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Stationary and ergodic probability distribution is derived and the stochastic balanced path of capital accumulation is defined via corresponding martingale path. Moreover, stochastic version of asymptotic turnpike theorem is established in the sense of uniform topology and also neighborhood type of stochastic turnpike theorem is demonstrated in the sense of ergodic measure.

In the current paper, we study the asymmetric normal-form game between two heterogeneous groups of populations by employing the stochastic replicator dynamics driven by Lévy process. A new game equilibrium, i.e., the game equilibrium of a stochastic differential cooperative game on time, is derived by introducing optimal-stopping technique into evolutionary game theory, which combines with the Pareto optimal standard leads us to the existence of Pareto optimal endogenous matching.

In the paper, a one-sector neoclassical model with stochastic growth has been constructed. The major goal of the study is to characterize relevant mathematical properties of efficient development paths for underdeveloped economies. Since economic maturity is a reasonable objective, we mainly focus on the long-run features of economic development. Indeed, the notion of economic maturity is well-defined in the model, and also a thorough characterization of the minimum time needed toward economic maturity is offered with intuitive interpretations discussed. Moreover, it is confirmed that the capital-labor ratio corresponding to the state of economic maturity provides us with a robust turnpike of the optimal path of capital accumulation.

In the paper, we are encouraged to investigate the effect of game structure imposed on the minimum-time needed to economic maturity in a dynamic macroeconomic model. Indeed, we have established a basic framework for the comparative study of the cooperative stochastic differential game and dynamic sequential game of economic maturity. Moreover, in a simple stochastic growth model, closed-form solution of the minimum-time needed to economic maturity has been derived with the explicit condition, under which it is confirmed that cooperation between the representative household and the self-interested politician will definitely lead us to much faster economic maturity than that of sequential action, supplied, too. Finally, our model supports the comparative study of the minimum-time needed to economic maturity under different political- institution constraints.

This study is encouraged to apply the methodology of economics to investigate the issue of gender selection of the traditional parents in China, which has been widely noted from the perspective of sociology. It is firstly argued that traditional society of China is a good object for economic analyses owing to its long‐run stability. Secondly,it is obviously seen that traditional parents are highly rational in gender selection owing to the corresponding economic and social environments around them. Hence, economics will play a crucial role in the analyses of gender selection. We have established two simple mathematical models corresponding to two different cases to derive some propositions about the gender selection of the rational parents.

As is well‐known,“foot‐binding”,regarded as an inefficient institution owing to its great harm to the women’s body and mind, existed and lasted for a very long period in the history of China. Furthermore, we are faced with the general question: why so many inefficient institutions in reality exist and persist? And this investigation is motivated to provide us with an economic explanation from micro‐perspective. Based upon some necessary assumptions and the definition of meta‐institution, it is argued in a simple mathematical model that equilibrium solution will always be inefficient institution even though the institutions themselves will experience various changes.

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.

A general equilibrium model has been constructed in a stochastic endogenous growth economy with the capital-labor ratio driven by an Itô-Lévy diffusion process. In particular, formal definition of the minimum-time needed to economic maturity is identified in the model and closed-form solutions of optimal savings strategy and optimal tax rates are established when the representative agent is assumed to exhibit log preference and there is a benevolent government in the economy. Moreover, the minimum-time needed to economic maturity is explicitly derived in the sense of sub-game perfect Nash equilibrium and one can further proceed to comparative static analysis with respect to the relevant parameters of the underlying economy such as the subject discount factor, the initial level of capital stock per capita, the utility-optimal and sustainable terminal path level of capital stock per capita, the natural growth rate of population, and the exogenous level of government spending. Finally, it is worth emphasizing that we focus on underdeveloped economies such as China and the present exploration presents a baseline mathematical model for studying the optimal policies needed to reach economic maturity as soon as possible.

In this paper, in order to study the strategic interactions between “cooperation”, “defection” and “altruistic punishment”, a mutation-selection dynamics, with the Prisoner's Dilemma as the background, has been established on an embedded Markov chain, proved the following conclusions: First, the “altruistic punishment”, even though not a Nash equilibrium, can be the only mutation-selection equilibrium when the population size goes to infinity; Second, the “cooperation”, even if been strictly dominated by the defection and altruistic punishment in the matrix game, will be the unique equilibrium of the evolutionary dynamics as the population size approaches infinity; that is to say, the altruistic punishment, even in very weak conditions, can effectively promote the evolution of cooperation.

In this paper, infinitely repeated prisoner's dilemma game as a benchmark being used to build a new model as the payoff matrix of an evolutionary game dynamics, with the comparative study of game performances between the behavior- pattern “tit for tat” and the behavior-pattern “always defection”, proving that there exists a strictly positive probability, which has a close link with the discount factor, that a single TFT individual can fully invade into a group of ALLD individuals; that is to say, TFT has some kind of evolutionary stability.