b= reward of getting home c= cost(doing the laborious job of shoveling) b>c>0 Player Player b--,b b-c, 2 R S b C 0 (T,s) Sucker payoff
b= reward of getting home c= cost (doing the laborious job of shoveling) b>c>0 Player 1 Player 2 C C , 2 2 c c b − b − ( ) ||| ||| R , R D ( , b b c − ) ( ) ||| ||| T , S D ( , b− c b) ( ) ||| ||| S , T ( , 0 0 ) ( ) ||| ||| P , P Sucker payoff
Player 2 c Player b b-c. b c-2MRb( R b 0 a b>c>0 defines the snowdrift game It follows that T>R>s> P(defines SDG)
Player 2 C C D D ◼ b > c > 0 defines the snowdrift game ▪ It follows that T > R > S > P (defines SDG) , 2 2 c c b − b − ( ) ||| ||| R , R ( , b b c − ) ( ) ||| ||| T , S ( , b− c b) ( ) ||| ||| S , T ( , 0 0 ) ( ) ||| ||| P , P Player 1
a Showing only the payoffs of player 1 Snowdrift Game: T>R>S>P R Prisoner's dilemma T>R>P>S Difficult to measure payoffs accurately SDG is an alternative to pd in studying cooperation in competing populations
◼ Showing only the payoffs of player 1: C C D D R T S P ▪ Snowdrift Game: T > R > S > P ▪ Prisoner’s Dilemma: T > R > P > S Difficult to measure payoffs accurately SDG is an alternative to PD in studying cooperation in competing populations
Often, use one parameter r to represent the payoffs T> R> S P(=0) 1+r 1-r>0 (0≤ cost [larger r(temptation) tends to promote D-character reward SDG 1+r
◼ Often, use one parameter r to represent the payoffs: T > R > S > P ( = 0 ) 1+r > 1 > 1 - r > 0 ( 0 < r < 1 ) cost reward r = C C D D 1 1+r 1-r 0 SDG [larger r (temptation) tends to promote D-character]
C○D○ C switch PC switch=r/2 D switch P D switch C rewire 1-r/2 D rewire D rewe How to assign switching probabilities(CS and DS events)? Dissatisfaction! Doesnt meet expectation, thus rational
PC,switch Nothing happens PD,switch PC,rewire PD,rewire PC,switch=r/2 PD,switch=(1-r)/2 PC,rewire=1-r/2 PD,rewire=(1+r)/2 How to assign switching probabilities (CS and DS events)? Dissatisfaction! Doesn’t meet expectation, thus rational! C D