ECS1050.06.post

ECS1050.06.post - Unit III: The Evolution of Cooperation...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Unit III: The Evolution of Cooperation Can Selfishness Save the Environment? Repeated Games: the Folk Theorem Evolutionary Games A Tournament How to Promote Cooperation 4/14 7/28 7/9
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Repeated Games Some Questions: What happens when a game is repeated? Can threats and promises about the future influence behavior in the present? Cheap talk Finitely repeated games: Backward induction Indefinitely repeated games: Trigger strategies
Background image of page 2
Can threats and promises about future actions influence behavior in the present? Consider the following game, played 2X : C 3,3 0,5 D 5,0 1,1 Repeated Games C D See Gibbons: 82-104.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Repeated Games Draw the extensive form game: (3,3) (0,5) (5,0) (1,1) 6,6) (3,8) (8,3) (4,4) (3,8)(0,10)(5,5)(1,6)(8,3) (5,5)(10,0) (6,1) (4,4) (1,6) (6,1) (2
Background image of page 4
Repeated Games Now, consider three repeated game strategies: D (ALWAYS DEFECT): Defect on every move. C (ALWAYS COOPERATE): Cooperate on every move. T (TRIGGER): Cooperate on the first move, then cooperate after the other cooperates. If the other defects, then defect forever .
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Repeated Games If the game is played twice, the V(alue) to a player using ALWAYS DEFECT (D) against an opponent using ALWAYS DEFECT(D) is: V (D/D) = 1 + 1 = 2, and so on. . . V (C/C) = 3 + 3 = 6 V (T/T) = 3 + 3 = 6 V (D/C) = 5 + 5 = 10 V (D/T) = 5 + 1 = 6 V (C/D) = 0 + 0 = 0 V (C/T) = 3 + 3 = 6 V (T/D) = 0 + 1 = 1 V (T/C) = 3 + 3 = 6
Background image of page 6
Repeated Games Time average payoffs: n V (D/D) = 1 + 1 + 1 + ... /n = 1 V (C/C) = 3 + 3 + 3 + ... /n = 3 V (T/T) = 3 + 3 + 3 + ... /n = 3 V (D/C) = 5 + 5 + 5 + ... /n = 5 V (D/T) = 5 + 1 + 1 + ... /n = 1 + ε V (C/D) = 0 + 0 + 0 + ... /n = 0 V (C/T) = 3 + 3 + 3 + /n = 3 V (T/D) = 0 + 1 + 1 + ... /n = 1 - ε V (T/C) = 3 + 3 + 3 + ... /n = 3
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Repeated Games Now draw the matrix form of this game: 1x T 3,3 0,5 3,3 C 3,3 0,5 3,3 D 5 ,0 1 ,1 5 ,0 C D T
Background image of page 8
Repeated Games T 3,3 1- ε, 1+ ε 3 ,3 C 3,3 0,5 3 ,3 D 5 ,0 1 ,1 1+ ε ,1- ε C D T If the game is repeated, ALWAYS DEFECT is no longer dominant. Time Average Payoffs
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Repeated Games T 3,3 1- ε, 1+ ε 3 ,3 C 3,3 0,5 3 ,3 D 5 ,0 1 ,1 1+ ε ,1- ε C D T … and TRIGGER achieves “a NE with itself.”
Background image of page 10
Repeated Games Time Average Payoffs T(emptation) > R(eward) > P(unishment)> S(ucker) T R,R P - ε, P + ε R ,R C R,R S,T R ,R D T ,S P ,P P + ε , P - ε C D T
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Discounting The discount parameter , δ , is the weight of the next payoff relative to the current payoff. In a indefinitely repeated game, δ can also be interpreted as the likelihood of the game continuing for another round (so that the expected number of moves per game is 1/(1- δ )). The
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/21/2010 for the course ECON 1050 taught by Professor Neugeboren during the Summer '09 term at Harvard.

Page1 / 40

ECS1050.06.post - Unit III: The Evolution of Cooperation...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online