On the Relation Between Perfect Equilibria in Extensive Form Games and Proper Equilibria in Normal Form Games

This paper examines the question of the extent to which it is true that any equilibrium that is quasi-perfect in any extensive form game having a given normal form is necessarily proper. If one fixes not only the equilibrium in question but also a a sequence of completely mixed strategies converging to that equilibrium then indeed the notions are equivalent. However the stronger result is not true. An example of a normal form game is given in which there is an equilibrium that is quasi-perfect in any extensive form game having a given normal form but not proper.