认真对待不承诺：连续时间下的子博弈完美均衡
Being serious about non-commitment: subgame perfect equilibrium in continuous time
摘要：
本文刻画了具有非常数折扣的连续时间跨期决策最优化问题的可微子博弈完美均衡。该平衡方程有两种不同的形式，其中一种形式类似于经典的最优控制Hamilton-Jacobi-Bellman方程，但带有非局部项。我们给出了一个局部存在性结果，并给出了几个在消费节约问题中的例子。然后，分析表明，非恒定的贴现率产生的不确定性的拉姆齐增长模型中的稳定状态。尽管它的不确定性，稳定状态的水平是稳健的小偏差从常数贴现率。
英文摘要：
This paper characterizes differentiable subgame perfect equilibria in a continuous time intertemporal decision optimization problem with non-constant discounting. The equilibrium equation takes two different forms, one of which is reminescent of the classical Hamilton-Jacobi-Bellman equation of optimal control, but with a non-local term. We give a local existence result, and several examples in the consumption saving problem. The analysis is then applied to suggest that non constant discount rates generate an indeterminacy of the steady state in the Ramsey growth model. Despite its indeterminacy, the steady state level is robust to small deviations from constant discount rates.
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