  We propose a projected gradient dynamical system as a model for a bargaining
scheme for an asset for which the two interested agents have personal
valuations which do not initially coincide. The personal valuations are formed
using subjective beliefs concerning the future states of the world and the
reservation prices are calculated using expected utility theory. The agents are
not rigid concerning their subjective probabilities and are willing to update
them under the pressure to reach finally an agreement concerning the asset. The
proposed projected dynamical system, on the space of probability measures,
provides a model for the evolution of the agents beliefs during the bargaining
period and is constructed so that agreement is reached under the minimum
possible deviation of both agents from their initial beliefs. The convergence
results are shown using techniques from convex dynamics and Lyapunov function
theory.
