FE Guerra-Pujol, ‘Modelling the Coase Theorem’

More than fifty years ago, in two classic papers published in the then obscure Journal of Law and Economics, the English economist Ronald Coase posited what has since become known among economists and lawyers as the “Coase Theorem.” Unlike most forms of economic analysis, however, Coase’s celebrated theorem is based on a verbal argument and is almost always proved arithmetically using arbitrary and artificial parameter values. That is to say, ironically, the Coase Theorem is not really a theorem in the formal or mathematical sense of the word. Our objective in this paper, then, is to remedy this deficiency by combining Coase’s original and intuitive insights with the formal methods of game theory. The paper is thus divided into two parts. Part I (sections 1-3) provides some background information regarding the Coase Theorem. Specifically, section 1 briefly discusses the theoretical and practical significance of the Coase Theorem. Section 2 describes two of the most famous illustrations of the Coase Theorem: Coase’s simple model of farmer-rancher interactions, the model which became the basis of the Coase Theorem, and Coase’s arithmetical analysis of the problem of railway sparks. And section 3 reviews previous analyses of the Coase Theorem (in summary, most statements of the Coase Theorem are expressed in words or in arithmetical terms with make-believe values) and reviews some previous attempts to formally model the Coase Theorem. Part II of the paper (sections 4-7) then presents some alternative approaches to the Coase Theorem and contains several simple game-theoretic models the Coase Theorem. Specifically, section 4 presents a generalized two-player “Coasian game” with probabilistic payoffs. Section 5 presents a generalized n-player evolutionary model of the Coase theorem, and then, returning to Coase’s model of rancher-farmer interactions. And section 6 models a Coasian farmer-rancher population game with high transaction costs and the presence of legal rules. Section 7 concludes and identifies some areas for future research.

Guerra-Pujol, F.E., Modelling the Coase Theorem (August 14, 2012).

First posted 2012-08-16 07:45:29

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