Price promotional tools, such as instant discount and gift card, are commonly used by firms, particularly those in vertically-related markets (including suppliers with direct channels and their retailers), to stimulate purchases. Compared with instant discount, gift card promotion leads consumers to perceive a delay discounting effect by discounting the gift card face value upon redemptions due to delayed reward payments, while it endows consumers with a perception of a price illusion effect that induces multiple mental reductions of purchasing costs despite a single gain. We develop a theoretical model to examine how a supplier and its retailer, under consideration of consumers' purchasing perceptions, strategically use the above two promotional tools. We find that in a fully covered market (i.e., all consumers choose to buy), despite competition, the supplier will not provide a price promotion under consumers' weak price illusion effect (but stronger than the delay discounting effect), while under consumers' strong price illusion effect, if neither firm offers a price promotion, both firms could benefit. By contrast, in a partially covered market (i.e., some consumers choose not to buy and each firm acts like a monopoly), both firms benefit from price promotions under market broadening, and their preferred promotional tool becomes the instant discount rather than the gift card promotion as consumers' price illusion effect and the marked price decrease. Additionally, the two competing firms' choices of promotional tools might lead to a Prisoner's dilemma, where the instant discount promotion is a dominant strategy, whereas the gift card promotion makes both firms better off. We provide some guidelines for suppliers and retailers to offer promotional tools in different covered markets, taking purchasing perceptions of consumers and marked prices of products into consideration.