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The stylized facts of ultimatum bargaining in the experimental lab are that offers tend to be near an equal split of the surplus and low, near perfect offers are routinely rejected. Bimmore et al (1995) use aspiration-based evolutionary dynamics to model the evolution of fair play in a binary choice version of this game, and show that incredible threats to reject low offers persist in equilibrium. We focus on two possible extensions of this analysis: (1) the model makes assumptions about agent motivations (aspiration levels) and the structure of the game (binary strategy space) that have not yet been tested experimentally, and (2) the standard dynamic is based on the problematic assumption that unhappy games who switch strategies may end up using the same strategy that was just rejected. To examine the implications of not allowing agents to switch back to their original strategy, we develop a no switchback dynamic and run a new, binary choice, experiment with induced aspirations. We find that the resulting dynamic predicts the evolution of play better than the standard dynamic and that aspirations are a significant motivator for our participants.

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