Game Theoretical Formulations of The Olson Problem*

Abstract

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.