In the “experience economy”, effectively delivering memorable and exciting customer experiences has become a key issue for service providers. Service experience delivery involves service encounters through which interactions between service providers and customers can be shaped into interactive artifacts managing customer expectations and dynamically delivering suitable services. Service interaction design aims to optimize customer interactions with services to match customer expectations and yield satisfactory service experiences. On the other hand, service providers typically make profits and cost the priority, despite knowing that high service quality can maximize satisfaction, particularly in markets served by an oligopoly, resulting in customers only accepting existing limited-value services. Hence, the oligopoly market can be regarded as a value-bounded context. Additionally, understanding customer expectations regarding a wide range of interactions is crucial to service providers selecting and designing services that match customer expectations. Therefore, this paper presents a service interaction design mechanism to help oligopoly service providers systematically and effectively manage customer expectations in dynamic interactions, even in value-bounded contexts. The proposed mechanism models this service interaction design problem as a series of Hawk-Dove games that approach an evolutionary stable state. The evaluation results suggest that oligopoly service providers should change their mindsets and design service interactions to manage customer expectations associated with service delivery, not only to ensure high satisfaction and profit but also to engage customers in co-creating value.