An elementary approach to the hold-up problem with renegotiation

So far, the existing literature on the hold-up problem with renegotiation has imposed assumptions such that the post-renegotiation payoffs are absolutely continuous functions. Since payoffs may fail to be differentiable at the investment profile to be sustained, first order conditions for incentives to invest must be handled with care. To avoid these difficulties, the present paper propagates a more elementary approach. A general condition is provided which necessarily must hold for an investment profile to be sustainable by a message contingent contract. If only one of the parties invests or, more generally, if investments can be aggregated into one dimension then the paper introduces assumptions leading to conditions which are necessary and sufficient for an investment profile to be sustainable.