A Game Theoretic Analysis of Olson's Game of Collective Action

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Abstract
Olson has argued that rational, self-interested individuals will not act to achieve their common goal or to satisfy their collective interests. Hardin interpreted the argument in terms of the classical prisoner's dilemma and offered a solution whereby the majority choice of the group would rationally be the joint cooperative strategy. The present paper considers the characteristic function of such a game and demonstrates that, within the terms of reference of game theory, there exists a solution in the sense that any coalition beyond a certain size must unanimously and rationally grow until it becomes the grand coalition. In other words the solution supposes that subgroups form within the primary group and considers the consequent, rational dynamics of the situation.

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