## ← 14-14 Tree Question Solution

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Showing Revision 1 created 11/28/2012 by Amara Bot.

1. And the answer is 1 + 1 is 2,
2. and so that's even, so it'd be a positive payoff to E.
3. 1 + 2 is 3, that's odd, so it'd be a -3.
4. Similarly, 2 +1 is 3, which is odd.
5. So, -3, 2 + 2 is 4.
6. That's a positive payoff.
7. Now E is maximizing,
8. so E would prefer 2 here
9. and would prefer 4 here.
10. And now O is minimizing,
11. so O would prefer 2 here.
12. And notice what we've done here is that
13. we're trying to figure out what the utility of the game is
14. to E, and the true game,
15. both players move simultaneously.
16. Over here, we've handicapped E.
17. And over here, we handicapped O.
18. The true value of the game must be somewhere in between there,
19. so we can say that the utility to E must be
20. less than or equal to 2, which is the value here,
21. and greater than or equal to -3, which is the value here.
22. We've narrowed it down to some degree, but we still haven't nailed down
23. exactly what the utility of the game is.