There are two contending schools of thought on how a victor should tre
at a defeated party after a war or other major dispute. Whereas magnan
imity might quell the desire of the defeated party for revenge, it mig
ht also be instrumental in the defeated party's resurrection. Similarl
y, the defeated party might face the conflicting choices of whether to
cooperate or not cooperate with the victor. These interdependent choi
ces am modeled by a generic 2 x 2 ''magnanimity game'' (MG), which sub
sumes 12 different specific games that might arise in the aftermath of
a war Rational choices in MG are based on two-sided analysis, in whic
h players can think ahead several moves and take account of each other
's preferences Cycling may or may not be permitted, if it is, which pl
ayer possesses ''moving power'' can be critical to the outcome. The an
alysis is illustrated by historical examples from 19th- and 20th-centu
ry wars.