This is the tree: https://i.stack.imgur.com/tqjeG.jpg
I solved for the normal form equilibria: (SS, SS), (SS, SC), (SC, SS), (SC, SC), and (CC, CC)
However, I am not sure how to go about backwards induction.
My specific point of confusion is that if player 1 chooses C, then player 2 can choose S or C and get the same payoff (3).
How does player 1 factor this into his decision making? I'm not sure if the risk of 2 choosing S will make player 1 choose S instead of C, even though C can potentially get him a higher payoff if player 2 chooses C as well.
Since player 2 can choose S or C to receive the same payoff, he will choose the decision which results in a lower payoff for his opponent. As such, player 2 should choose S in order to give player 1 a payoff of 0 rather than 3. Knowing this, player 1 will choose S in his first turn in order to maximize his payoff of getting 1 instead of 3.