The paper examines the evolutionary foundations of bilateral bargainin
g behavior. Interaction is assumed to be personal, in the sense that a
gents may recognize each others' bargaining strategies. In particular,
the model allows interaction between ''obstinate'' agents, whose dema
nds are independent of the opponent, and ''sophisticated' agents, who
adapt to their opponent's expected play. When the pie's size is certai
n, evolution favors obstinate agents who insist on getting at least ha
lf the pie. The unique outcome is an equal split. In sufficiently nois
y environments, sophisticated behavior appears in equilibrium together
with greedy obstinate behavior. There is then a positive probability
of conflict.