Consider the game below.
The goal is to find all pure strategy Nash Equilibria. It's clear to me that D/L results in a Nash Equilibria. However, it's not clear whether or not U/R does the same.
If Player B chooses R, the best response of Player A is U. However, if Player A chooses U, the best response of Player B is either L or R. It's a draw for Player B. Does it still result in a Nash Equilibria?
Update
Additionally, choice L is a dominant strategy for Player B. So, does it make sense talking about Nash Equilibrium for D/R?
Everywhere I have seen it defined (Game Theory by Fudenberg and Tirole, Wikipedia), the definition of a Nash equilibrium allows for equality, so $(U,R)$ is a Nash equilibrium according to these sources.
However, $(U,R)$ is not a strict Nash equilibrium.