Game Theoretical Formulations of The Olson Problem*

Abstract This paper takes up one of the basic themes of Mancur Olson's Logic of Collective Action (Harvard University Press 1965). that is a group size as a cause of suboptimal provision of collective or public goods. A general framework is developed for classifying collective action situations involving public goods provisions. This framework focuses on the two characteristics: relations between contribution and provision, and rivalness or jointness in consumption of the collective goods. This framework distinguishes six types of collective actions, for each of which a game theoretical formulation is developed to obtain. models concerning social movements against (or for) new legislations, a petition for the recall of an official, a strike, lobbying, building a lighthouse, creation of a database, etc. These models, formulated either as an N-person chicken game or as an N-person prisoner's dilemma game. are examined with respect to how a group size affects non-cooperative equilibria and their Paretooptimality. There is no group size effect in the collective action situations formulated as an N-person chicken game, while large groups may suffer from suboptimal provision of the public goods in the collective action situations formulated as an N-person prisoner's dilemma game. Two types of the group size effect in N-person prisoner's dilemmas must be distinguished. In some cases. “no contribution” is the equilibrium regardless of the group size. but increase in the group size makes the equilibrium Pareto-deficient. In other cases, increase in the group size changes the equilibrium from the Pareto-efficient one with N contributors to the deficient one with no contributors.