by Gorkem Celik
, 14.10.19
In her celebrated novel, Sense and Sensibility, Jane Austen describes the lives of the Dashwood sisters in 18th century England. Elinor Dashwood falls in love with Edward Ferrars. The attraction is mutual, but Edward is already secretly engaged to another woman who is, in fact, more interested in Edward’s family fortune than in Edward himself. At the end of the novel, Edward loses his rights to the family money but ends up marrying Elinor. Of course, not all love stories have such happy endings. In the same novel, Elinor’s sister, Marianne, is romantically involved with John Willoughby. However, unlike Edward, Willoughby prefers living a comfortable lifestyle to pursuing true love. Thus, Willoughby marries a young lady with a large fortune rather than Marianne.
From a cold-blooded economic perspective, it is simple to design a straightforward mechanism that would generate an allocation rule pursuant to which idealist Edward would lose his fortune but succeed in love and materialist Willoughby would secure a financially comfortable life but fail to find romance. All we need to do is to ask each gentleman whether he is more of an idealist or more of a materialist and then assign him the appropriate spouse.
Mechanism design theory has been an essential tool in analyzing what types of institutional rules are needed to achieve specific objectives in organizations such as markets and firms [1]. This theory is especially useful in analyzing situations where the individuals within an organization hold relevant private information, but they are unwilling to reveal this information right away due to conflicting interest. An appropriately designed mechanism can motivate these economic agents to report their information truthfully.
Although mechanism design is an essential tool for analyzing many economic problems, it does not provide a good formula for writing a literary masterpiece. In Sense and Sensibility, it takes three volumes and 300 pages for Elinor and Edward to unite. First, Edward begins acting detached and Elinor concludes that he has lost interest in her. Then, she learns of Edward’s prior engagement, which he feels compelled to honor. However, Edward’s mother also finds out about the engagement and disinherits him in disapproval. Once Edward loses the connection to his wealthy family, Edward’s fiancé breaks up with him and marries his brother, who is now the sole heir of the family estate. Elinor hears about the marriage in Edward’s family and assumes that it was Edward who was married. Near the end of the novel, Edward shows up unexpectedly and announces to Elinor that he is no longer burdened by his earlier engagement nor by his family obligations.
To generate suspense throughout the novel, Austen does not reveal the traits of her characters at once. Instead, the revelations are supported by a sequence of decisions made by the characters. These decisions make sense from the characters’ perspective: Each decision reflects the preferences of the decision-maker given what he/she knows about the other characters at the time that the decision is made. The decisions not only serve to reveal the qualities of the characters to readers (and to the other characters in the book) but also lead to the outcomes that the characters will face at the end of the novel.
Applying Austen’s Methodology to the Theory of Firm
In one of the most influential early applications of mechanism design, Harris, Kriebel, and Raviv study the intra-firm research allocation problem [2]. They model the firm as a combination of a number of different product divisions and a single resource division. Each product division is tasked with producing a pre-determined level of output by using either its own effort or an intermediate good that is sourced from the resource division. The productivity of each product division in utilizing the intermediate good is its private information, as is the efficiency of the resource division in transforming a primary resource into the intermediate good. The management of the firm must decide how to allocate the intermediate good across different divisions and how much monetary transfer to make to each division to compensate for the cost of the effort. Harris, Kriebel, and Raviv show that, from the management’s perspective, the most cost-effective way of motivating these different divisions involves using a transfer-pricing mechanism: the product divisions and the resource division simultaneously report all their private information to the firm’s management and Harris, Kriebel, and Raviv’s mechanism determines the transfer prices under which the intermediate good will be exchanged among the different divisions within the firm.
In a recent article published in the Rand Journal of Economics [3], I argue that the modern firm, with a constant in- and out-flow of diverse employees, is more similar to the story plot in a Jane Austen novel than it is to the firm in the standard economic model [4]. For many real-life firms, a mechanism that requires management to simultaneously communicate with all its divisions is not a realistic solution to the resource allocation problem. A more practical design would ask for the different divisions of the firm to report their private information to the management sequentially. This design will involve a less-demanding communication procedure than the standard simultaneous mechanism because an individual division will need to reveal information only to the extent that it is going to make a difference in the resource allocation of the firm. For instance, if the resource division had already revealed that it is very expensive to produce the intermediate good, the management can directly instruct the product divisions to produce the final good by using their own effort without the intermediate good. This allows the firm to avoid losing time by trying to figure out the productivity of each division in using an intermediate good which will not be available for them.
Unfortunately, Harris, Kriebel, and Raviv’s transfer pricing scheme is not compatible with the gradual revelation of information explained above. The problem is that, after learning the costs of producing the intermediate good from the resource division, a product division may now understate its productivity in order to reduce the transfer price it pays. Nonetheless, the results in my article identify an alternative set of monetary transfers that provide the right incentives for the divisions. Moreover, these alternative transfers are equal to the original Harris-Kriebel-Raviv transfers in expectation (from each division’s perspective) and they respect the overall budget requirements of the firm’s management.
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[1] The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel was awarded jointly to Leonid Hurwicz, Eric S. Maskin and Roger B. Myerson in 2007 "for having laid the foundations of mechanism design theory." See http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2007/
[2] Harris, M., Kriebel, C.H., and Raviv, A. “Asymmetric Information, Incentives and Intrafirm Resource Allocation,” Management Science, Vol. 28 (1982), pp. 604-620.
[3] Celik G. “Implementation by Gradual Revelation,” The RAND Journal of Economics, Vol. 46 (2015), pp 271-296. In addition to the intra-firm resource allocation, this article discusses the relevance of gradual revelation mechanisms in the contexts of auctions and litigation.
[4] For many other examples of economic thinking in Austen’s work, see the intriguing book by Chwe, M.S.Y., Jane Austen, game theorist. Princeton University Press, 2014.
