Edward Glaeser in Honoring the Nobel Laureates explains the work of both. About Williamson:
"To understand Mr. Williamson’s part of the prize, it is necessary to go back 72 years to the precocious product of a 27-year-old English economist, Ronald H. Coase, who won the Bank of Sweden Prize in 1991.
While there had been a long literature debating the effect of firms’ size on productivity, Mr. Coase asked an even more fundamental question: Why do firms exist at all? Why should an entrepreneur hire workers and create a durable employer-employee relationship inside a firm, instead of just writing contracts with independent laborers?
Mr. Coase’s question began the modern discussion, in which Mr. Williamson has played a leading role, of why some transactions occur within firms while others take place in markets.
Mr. Coase’s answer to this question, which has also been Mr. Williamson’s answer, is that “the operation of the market costs something and by forming an organization and allowing some authority (’an entrepreneur’) to direct the resources, certain marketing costs are saved.”
When the costs of transacting in the market are high, either because of costly contracts or sales taxes, then it makes more sense to move transactions inside firms. The phrase “transaction costs” has come to define a school of institutional economists, of which Mr. Williamson is the dean.
Mr. Coase produced an answer to his question but did relatively little to flesh out what transaction costs actually mean. Mr. Williamson took on that task. In a series of remarkable articles and books, he enumerated the reasons markets may be less than perfect, including bounded rationality, asymmetric information, imperfect contracting and ex-post opportunism.
His seminal article, “Markets and Hierarchies: Some Elementary Considerations,” later fleshed out in book form, compared markets with peer group associations and hierarchies. He followed another Nobel laureate, George A. Akerlof, by emphasizing information asymmetries and the difficulty of ascertaining the productivity of particular workers. Mr. Williamson argued that a simple hierarchy with workers, ground level managers and an entrepreneur was a remarkably efficient way of handling production when information was imperfect.
Mr. Williamson clearly saw the limitations, as well as the benefits, of hierarchies. Longer hierarchies invariably involved a loss of information and a failure of subordinates to adhere to the entrepreneur’s original intent. Mr. Williamson’s most cited work, “The Economic Institutions of Capitalism,” is a far-ranging document that thoughtfully addresses the advantages and disadvantages of different modes of economic organization.
Mr. Williamson, himself, was a bridge between Mr. Coase and the more formal treatment of the theory of the firm associated most strongly with my colleague Oliver Hart, and his co-authors Sandy Grossman and John Moore. Their work followed Mr. Williamson, and others like Armen Alchian, Benjamin Klein and Robert Crawford, in pointing to contracting difficulties that precluded arms-length transactions.
Mr. Hart favored a more mathematical approach and a precise and particular definition of particular transaction costs. Mr. Williamson argued that much was lost in the translation to mathematics, especially his emphasis on bounded rationality and the difficulty of adapting well to changing circumstances. A modest but growing literature is now following Mr. Williamson’s call for models of the firm that more realistically reflect humanity’s psychological limitations.
Mr. Williamson’s work suggests that institutions emerge to address the transaction costs inherent in different settings. Ms. Ostrom’s most influential work has focused on the ability of institutions to handle one of the most challenging of all situations."
John Quiggin in Ostrom and Williamson win Nobel:
"Of the two winners, Williamson was on most lists of people (actually, men) who were bound to win sooner or later. His fundamental work on transactions costs and economic organization, largely done in the 1970s and 1980s changed the way economists think about these things. That said, it raised more questions than answers. Economists still tend to use ‘transactions costs’ as a kind of black box, in which to put anything that prevents markets working as they should. My view is that the ultimate answer will be found by dropping the assumption that market participants are perfectly rational agents, capable of considering all possible outcomes of the transactions into which they enter. But I would say that – most of my theoretical work these days is about bounded rationality in one form or another.'
and also answers a question of mine on the limitations of Ostorm approach. Much more in the comments section of CT post Honoring the Nobel Laureates The Ostrom Nobel. It has this quote from Ostrom (CPR stands for Common Pool Resource):
"Evolved norms, however, are not always sufficient to prevent overexploitation. Participants or external authorities must deliberately devise (and then monitor and enforce) rules that limit who can use a CPR, specify how much and when that use will be allowed, create and finance formal monitoring arrangements, and establish sanctions for nonconformance. Whether the users themselves are able to overcome the higher level dilemmas they face in bearing the cost of designing, testing, and modifying governance systems depends on the benefits they perceive to result from a change as well as the expected costs of negotiating, monitoring, and enforcing these rules" and this from gsmoke's diary:
"Based on a survey of several thousand cases, political scientist Elinor Ostrom has listed several basic requirements for locally sustainable, collective environmental management (Governing the Commons, Cambridge University Press, 1990, p. 90):
clearly defined boundaries
congruence between rules & local conditions
recognition of rights to organize
nested in & recognized by higher institutional levels
As Elinor Ostrom notes for successful common property systems, "the populations in these locations have remained stable over long periods of time. Individuals have shared a past and expect to share a future..." (Elinor Ostrom, Governing the Commons: The Evolution of Institutions for Collective Action, 1990, op. cit., p. 88)."
In other words, it is hard.
Political Scientist Elinor Ostrom Wins Nobel Prize in Economics has links to an Article by Ostrom and excerpts to her work and finally (via John Quiggin) The Myth of the Tragedy of Commons by Ian Angus