Modeling the minimum time needed to economic maturity

A general equilibrium model has been constructed in a stochastic endogenous growth economy driven by an Ito-Levy diffusion process. The minimum time to “economic maturity” for an underdeveloped economy has been computed both in the preference manifold of the modified Ramsey fashion and in that of the modified Radner fashion with its support, i.e., fiscal policies and savings strategy, endogenously determined. Furthermore, the effects of different information structures to the endogenous time have been thoroughly investigated, and local sensitivity analyses of optimal consumption per capita with respect to the initial level of capital stock per capita have been smoothly incorporated into the current macroeconomic model

A New Exploration of Optimal IPR Protection and International Policy Cooperation

In this paper, a variety-expanding growth model has been constructed in the classical North-South framework. Optimal degree of IPR protection has been explicitly computed both for the North and the South in the sense of welfare maximizing, in the short run and non-short run of the economies. Endogenous innovation growth rate and the policy of innovation subsidy for the Southern government have been introduced into our model. The relationship between IPR protection and long-term growth rate has also been thoroughly investigated. Finally, the issue about international policy cooperation has been explored and we show that it is possible that an optimal degree of Southern IPR protection would also be globally efficient in some comparatively weak conditions

Independence and Uniqueness of the Mixed-Strategy Equilibrium in Social Networks

We develop topological analysis of social-network effect on game equilibrium in the context of two- player asymmetric normal-form games and also in evolutionary sense. Firstly, it is confirmed that the game equilibrium in many social networks cannot be established through that in a well-mixed population. In other words, we have proved the independence of the mixed-\ud strategy equilibrium in social networks. Secondly, it is demonstrated that the game equilibrium exhibits injective property with respect to the corresponding social-network effect under\ud consideration. That is, the uniqueness of the mixed-strategy game equilibrium in a given social network is identified. Thirdly, it is argued that uniqueness implies independence for a wide\ud range of social networks and we have even derived the biggest sets of social networks in which independence and uniqueness hold true, respectively, in the underlying game. To sum up, we\ud have provided qualitative characterizations about topological properties of the mixed-strategy game equilibrium in general social networks

Learning Nash Equilibria

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

Essays in Nonlinear Labor Income Taxation with Tax-Driven Migrations

This dissertation includes two essays in nonlinear labor income taxation with tax-driven migrations. In the first essay, we study optimal nonlinear income taxation in an open economy with migration possibilities and social comparisons. Recent evidence suggests that globalization has not just reduced the barriers to international labor mobility but also induced more cross-country comparisons. In an open economy with tax-driven migrations and consumption externalities motivated by altruism or jealousy, we derive an optimal tax formula that subsumes existing ones obtained under maximin social objective and additively separable utility, and identify the sign of second-best marginal tax rates for all skill levels. We establish thresholds of the elasticity and level of migration to determine when relativity and inequality are complementary (or substitutive) in shaping the optimal top tax rates. These thresholds are in general different between altruism-type and jealousy-type relativity. Surprisingly, there exist reasonable combinations of relativity, mobility and inequality such that tax competition results in higher equilibrium top tax rates than proposed in autarky. Also, under both Nash and Stackelberg tax competition, we have the following numerical finding by plugging realistic parameter values in our tax formula. If the migration probability of top-income workers is around 50%, then the country facing labor inflow (respectively, outflow) of these types of workers implements around 10% lower (respectively, higher) top tax rates than suggested by the autarky equilibrium which does not allow for migration possibilities. In the second essay, we study majority voting over selfishly optimal nonlinear income tax schedules proposed by a continuum of workers who can migrate between two competing jurisdictions at the expense of some migration cost. Both skill and migration cost are the private information of each worker. Assuming quasilinear-in-consumption preferences, the tax schedule proposed by the median skill type is the Condorcet winner that redistributes incomes from the rich and poor toward the middle. While it features negative marginal tax rates for low skills, it features positive marginal tax rates for high skills who have elasticities of migration smaller than a threshold. In a comparison with the autarky economy, we establish the skill-dependent threshold of migration elasticity for all types of workers. If their migration elasticities are higher than their respective threshold, then migrations induce lower marginal tax rates than does autarky; otherwise migrations induce higher marginal tax rates for the jurisdiction facing net labor inflow in low skills while net labor outflow in high skills. Counterfactual simulations using empirical parameter estimates show that eliminating migrations in the U.S. would generate top tax rates over 20% higher than the 42.5% that was actually implemented

Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology

In this paper, a stochastic endogenous aggregative growth model is constructed and two main results are established, based on endogenous horizon of the economy and endogenous terminal capital stock, which is also efficient capital accumulation in some sense. First, strong turnpike theorems under uncertainty and in the sense of uniform topology are obtained; second, inefficacy of temporary fiscal policy, which is chosen to be capital income taxation, has been demonstrated in comparatively weak conditions different from Yano (1998)'s.Stochastic endogenous growth, Uniform-topology turnpike theorems, Endogenous terminal stock, Endogenous welfare function, Capital income taxation

On the existence and stability of Pareto optimal endogenous matching with fairness

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. Moreover, stability of the Pareto optimal endogenous matching is confirmed by essentially using the well-known Girsanov Theorem

On the Existence and Stability of Pareto Optimal Endogenous Matching with Fairness

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. Moreover, stability of the Pareto optimal endogenous matching is confirmed by essentially using the well-known Girsanov Theorem

利他惩罚：通往演化彼岸的桥

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