In some markets consumers seek exclusive consumption experiences, yet in these markets businesses sometimes market their goods widely and at low prices during an introduction period. We use a two-period game-theoretic model to provide a signaling explanation for this phenomenon. In our model, exclusivity-seeking consumers must infer product quality from its price and level of exclusivity in the initial stage. After purchase consumers communicate the true learned quality through word-of-mouth (WOM) so that the entire market becomes informed, including a group of new consumers whose size depends on the number of introductory purchasers and the strength of WOM. We show that a high-quality seller signals by marketing widely when the desire for exclusivity is intermediate and WOM is strong.
We thank the seminar participants at the Summer AMA conference 2016 in Atlanta, Georgia and at the Marketing Science conference 2016 in Shanghai, China, for comments on an earlier version of this paper. The article is based in part on essay 2 of Minoo Talebi Ashoori’s dissertation at the University of Central Florida. We thank Anna Malaj for research assistance. All errors are our own.
Proof of Proposition 1
Since L will induce beliefs in any separating equilibrium and is the unique maximizer when , L uses in any separating equilibrium. We henceforth restrict attention to H’s choice of α.
Next, it is necessary and sufficient to satisfy MC and PC (given immediately below line (5)) to establish an equilibrium. The shaded region in Figure 4 shows the points satisfying both constraints, which is the feasible set over which we perform the maximization problem from line (5). Both PC and MC bind at points B and C, which can be explicitly solved for by substituting the binding MC into the binding PC and solving the resulting quadratic in α:
Solving yields solutions , where . Note when k is sufficiently small which lies outside the domain , in which case the corner solution obtains. We therefore redefine . An analogous issue does not arise with since always. Note that even in the case where and signaling is still costly since in the former case MC binds and so price is lower than in the latter case.
Mimicking Constraint Non-binding
When the MC is non-binding, full information pricing and exclusivity level given below line (3) achieve separation. This can occur in one of two ways. First, it is possible that PC binds tighter than MC for all . Mathematically, both solutions to line (10) lie outside [0, 1], and in particular . In the second case MC and PC do intersect on [0, 1] but MC may still not bind, as for example in panel (a) of Figure 2. These cases correspond to and , respectively. A calculation shows
where we use the substitution . A similar calculation shows that
Thus full information exclusivity level separates when .
Mimicking Constraint Binding
Now suppose . Since we look for an equilibrium where type H earns the highest profits possible subject to the MC and PC, we substitute the binding MC, , into line (5) to get
The maximand is everywhere decreasing in α if while it is increasing if . In the former (latter) case profits are maximized with α as low (high) as possible, which occurs where MC and PC both bind, namely point B (point C) of Figure 4, with corresponding exclusivity level (). Substituting these α into the PC and simplifying yields the pricing and exclusivity level in the proposition.
Finally, when price is found by substituting into PC to get . However, in the boundary case where the calculated we are restricted to , and so MC binds but PC does not. The price charged is thus found by substituting into MC (line 6): .
Off the Equilibrium Path (OEP) Deviations and the Intuitive Criterion
In the Online Appendix we show OEP deviations will not occur. Additionally, we show the OEP beliefs we specify uniquely satisfy the intuitive criterion (Cho and Kreps 1987).
Proofs of Corollary 1, Propositions 2, and 3
See the Online Appendix.
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The online version of this article offers supplementary material: https://doi.org/10.1515/roms-2020-0022.
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