Anarchy and Agreement — A Game Theoretic Analysis of Some Aspects of Contractarianism
Our paper is an exercise in “the logic of collective action”. It analyzes some difficulties that arise if we take seriously the fundamental ethical premise of contractarianism, namely, that nothing short of free consent of all individuals concerned can justify an institutional order. The discussion is based on an extensive game of consensual choice of rules or institutions in prisoner’s dilemma situations. In this game the fundamental distinction between collective consent under the unanimity rule -- a collective act in a predefined group -- and private consent of individuals -- an act that precedes group formation -- shows up in the process of institution creation. We think that an explicit game theoretic formulation of these two forms of unanimity may be helpful for a better understanding of the scope and limits of contractarian theories of social institutions: In a purely private decision rational players of a set N of concerned individuals who share a common interest decide whether or not they become members of a group S. Only after the group has been constituted its members may make decisions according to some collective decision rule. The decision of whether or not a rational player should join S depends on the predictable results of the game for a member or for an outsider of S. If group membership is purely voluntary well known arguments suggest that S=N will hold good only under quite specific circumstances. Some of the relevant circumstances are explicitly modeled subsequently (II.–IV.). We describe a general model although, in the present paper, our explicit analysis is restrained to the special case of three interacting individuals and a numerically specified prisoner’s dilemma situation.
KeywordsNash Equilibrium Collective Action Extensive Form Payoff Matrix Decision Stage
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