Incomplete property rights and overinvestment

I consider a model in which an asset owner must decide how much to invest in his asset mindful of the fact that an encroacher’s valuation of the asset is increasing in the asset owner’s investment. Due to incomplete property rights, the encroacher and asset owner engage in a contest over the control of the asset after investment has taken place. A standard result is that the asset owner will underinvest in the asset relative to the first-best level of investment when property rights are complete. Contrary to this standard result, I find that when the interaction between the asset owner and the encroacher is infinitely repeated and the encroacher has some bargaining power over the size of the transfer from the asset owner to him, then there is a cooperative equilibrium in which the asset owner finds it optimal to over-invest in the asset when property rights are incomplete relative to the first-best level of investment when property rights are complete. Overinvestment is used to induce cooperation. However, this result depends on the encroacher’s bargaining power or, more generally, whether the transfer is an increasing function of investment.