Sanford Grossman, Oliver Hart, and John Moore have developed a theory of the firm based on incomplete contracting (Hart was awarded the Nobel Prize in 2016 for this branch of the literature). In the Grossman/Hart/Moore model, ex-post negotiations always yield an efficient outcome. (Ownership rights influence only the division of the ex-post surplus, which in turn influences incentives to make investments.) In contrast, Oliver Williamson (who was awarded the Nobel Prize in 2009) emphasizes that ex-post negotiations may well yield inefficient outcomes (see e.g. Williamson’s article on the new institutional economics in the Journal of Economic Literature, 2000). Are there any formal models (assuming standard profit-maximization goals of the firm owners) that somehow incorporate Williamson’s insight in the Grossman/Hart/Moore theory of the firm?
Yes, there are models that reconcile Hart’s property rights theory with Williamson’s emphasis on haggling and ex post inefficiencies.
Hart and Moore have developed a behavioral theory of contracts as reference points. They argue that contractual parties engage in ex post inefficient shading activities when they are aggrieved (which happens when they do not get what they feel entitled to given the reference point that was set by a contract). In this sense, the theory is based on non-standard preferences: Hart, O. and Moore, J. (2008). Contracts as Reference Points, Quarterly Journal of Economics, Vol. 123, pp. 1–48. See also Hart (2009) for an extension of this approach.
Another possibility to formalize ex post inefficiencies in a Grossman/Hart/Moore framework is to allow for asymmetric information: Schmitz, P.W. (2006). Information Gathering, Transaction Costs, and the Property Rights Approach, American Economic Review, Vol. 96, pp. 422–434. This approach maintains the standard assumption of profit-maximizing behavior and studies the trade-off between investment incentives and ex post inefficiencies (see also the more recent contribution by Schmitz (2017) and the literature mentioned there).
Finally, while less related to the Grossman/Hart/Moore framework, there are also models that study property rights in adverse selection models without investments (building on the prominent paper by Myerson and Satterthwaite, 1983), where the optimal ownership allocation minimizes ex post inefficiencies: McKelvey, R.D. and Page, T. (2002). Status quo bias in bargaining: An extension of the Myerson–Satterthwaite theorem with an application to the Coase theorem, Journal of Economic Theory, Vol. 107, pp.336–355. A literature review with particular emphasis on models building on the Myerson/Satterthwaite framework: Segal, I. and Whinston, M.D. (2012), Property rights. Handbook of Organizational Economics, pp. 100–158.