The consistency principle and an axiomatization of the -core

This paper examines the -core of strategic games by means of the consistency principle. I provide a new definition of a reduced game for strategic games. And I define consistency (CONS) and two forms of converse consistency (COCONS and COCONS*) under this definition of reduced games. Then I axiomatize the -core for families of strategic games with bounded payoff functions by the axioms CONS, COCONS*, weak Pareto optimality (WPO) and one person rationality (OPR). Furthermore, I show that these four axioms are logically independent. In proving this, I also axiomatize the -individually rational solution by CONS, COCONS and OPR for the same families of games. Here the -individually rational solution is a natural extension of the classical `maximin' solution.