Incomplete Contracts with Cross-Investments

We study an incomplete contract model where both contracting parties can invest, and the investments have both self- and cross-effects. We analyze the performance of non-contingent contracts, message games, option contracts and property rights. We find that the first best is implemented if (i) the cross effects are negative or weaker than self-effects; (ii) the strength of cross-effects relative to self-effects is symmetric across parties. If either of these conditions is violated, even message contingent revelation mechanisms fail to provide efficient incentives. For this case, we obtain a number of results characterizing the second best. We find that property rights outperform contracts and partially relax the symmetry constraint. In either first best or second best, the stronger the cross-effects, the lower the value of contracting. The optimal allocation of property rights assigns ownership to the party with stronger cross-effects.