我們建構了三個優惠券競爭的經濟模型來分析優惠券的發行會如何改變電商平台跨期的價格和市場結構。以兩期Hotelling模型為基礎。第一個模型分析兩個電商平台皆有發行優惠券之下的對稱經濟體。第二個模型考慮到優惠券的使用量與顧客的忠誠度呈線性相關。第三個模型考慮到消費者第二期的偏好分布會偏向於發行優惠券之平台。我們的核心發現是優惠券的發行能夠舒緩電商平台之間在第二期的價格競爭壓力。此外，對於發行優惠券之平台而言，兩期的總利潤將會增加。

We construct three economic models of coupon competition to analyze how the issuance of coupons will change the intertemporal price and market structure of e-commerce platforms. Based on the two-period Hotelling model, our first model analyzes a symmetric economy under both platforms issue coupons. In the second model, we consider that the usage of coupons is linear in customer loyalty. In the third model, we consider that the distribution of customer preference in the second period will be biased toward the platform that issues coupons. Our core finding is that the issuance of coupons can relax the price competition between platforms in the second period. Moreover, for the platform issuing the coupons, the total profit of the two periods will increase.

1. Introduction 1
2. Related Literature 3
3. Coupon Competition and Intertemporal Effects 8
3.1 Characterization of equilibrium 9
3.1.1 To stay or to switch? 9
3.1.2 Period-two equilibrium prices 11
3.1.3 Purchase decisions for t=1 13
3.1.4 Market prices and sizes of coupons for t=1 15
3.2 Impacts of Coupons 16
4. Linear Usage of Coupons 18
4.1 Characterization of Equilibria 19
4.1.1 To stay or to switch? 19
4.1.2 Period-two equilibrium prices 21
4.1.3 Purchase decisions for t=1 24
4.1.4 Market prices for t=1 26
4.1.5 The optimal size of coupons for t=0 29
5. Biased Customer Preference 32
5.1 Characterization of Equilibria 32
5.1.1 To stay or to switch? 32
5.1.2 Period-two equilibrium prices 33
5.1.3 Purchase decisions for t=1 35
5.1.4 Market prices for t=1 38
5.1.5 The optimal size of coupons for t=0 42
6. Concluding Remarks 45
References 48
Appendix A 52
Appendix B 52
Appendix C 55
Appendix D 58
Appendix E 61
Appendix F 64

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