Abstract
Provision of real-time information by a firm to its customers has become prevalent in recent years in both the service and retail sectors. In this chapter, we study a retail operations model where customers are strategic in both their actions and in the way they interpret information, while the retailer is strategic in the way it provides information. This chapter focuses on the ability (or the lack thereof) to communicate unverifiable information and influence customers’ actions. We develop a game-theoretic framework to study this type of communication and discuss the equilibrium language emerging between the retailer and its customers. We show that for a single-retailer and homogeneous customer population setting, the equilibrium language that emerges carries no information. In this sense, a single-retailer providing information on its own cannot create any credibility with the customers. We study how the results are impacted due to the heterogeneity of the customers. We provide conditions under which the firm may be able to influence the customer behavior. In particular, we show that the customers’ willingness-to-pay and willingness-to-wait cannot be ranked in an opposite manner. However, even when the firm can influence each customer class separately, the effective demand is not impacted.
This chapter is based on Allon and Bassamboo (2011).
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- 1.
The authors of this chapter refrain from claiming that these announcements are indeed made only when the inventory is low.
- 2.
A variety of chapters study mixed-motive economic interaction involving private information and the impact of cheap talk on the outcomes. Farrell and Gibbons (1989) studies cheap talk in bargaining; in political context cheap talk has been studied in multiple papers including Austen-Smith (1990), and Matthews (1989).
- 3.
One should note that the results in Crawford and Sobel and most of the cheap talk literature are stated, based on the bias between the sender’s and the receiver’s preferred actions, which are exogenously given. In our model, the extent of the misalignment depends endogenously on the preferred action of the customers as it arises in equilibrium in the game they play. Thus, even the most basic results cannot be directly borrowed from this literature.
- 4.
We also provide a discussion of the setting where the pricing is a decision of the firm and contingent on the initial inventory in Sect. 12.7.
- 5.
Note that when we say that a customer decides to buy, we merely mean that the customer attempts to buy, but they might not be able to purchase due to limited availability.
- 6.
One can view a more detailed description of the bargain hunter. For instance, D 2 can emerge as an aggregate number of arrivals during the regular season of customers whose valuation is below the regular price p.
- 7.
It is worth noting that the equilibrium may not be unique.
- 8.
We assume that, off the-equilibrium-path, a message that was not supposed to be used will result in a “wait” decision by the customer.
- 9.
if the demand and the quantity do not grow proportionally, it is easy to see that the results are quite trivial. For example, assume that p − s > c. If Q grows faster than the demand, then everybody waits. If the demand grows faster, everybody purchases immediately. In both cases the messages play no role
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Appendix: Proofs
Appendix: Proofs
Proof of Proposition 3. The proof follows along the same line as the proof of Proposition 2. As before the firm’s incentive compatibility condition requires that the firm signals from the set of messages that maximizes
Thus, given the equilibrium (ν, y L , y H ), we have that there exist a constant \(\theta\) for all realization of quantity on hand that satisfies the definition of AGNI. This completes the proof.
Proof of Proposition 4. Let \(A_{R,i}^{m_{1}}\) be the implied availability in equilibrium for class i customer during the regular season when the firm signals m 1. Let \(A_{S,i}^{m_{1}}\) be the implied availability in equilibrium for class i customer during the sales season when the firm signals m 1. We know from Lemma 1 that
For the equilibrium to be CWI, there must be a message such that
Using (12.16), we have that
Thus, (12.17) implies that
Rearranging we obtain
where (a) follows by noting that v H > v L and \(A_{R,H}^{m_{1}} \geq A_{S,H}^{m_{1}}\), and (b) follows from (12.16). This completes the proof.
Lemma 1.
For any equilibrium, we have that for any message m
Proof of Lemma 1. Let y be the equilibrium behavior for the customers. Thus, for the message m 1 customer of class-L and class-H purchase during the regular season with probability y L (m 1) and y H (m 1). Thus, we can represent the
where ω j H and ω j L are iid sequences of uniform random variables on [0, 1]. Let us define
Since,
we obtain that
Using the definitions of X L and X H , we have
Here (a) and (b) follows by noting that X L and X H are bounded by 1, \(\mathbb{P}(N_{L} = 0) = e^{-\lambda _{L}}\) and \(\mathbb{P}(N_{H} = 0) = e^{-\lambda _{H}}\). The inequality in (c) follows by (12.24) and mutual independence of random variables Q 0, N L and N H . This completes the proof for (12.20). The proof of (12.21) follows along the same line and using the definitions:
Proof of Theorem 1. As in the proof of Proposition 4, we let \(A_{R,i}^{m_{1}}\) be the implied availability in equilibrium for class i customer during the regular season when the firm signals m 1, and \(A_{S,i}^{m_{1}}\) be the implied availability in equilibrium for class i customer during the regular season when the firm signals m 1. We know from Lemma 1 that
For the equilibrium to be CWI, there must be a message m 1 and m 2 such that
Further, using (12.18), we have
We thus obtain:
The other inequalities follows in the same manner. This completes the proof.
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Allon, G., Bassamboo, A. (2017). Buying from the Babbling Retailer? The Impact of Availability Information on Customer Behavior. In: Ha, A., Tang, C. (eds) Handbook of Information Exchange in Supply Chain Management. Springer Series in Supply Chain Management, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-32441-8_12
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DOI: https://doi.org/10.1007/978-3-319-32441-8_12
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