Non-existence results for diagonal transfer continuity, diagonal quasi concavity, better reply security

In this brief note a sufficient condition for a non-existence result of diagonal transfer continuity is presented. It is based on the definition of anti-kernel point for a payoff function. A sufficient condition for better reply security in terms of sup inf property on the aggregate bifunction is presented. Two non-existence results for diagonally quasi concavity based on concepts of corner set with respect to a point are presented. This brief note is included in a richer research-agenda.