A note on tight extensive game forms

Associated with each extensive game form are the α- and β-effectivity functions,E _α andE _β. These functions characterize the effective capabilities which coalitions command under pessimistic and optimistic cooperative behavior respectively. A game form is said to be tight whenE _α ≡E _β, in which case pessimistic, optimistic, and intermediate types of behavior all support the same effective power. Dalkey's condition for Nash consistency, essentially perfect information, is found to be a necessary and sufficient condition for a game form to be tight.