Demands and concessions in a multi-stage bargaining process are shaped by the probabilities that each side will prevail in an impasse. Standard game-theoretic predictions are quite sharp: demands are pushed to the precipice with nothing left on the table, but there is no conflict regardless of the degree of power asymmetry. Indeed, there is no delay in reaching an agreement that incorporates the (unrealized) costs of delay and conflict. A laboratory experiment has been used to investigate the effects of power asymmetries on conflict rates in a two-stage bargaining game that is (if necessary) followed by conflict with a random outcome. Observed demands at each stage are significantly correlated with power, as measured by the probability of winning in the event of disagreement. Demand patterns, however, are flatter than theoretical predictions, and conflict occurs in a significant proportion of the interactions, regardless of the degree of the power asymmetry. To address these deviations from the standard game-theoretic predictions, we also estimated a logit quantal response model, which generated the qualitative patterns that are observed in the data. This one-parameter generalization of the Nash equilibrium permits a deconstruction of the strategic incentives that cause demands to be less responsive to power asymmetries than Nash predictions.