We have collected and analyzed experimental data in two waves (January 2020 and January 2021) at LEEP (Paris, France). We have created four treatments to study unstructured bilateral bargaining.

Our preliminary findings suggest that the amount of information available regarding the opponent's preferences has a significant impact on the bargaining outcome if earnings are deterministic: with full information there is a tendency to equalize monetary earnings, while with partial  information it is simply the number of objects that guides the negotiation. Interestingly,  probabilistic earnings (which are in line with theoretical models) lead to similar outcomes independently of the amount of information. As a consequence, the well-known Nash bargaining solution is a poor predictor in the "full information" + "deterministic earnings" setting (which often appears in empirical work), but performs much better in the other three environments that we have considered. 

An important conclusion of our study is that empirical tests (in the laboratory or outside) of bargaining theory should be carried out under a tight control of the decision-makers'  preferences. Otherwise, bargaining could be happening in units that differ from the theoretical ones and the ones assumed by the experimenter.