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In the present paper, a new approach to equilibrium selection for very general normal form games has been constructed by introducing stochastic optimal stopping theory into classical evolutionary game theory. That is, the new game equilibrium is induced by both stochastic group evolution and decentralized rational individual choice. Moreover, stability of the game equilibrium is confirmed from both time and space dimensions.

In the paper, we re-investigate the long run behavior of an adaptive learning process driven by the stochastic replicator dynamics developed by Fudenberg and Harris (1992). It is demonstrated that the Nash equilibrium will be the robust limit of the adaptive learning process as long as it is reachable for the learning dynamics in almost surely finite time. Doob’s martingale theory and Girsanov Theorem play very important roles in confirming the required assertion.

In the paper, a one-sector neoclassical model with stochastic growth has been constructed. The key concept of economic maturity is well-defined in the abstract model economy, and also a thorough characterization of the minimum time needed to economic maturity is supplied for the first time. Moreover, it is confirmed that the capital-labor ratio corresponding to the state of economic maturity indeed provides us with a robust turnpike of the optimal path of capital accumulation.