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5 6 ABSTRACT. Aspiration-based evolutionary dynamics have recently been 7 used to model the evolution of fair play in the ultimatum game showing that 8 in-credible threats to reject low offers persist in equilibrium. We focus on two 9 extensions of this analysis: we experimentally test whether assumptions 10 about agent motivations (aspiration levels) and the structure of the game 11 (binary strategy space) reflect actual play, and we examine the problematic 12 assumption embedded in the standard replicator dynamic that unhappy 13 agents who switch strategies may return to a rejected strategy without 14 exploring other options. We find that the resulting ‘‘no switchback’’ dynamic 15 predicts the evolution of play better than the standard dynamic and that 16 aspirations are a significant motivator for our participants. In the process, we 17 also construct and analyze a variant of the ultimatum game in which players 18 can adopt conditional (on their induced aspirations) strategies.