Mathematical Model of Dynamic Games of Imperfect Agency--Based on Conspiracy of SMEs and Bank Managers

: In China, state-owned commercial banks have monopoly position on the banking loan market. This paper constructs a two-stage dynamic game model to analyze the conspiracy in decision-making of bank loans, based on the establishment of relationship lend between SMEs and managers in large banks. Results indicate the existence of an optimal equilibrium as the solution of conspiracy. A revised mathematical model analysis with relaxed assumption shows that: if the state-owned banks have the mastery of large amounts of capital, supervision of SMEs lending are weak, and bank manager has the control of complete information of enterprises, the conspiracy tendencies for both parties will be more obvious. The conspiracy based on relationship lends between banks and enterprises will greatly damage the interests of banks and extrude high-quality SMEs. Key words: Mathematical Model; Dynamic Game; Conspiracy;Relationship Lend