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Consider the game below.

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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?

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  • $\begingroup$ Another similar question is whether $L$ dominates $R$ (weakly yes, strictly no). Player B's best strategy is to destroy the $R$ option and let Player A see this $\endgroup$ – Henry Sep 27 '17 at 14:16
  • $\begingroup$ I did not realize the dominant strategy L for Player B. Thanks for pointing that out! $\endgroup$ – André Gomes Sep 27 '17 at 15:05
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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.

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