A Study On Principal-agent Pattern With Nonlinear Cost Function

The single-agent and multi-agent phenomenon spread widely in the realistic economy.In this paper we build a principal-agent model with the nonlinear cost under the adverse selection to discover the economic factors behind this phenomenon.The existing literature mainly focuses on the angle of the marketing,such as the customer loyalty and so on.We find that the right approach to analyze the choice of different agency pattern for principal is based on the characteristic of the agent cost function.In this article,firstly we elaborate the mechanism design theory in the adverse selection. Based on the mechanism design theory,the principal-agent model under the linear cost condition is considered and we point out its insufficiency to explain the realistic economic phenomenon. Then we introduce a nonlinear cost function to analyze the cost characteristic of the enterprise production operation in reality,and a principal-agent model with the nonlinear cost condition is built by using game theory and optimized method.We separately analyze and compare the single agent model and the multi-agent model.We find that the choice of different agency pattern for principal will be determined by the agent cost function characteristic if the principal aims to design the most optimum mechanism.Namely,based on the agent cost function character,the monotonically increasing or decreasing of marginal costs,the principal will choose multi-agents or single agent pattern separately.Thus we think that the agency pattern choice for the principal is endogenie.