. To see this, for example, should the firm assign 0 probability to the low type after observing the out-of-equilibrium signal m = 1, the high type can deviate and achieve his first best utility level (given that the firm knows his type) 2 > 16/9 by sending the signal 1.…”

“…In this paper we investigate the usage of the extremely simple and powerful restriction of Bagwell and Ramey (1991), dubbed unprejudiced beliefs, in signaling games with multiple senders. In several applications, see e.g., Bagwell and Ramey (1991), Bester and Demuth (2015), Schultz (1996), (1999), and Hartman-Glaser and Hébert (2019), this restriction is used together with versions of the intuitive criterion (see Cho and Kreps (1987)), so as to be able to eliminate (or to justify) undesirable pooling, yet unprejudiced equilibria. 1 Some of these papers report the non-existence of pure equilibrium outcomes which can be supported both by unprejudiced and by intuitive beliefs.…”

Competition in Signaling

“…First, in my model the messages or signals of senders are used only to transmit information, and thus do not directly affect how players value each alternative. This is not the case, e.g., in related models of limit entry (Bagwell & Ramey, 1991;Schultz, 1996), price competition (Bester & Demuth, 2015;Fluet & Garella, 2002;Hertzendorf & Overgaard, 2001;Yehezkel, 2008), and public good provision (Schultz, 1996). 8 Second, I model a setting where the signals of senders are fully observable.…”