A hybrid profit and loss sharing model using interest free debt and equity financing : an application of game theory as a decision tool

In this paper two models are contrasted whereby a corporation is seeking to finance the purchase of a merchandise from a supplier through a profit and loss sharing contract. The first mode consist of financing the purchase totally through equity. The second model is a new hybrid model that engages the supplier in the process as a shareholder. Both models are based on the principle of profit and loss sharing which suffers from the issue of moral hazard. This is manifestedin the form of the corporation shirking (providing low effort) and/or misreporting profits. It is argued that under equity financing, where the financier is the only shareholder, the corporation can hide part of the merchandise it sold and therefore misreport profits. This is, however, not possible under hybrid financing where, in addition to the financier, the supplier is interested in the financial reporting of the corporation. We apply a game theoretical approach where, under a hybrid financing, the financier and the supplier have mutual interest in true revenue reporting and therefore constitute a coalition (one player) against the corporation. Our game incorporates the effect of sharing markets and corporations’ discounts between the game participants under each model. We show theoretically that a non-conditional good Nash equilibrium exists under hybrid financing. This case does not apply to an all equity financing where the existence of a good Nash equilibrium is conditional upon the financier and the supplier sharing ratios. This shows that under the hybrid model the corporation is always induced to provide more effort (not shirk) and truly report profits.