Strongly consistent game forms

This paper characterizes strongly consistent game forms in terms of power structure and cardinality (i.e. the number of persons, alternatives or strategies). There are three main new results in this paper. First, I give a necessary condition for a game form to be strongly consistent; it is also sufficient in several cases. Second, from the view point of informational requirements and based on the first result, I give a sharp lower bound on the cardinality of each agent's strategy space, for a game form to be strongly consistent and individually rational. Third, I show that the unanimous rule is the unique game form that attains this lower bound for strong implementation of the individually rational Pareto correspondence.