This study introduces a computational tool to analyze how a population of decision makers communicates and learns to coordinate to attain an equilibrium or a social convention in a two-sided matching game with incomplete information. Genetic algorithms are used in an environment where agents are heterogeneous and have private information. In the contexts of centralized and decentralized entry-level labor markets, evolution and adjustment paths of "unraveling" are explored using this tool. The situation of the Kagel and Roth (1997) laboratory experiment is generalized under a variety of markets and institutions. Evolution paths of unraveling are investigated, particularly for the historic entry-level British medical labor markets. As one result, it is demonstrated that "stability" need not be required for the success of a matching-mechanism under incomplete information in the long run. Evolutionary evidence is found to support the field success of unstable linear programming mechanisms used in Britain.