The Study Of Nash Equilibrium Of The Principal-agent In The Open-end Fund

In the open-end funds, small amount funds from individual investors are focused together and professional Fund Management Company are entrusted to invest these funds. Investors will share the investment income according to their investment proportion. Compared with the general principal-agent relationships, there are two different characteristics in the open-end fund. Principal-agent problem in open-end fund would be solved in some extent because Investors can purchase or redeem their investment fund shares. Fund Management Companies(Agents) are restricted. The possibility of moral hazard will decrease because of the restriction. In the open-end fund, fund investors can redeem fund shares through the application of incentives and punishment for fund managers. The possibility of moral hazard will reduce. And the principal and the agent's utility tends to equilibrium. Utility balance can be reached between the investors (principals) and Fund Management Companies (agents).This article analysis the restrictions that principals and agents facing based on the characteristics of the principal-agent relationship in the open-end funds and establish the utility functions of principals and agents according to the Principal-agent Theory. Then the article focus on to analysis the investors'and fund companies'behaviors that will make the two sides reach the Nash equilibrium. Since the Nash equilibrium are different when there is moral hazard or not, the article analysis the balanced behavior of the two separated models. The research results show that the Nash equilibrium of behaviors are affected by the cost coefficient, the behaviors'impact of fund performance, the incentive intensity from investors and etc. The balanced utility level with moral hazard is small than it without moral hazard.In practice, it would be more likely multi-principals and one-agent relationship in the open-end fund. After analyzing the utility functions of different investors, the article establish the common agency model to get the Nash equilibrium behavior. The research results show that in the common agency model, the investors'behavior is affected not only by agent by also by other investors. The balanced utility level in non-cooperative model is less than it in the cooperative model.