# Game theory: SPNE and simultaneous move games, Interpret it in a tree [duplicate]

Question:

And the solution:

It says in the question, that Franco can eat half or almost all. And after that, Francisco can choose to give the whole roll to the ducks or eat the rest of it.

I don't get the matrix in the solution.

• If Bob eats all. We're looking at the top row. And therefore Francisco can choose to accept, or feed the ducks. I don't get it where he can (Accept, Accept).. Like, what. Accept first that Bob eats almost all, and then eat the rest of the whole roll?
• Still on the first row, where Bob eats almost all. (Accept, Feed) does that mean that Francisco accept that Bob eats the whole roll, and then feed the ducks? (*)

Beacuse this is a simultaneous move, which means Bob and Fransicso dosen't know what either the other know.

So if we talk about the first rows in the matrix again, does it mean that - If Bob choose to eat almost all, then Fransicso - whitout knowing Bobs move - that he have to think "ooh I don't know if Bob is gonna acceptet, but if he do I can either choose (Bob eats all => I accept, I eat all) - If Bob eats all, => I accept, I will throw the roll to the ducks.

Is it like that I should think? when it comes to this simultaneous move. And the first list (*) is how I should think if it was a sequential move?

• Do you know what the definition of "strategy" is in these games, particularly in decision trees? Mar 9, 2020 at 14:15
• @Giskard it is a complete action plan that tells the player what to do at all points in the game where they may need to make a decision. That is, a strategy for Francisco must tell him what to do if Bob plays "Almost all" and what to do if Bob plays "Half"? Mar 9, 2020 at 15:11
• So what do you mean by "I don't get it where he can (Accept, Accept)"? Mar 9, 2020 at 15:33
• Your confusion might result from the strange wording of the exercise. This game is really what has been called an ultimatum-minigame. What goes on is that Bob offers a share of the roll to Francisco, either half or almost nothing. Then Francisco either accepts the offer and eats his share, or he rejects the offer, in which case neither of the two gets anything (instead, the whole roll ends up with the ducks). Does this clarify the question? Mar 9, 2020 at 16:49
• So you mean, if I have a cinnamon bun, and I offer to you to take it or not, and if you don't want it. Neither do I get the bun? @VARulle Mar 9, 2020 at 20:18