Models of international conflict often omit the option of offering rew
ards as a means of exerting influence. The author has developed a revi
sed version of Bueno de Mesquita and Lalman's (1992) international int
eraction game that allows states either to offer rewards or threaten m
ilitary force once they have made political demands and their adversar
y has rejected them. After laying out the game's logic, the author der
ives predictions about the conditions under which war occurs and rewar
ds are offered and accepted with complete information. The costs of us
ing force, relative military capabilities (i.e., the probability of vi
ctory in war), and the value of the rewards drive these predictions. T
he author also relaxes the complete information assumption and shows h
ow uncertainty can affect the choices of both the maker of the demand
and the recipient. Finally, the model is illustrated by applying it to
two crises: the United States-Japan crisis leading to the Pearl Harbo
r attack and the Cuban missile crisis. The variables in the model help
to explain both the outbreak of war in the first case and the avoidan
ce of war in the second.