Multistage and Finitely Repeated games

Question 1

How many strategies does a player have in a game where each player has 2 actions and it is repeated once

Answer 1

1 information set for stage one, 4 different information sets in stage 2, given that there are 4 different outcomes from stage 1. As there are 2 actions, total strategies is 2^5=32.

Question 2

What are requirements to having a non-equilibrium points as part of SPNE?

Answer 2

1) 2 pareto rankable NE in final stage (carrot, stick)

2) A large enough discount factor

Question 3

If a multi-stage game has a unique NE in each stage?

Answer 3

Then it has a unique SPNE