A note on equalized proper equilibria

This short note is devoted to a remark on a refinement of proper equilibria: it considers the possibility of relaxing the assumptions made in Garcia Jurado and Prada Sanchez, where equalized proper equilibria are defined. The authors do not insist on the requirement that players should put exactly the same probability on all strategies which are best reply equivalent for them: in this way they obtain what the authors call quasi-equalized proper equilibria. It is shown that this refinement is an intermediate one between proper and equalized proper equilibria.