 This game has four NE: (L, l2, l3), (L, r2, l3), (R, r2, l3) and (R, r2, r3). Consider the fourth of these NE. It arises because when Player I plays R and Player II plays r2, Player III’s entire information set is off the path of play, and it doesn’t matter to the outcome what Player III does. But Player I would not play R if Player III could tell the difference between being at node 13 and being at node 14. The structure of the game incentivizes efforts by Player I to supply Player III with information that would open up her closed information set. Player III should believe this information because the structure of the game shows that Player I has incentive to communicate it truthfully. The game’s solution would then be the SPE of the (now) perfect information game: (L, r2, l3). 