- The experimental evidence on the “endowment effect” [Kahneman et al., J. Polit. Economy 98 (1990) 1325–1348] and the “self serving bias” in negotiations [Babcok and Loewenstein, J. Econ. Perspect. 11 (1997) 1337–1343] suggests that individuals enter a tough state of mind when they have to make a stand vis-a-vis somebody else. In this work we show how a toughness bias in bargaining may indeed be evolutionary viable. When the inherent toughness of the bargainer is observed by the opponent, this opponent will adjust his behavior accordingly, in a way which may enhance the actual payoff of the biased bargainer. Suppose, then, that a population consists initially of individuals with different inherent degrees of toughness or softness. They are often matched at random to bargain, and biases which are objectively more successful tend to appear more frequently in the society. We characterize a salient class of bargaining mechanisms under which the population will consist, asymptotically, of individuals with some moderate degree of toughness.