The table below shows the total suffering given the four possibilities:
Your partner ----------------------- confess not confess Y confess: 10*2+10=30 0+20=20 o u not confess: 2*20+0=40 2*3+3=9So given the probability p of your partner confessing if you confess the expected, or average, amount of suffering would be 30p + 20(1-p)=10p+20. If you don't confess the expected amount of suffering would be 40p + 9(1-p)=31p+9. To find the indifference point equate the two expressions:
10p+20 = 31p+9
11 = 21p
p=11/21 =~ 52.4%.
Thus if you think your partner's probability of confessing is greater than 11/21 you should confess, otherwise you should keep your mouth shut.
Michael Shackleford, A.S.A.