Verifying Competitive Equilibria in Dynamic Economies
研究了异质性代理人动态经济中的ε-均衡，发现即使ε很小，近似解也可能远离真实均衡，并给出了确保近似解接近真实均衡的充分条件，对计算均衡验证有用。
In this paper, I examine ϵ-equilibria of stationary dynamic economies with heterogeneous agents and possibly incomplete financial markets. I give a simple example to show that even for arbitrarily small ϵ > 0, allocation and prices can be far away from exact equilibrium allocations and prices. That is, errors in market clearing or individuals' optimality conditions do not provide enough information to assess the quality of an approximation. I derive a sufficient condition for an ϵ-equilibrium to be close to an exact equilibrium. If the economic fundamentals are semi-algebraic, one can verify computationally whether this condition holds. The condition can be interpreted economically as a robustness requirement on the set of ϵ-equilibria which form a neighbourhood of the computed approximation. I illustrate the main result and the computational method using an infinite horizon economy with overlapping generations and incomplete financial markets.