# Pure Strategy SPNE

Quick question here:

I am evaluating an extensive-form game with five subgames. Four of the five subgames are easily handled. However, the fifth subgame is making me second guess myself.

My question:

Can there be a pure strategy subgame perfect N.E. in an extensive form game if there is a subgame where a player is indifferent between actions?

So, this fifth subgame is a node followed only by payoffs. The player deciding between playing L and R will generate an equivalent payoff whether he plays L or R. So, he is indifferent. Since this player is indifferent at this node, it makes me think I cannot define a SPNE in pure strategies.

Also, I know that a SPNE in pure strategies must be a backward induction solution. Well, since this node is considered first during backward induction, it seems to nix a backward induction solution to the game.

Is this correct? Can anyone clarify?