Large-scale online service providers have been increasingly relying on geographically distributed cloud infrastructures for service hosting and delivery. In this context, a key challenge faced by service providers is to determine the locations where service applications should be placed such that the hosting cost is minimized while key performance requirements (e.g., response time) are ensured. Furthermore, the dynamic nature of both demand pattern and infrastructure cost favors a dynamic solution to this problem. Currently most of the existing solutions for service placement have either ignored dynamics, or provided solutions inadequate to achieve this objective. In this paper, we present a framework for dynamic service placement problems based on control- and game-theoretic models. In particular, we present a solution that optimizes the hosting cost dynamically over time according to both demand and resource price fluctuations. We further consider the case where multiple service providers compete for resources in a dynamic manner. This paper extends our previous work [1] by analyzing the outcome of the competition in terms of both price of stability and price of anarchy. Our analysis suggests that in an uncoordinated scenario where service providers behave in a selfish manner, the resulting Nash equilibrium can be arbitrarily worse than the optimal centralized solution in terms of social welfare. Based on this observation, we present a coordination mechanism that can be employed by the infrastructure provider to maximize the social welfare of the system. Finally, we demonstrate the effectiveness of our solutions using realistic simulations.