Mixed strategy equilibrium for subgame

Question

A game has 3 players and the last player to move is player 3. In determining the subgame perfect equilibrium there is a subgame where player 3 has two choices and for each choice the payoff for that player is 0. The full payoff vectors are [3, 0, 0] and [0, 3, 0]. Are there infinite mixed strategy equilibria for this subgame? If not, what is the equilibrium? What is the expected payoff?

Answer 1

When solving by backwards induction, whenever there is an indifference, that player can play any distribution over their equivalent choices. You will need to solve for the rest of the equilibrium in terms of each distribution they might choose.

This does mean potentially infinitely many equilibria depending on the rest of the game.