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This paper gives a general mathematical definition of an institution, and presents an explicit formal method by which to incorporate institutions in a standard general equilibrium model. We illustrate our concept using a modified Prisoner's dilemma game in which property rights over natural resources emerge from an anarchy-like state of nature. Two players decide voluntarily and non-cooperatively whether to give up some fraction of their personal resource to set up an enforcement mechanism that punishes defecting players (i.e., players that do not opt to cooperate). This enforcement mechanism constitutes a credible threat, and is central to the establishment of bilateral cooperation (i.e, government). We highlight the importance of imperfect information (proposition 1) and risk averse behavior (propositions 2 and 3) for bilateral cooperation to be sustained as the unique Nash-equilibrium. Proposition 1 formalizes an idea of Brennan and Buchanan (1985) that the legitimacy of governments is based on their contribution to reducing uncertainty. Proposition 3 justifies an assumption made by Sened (1997) that rational individuals respect governments dictating specific institutions.
