Bargaining results emerge from the interplay of strategic options and social preferences. For every bargaining game, however, the advantage of a player having certain preferences in terms of negotiated equilibrium revenues might differ. We explore the hypothesis that preferences change according to the players' strength combination. Simple 1×1 bargaining experiments from the literature are discussed, and 2×2 as well as 2×3 assignment market experiments with possible renegotiations are investigated. The assumption that players adopt preferences for two to five roles, defined by strength combinations of the two bargainers, explains the experimental results better than individually constant preferences.