Inventory and financial strategies with capital constraints and limited joint liability

We study the financial and operational decisions of two capital-constrained firms via a limited joint liability (LJL) financing scheme offered by a bank. We construct a two-stage game model in which the firms separately determine their individual ordering decisions according to the prior joint liability agreement between the firms and the bank. Applying non-cooperative game theory to analyze the decision-making problems of the two firms, we establish the existence of equilibrium decisions for the two firms.We derive mild conditions under which the LJL financing scheme is simultaneously preferred by the two firms. We show that the two firms' strategies are complementary and the firms' equilibrium order quantities are always positively influenced by the risksharing term. We find that a greater bank loan leverage ratio may not simultaneously improve the two firms' performance. When the credit line and interest rate are endogenized by the bank, we provide insights on the relationship between the optimal interest rate and bank loan leverage ratio through risk hedging.