With the ever-increasing popularity of Service-oriented Architecture (SoA) and Internet of Things (IoT), a considerable number of enterprises or organizations are attempting to encapsulate their provided complex business services into various lightweight and accessible web APIs (application programming interfaces) with diverse functions. In this situation, a software developer can select a group of preferred web APIs from a massive number of candidates to create a complex mashup economically and quickly based on the keywords typed by the developer. However, traditional keyword-based web API search approaches often suffer from the following difficulties and challenges. First, they often focus more on the functional matching between the candidate web APIs and the mashup to be developed while neglecting the compatibility among different APIs, which probably returns a group of incompatible web APIs and further leads to a mashup development failure. Second, existing approaches often return a web API composition solution to the mashup developer for reference, which narrows the developer's API selection scope considerably and may reduce developer satisfaction heavily. In view of the above challenges and successful application of game theory in the IoT, based on the idea of game theory, we propose a compatible and diverse web APIs recommendation approach for mashup creations, named MCCOMP+DIV, to return multiple sets of diverse and compatible web APIs with higher success rate. Finally, we validate the effectiveness and efficiency of MCCOMP+DIV through a set of experiments based on a real-world web API dataset, i.e., the PW dataset crawled from ProgrammableWeb.com.