Prisoner's dilemma(pd) of two criminals Cooperator; obey the alliance with another criminal to deny the accusation Defector defect the alliance and admit the accusation C D Not Guilty Guilty C(den)(2,2)(-5,-1) D(a)(,5(3,3 2 Years 5 Years If your opponent plays C: you'd better play D If your opponent plays D: you' d better play D aeaa 5 Years 1 Y 3 Years But Copyright 2005-Investopedia, com CC is better than DD T>R>P>S and R>1/2(S+T) Dilemma: Despite mutual cooperation being the best, individual tends to DD
11 Prisoner’s dilemma (PD) of two criminals C D C(deny) (-2,-2) (-5,-1) D(admit ) (-1,-5) (-3,-3) Cooperator: obey the alliance with another criminal to deny the accusation Defector: defect the alliance and admit the accusation If your opponent plays C: you’d better play D. If your opponent plays D: you’d better play D. But, CC is better than DD Dilemma: Despite mutual cooperation being the best, individual tends to DD. T>R>P>S and R>1/2(S+T) T R P S
PD game and repeated Pd game Two strategies: cooperation, defection Two players Payoff matrix: the payoff to get when a player select a strategy while another player selects one s strategy If two players repeat the Pd game, how to decide his/her strategy at each round?
PD game and repeated PD game • Two strategies: cooperation, defection • Two players • Payoff matrix: the payoff to get when a player select a strategy while another player selects one’s strategy • If two players repeat the PD game, how to decide his/her strategy at each round?
Axelrod’ s tournament Prof Robert Axelrod, Univ. Michigan Ann Arbor 1978. Downing algorithm <Evolution of Cooperation> friedman algorithm The instructions:R=3.P=1.s=0.T=5 Joss algorithm (A)each submitted algorithm would play 200 rounds against each other algorithm, itself and an algorithm that randomly plays cooperate and defect (B)every round of the game have a small probability to stop TFT algorithm is the best
Axelrod’s tournament • Prof. Robert Axelrod, Univ. Michigan Ann Arbor, 1978. • <Evolution of Cooperation> • The instructions: R=3, P=1, S=0, T=5 (A) each submitted algorithm would play 200 rounds against each other algorithm, itself and an algorithm that randomly plays cooperate and defect. (B) every round of the game have a small probability to stop. TFT algorithm is the best. Downing algorithm Friedman algorithm Joss algorithm ……
One may repeat the game as ·ALL-C ALL-D Tit for Tat(tFt) Generous TFT(GTFT) Win-stay, lose-shift (WSLS)
One may repeat the game as • ALL-C • ALL-D • Tit for Tat (TFT) • Generous TFT (GTFT) • Win-stay, lose-shift (WSLS)
Tit-For -Tat TFT: start with a cooperation and then does whatever the opponent did in the previous round (mirror with one round shift) Will not be the top i at every round but will be the wholly Top I with many rounds Flaw: not robust for mistakes and can not correct mistakes TET: CCCDCDCDDD TET: CCCCDCDDDD
Tit-For-Tat • TFT: start with a cooperation and then does whatever the opponent did in the previous round. (mirror with one round shift) • Will not be the Top 1 at every round, but will be the wholly Top 1 with many rounds. • Flaw: not robust for mistakes, and can not correct mistakes