The iterated Prisoner's Dilemma is the standard model for the evolutio
n of cooperative behavior in a community of egoistic agents. Within th
at model, a strategy of ''tit-for-tat'' has established a reputation f
or being particularly robust. Nowak and Sigmund have shown that in a w
orld of imperfect information it is not tit-for-tat that finally trium
phs, however, but ''generous tit-for-tat''-a variant which ''forgives'
' with a probability of 1/3. In the present study, a spatial dimension
is added to the standard model. The surprising result is that generos
ity is favored even more: the optimal strategy in a spatialized Prison
er's Dilemma carries a forgiveness probability of 2/3-twice as generou
s as ''generous tit-for-tat''.