The role of completely joint liability in financing multiple capital-constrained firms: Risk sharing, inventory and financial strategies

This paper makes an attempt to explore the relative value of a completely joint liability (CJL) financing scheme over traditional individual financing scheme for two financially-constrained firms. We develop a risk-sharing non-cooperative Nash-game model for the two firms in which they make unilateral ordering and financial decisions based on the CJL financing agreement as to the additional benefit (i.e., unit financing cost reduction) because of joint liability. We prove the existence of the firms' equilibrium inventory decisions in a Nash game that is in general not quasi-concave or even supermodular. We show that in equilibrium, the completely joint liability of CJL financing induces the two firms to order more (compared to individual financing case), and meanwhile, the firms become more aggressive in ordering as the shared risk goes up. However, such over-investment in ordering under CJL financing does not always result in higher bankruptcy risks for the firms. Importantly, we show that the choice of the proposed financing schemes for both the firms is completely determined by a simple two-threshold policy in terms of the firms' initial capitals and loan terms, and provide insights on how a financing-need firm to select proper partners to use CJL financing together, and how a profit-seeking bank to strategically set the proper financing terms to make the CJL financing scheme generate more benefits to itself and the two firms simultaneously (i.e., "win-win-win" situation).