Total tightness implies Nash-solvability for three-person game forms

Abstract

It was recently shown that every totally tight two-person game form is acyclic, dominance-solvable, and hence. Nash-solvable too.

In this paper, we exhibit an example showing that the first two implications fail for the three-person (n = 3) game forms. Yet, we show that the last one (total tightness implies Nash-solvability) still holds for n = 3 leaving the case n > 3 open.

Keywords

• Nash equilibrium
• Nash-solvability
• Totally tight
• Acyclic
• Dominance-solvable game forms