# SPNE with 3 players in a three

First picture: we always do the roll back scenario, (B,M,F) so Francisco start and 2 > 0 in the last node so therefore he will be in.

And if Franscisco is in, McDonalds at the last node, have to choose to fight or coop, and since 4 > 2, they will coop.

And at McDonalds first node, he will coop since fight will have a payoff of 0.

And first node, Bobs burger, he choose in because if he is out he will get 0.

Is this correct?

And when it comes to this:

We look at player 3's payoff, shown with the highlighted lines.

And then player 2, will choose F since it is his best payoff at that node

And then we look at player 2 again at the second node, he will choose D since it is his best payoff,

And then last, at the first node, player 1, he will choose A since it is his best payoff?

And therefore the correct answer is (A).

Is it right?

• In the second game, why would P2 choose F? P2 gets 1 if he chooses F, but what if he chooses E? Mar 12, 2020 at 6:44
• @HerrK. I think that he should play F because if he chooses E, he will get pay off of 2 or 0.. And if he goes F he would get a pay off of 1 or 5? Mar 12, 2020 at 8:33
• @soetirl: You highlighted the choice of X by P3, meaning that if P3 gets to choose, he will choose X. Now if P2 chooses E, what will happen next? Mar 12, 2020 at 10:54
• @VARulle If P2 chooses E he will get a pay off of 2. But If he P2 choose D he will get a payoff of 3? 3 > 2 :( Mar 12, 2020 at 11:18
• @soetirl: Yes, but I'm talking about P2's second decision node here. If he chooses E, he gets 2. If he instead chooses F, what does he get? So which of the two possible choices at his second node is better, E or F? Mar 12, 2020 at 11:26