1. Game Theory “Life must be understood backward, but … it must be lived forward.” - Soren Kierkegaard James Bednar

2. Sequential Rationality COMMANDMENT Look forward and reason back. Anticipate what your rivals will do tomorrow in response to your actions today

3. Decision Trees A B 1,01,0 2,1 0,20,2 Sequential games can be represented with decision trees: n s t b Assume that the higher the number, the better.

4. A B 1,01,0 2,1 0,20,2 Assume that the higher the number, the better. n s t b

5. A B 1,01,0 2,1 0,20,2 Assume that the higher the number, the better. n s t b

6. Solving Sequential Games Start with the last move in the game Determine what that player will do Trim the tree This results in a simpler game Repeat the procedure, if necessary

7. David Hume “Your corn is ripe to-day; mine will be so to-morrow. ‘Tis profitable for us both, that I should labour with you to-day and that you should aid me to-morrow. I have no kindness for you, and know you have as little for me. I will not, therefore, take any pains upon your account; and should I labor with you upon my own account, in expectation of a return, I know I shou’d be disappointed, and that I shou’d in vain depend upon your gratitude. Here I leave you to labour alone: You treat me in the same manner. The seasons change; and both of us lose our harvests for want of mutual security.” Treatise on Human Nature

8. Should I help my neighbor? You have to decide first. We’ll call you “A”. You’re trying to decide between “help” and “don’t help” A h ~h

9. Should I help my neighbor? Your neighbor goes second. Call him “B”. He has to decide whether to return the favor. A h ~h B r ~r Now have to add payoffs to the end nodes.

10. Should I help my neighbor? A 1,01,0 0,2 2,12,1 Assume that the higher the number, the better. h ~h B r ~r A = You. B = Your Neighbor. h = Help B with crops. r = Return the favor to A.

11. Solving Sequential Games Start with the last move in the game Determine what that player will do Trim the tree This results in a simpler game Repeat the procedure, if necessary

12. Solving with Rollback A B Assume that the higher the number, the better. h ~h r ~r 1,01,0 0,2 2,12,1

13. Solving with Rollback Assume that the higher the number, the better. A B h ~h r ~r 1,01,0 0,2 2,12,1

14. What would happen if I didn’t use rollback?

15. Reasoning Forward A B Assume that the higher the number, the better. h ~h r ~r 1,01,0 0,2 2,12,1

16. Reasoning Forward A B Assume that the higher the number, the better. h ~h r ~r 1,01,0 0,2 2,12,1

17. Reasoning Forward Assume that the higher the number, the better. A B h ~h r ~r 1,01,0 0,2 2,12,1

18. Compare A B h ~h r ~r Looking Forward and Reasoning Backward A B h ~h r ~r Reasoning Forward 1,01,0 0,2 2,12,1 1,01,0 2,12,1

19. Sequential Rationality COMMANDMENT Look forward and reason back. Anticipate what your rivals will do tomorrow in response to your actions today