On Cores of Weakly Balanced Games

A new concept of balancedness for games in normal form is introduced, called weak balanacedness. It is shown that the a-core of a weakly balanced game with an infinite dimensional strategy space and without ordered preferences is nonempty. Using this result we prove core existence theorems for economies (either exchange economies of coalitional production economies) with infinitely many commodities and without ordered preferences, by converting the economy to a game and showing that the derived game is weakly balanced. Surprisingly, no convexity assumption on preferences is needed to demonstrate that the game derived from the economy is weakly balanced.