Todays complex online applications often require the interaction of multiple services that potentially belong to different business entities. Interoperability is a core element of such an environment, yet not a straightforward one. In this paper, we argue that the emergence of interoperability is an economic process among rational agents and, although interoperability can be mutually beneficial for the involved parties, it is also costly and may fail to emerge. As a sample scenario, we consider the emergence of semantic interoperability among rational service agents in the service-oriented architectures (SOA) and analyze their individual economic incentives with respect to utility, risk and cost. We model this process as a positive-sum game and study its equilibrium and evolutionary dynamics. According to our analysis, which is also experimentally verified, certain conditions on the communication cost, the cost of technological adaptation, the expected mutual benefit from interoperability as well as the expected loss from isolation drive the process.