本文中，我們探討當企業間互相影響而做出不同的借貸策略。一開始我們考慮兩間異質的銀行，為了找出一最佳化策略使得某家銀行在向另一家銀行借貸時花費最小的成本，若我們的資產額低於對手則向他借錢，相反地若我們的資產額高於對手時則放款給他，我們利用Hamilton-Jacobi-Bellman(HJB)方程式去找出奈許均衡點。第二部份我們討論同質的N家銀行，一樣藉由HJB方程式來找出奈許均衡點並觀察相對表現的比值如何影響存活機率。;In this paper, we consider the problem of optimal lending and borrowing where executives take into account the relative to their peers. First, we study two heterogeneous banks. In order to find the optimal strategy through minimizing the quadratic cost for borrowing or lending and an intention to borrow if the capital is low or lend if the capital is high by comparison to the fund of opponent, we use the Hamilton-Jacobi-Bellman(HJB) equations to obtain the Nash equilibrium. Second, the case of $N$ homogeneous banks is discussed. We obtain the Nash equilibrium by using the HJB equations and observe the influence of the ratio of relative performance on the survival probability.
