  We solve the two-player bargaining problem using Weber's law in
psychophysics, which is applied to the perception of utility changes. By
applying this law, one of the players (or both of them) defines lower and upper
utility thresholds, such that once the lower threshold is established,
bargaining continues in the inter-threshold domain where the solutions are
acceptable to both parties. This provides a sequential solution to the
bargaining problem, and it can be implemented iteratively reaching well-defined
outcomes. The solution is Pareto-optimal, symmetric, and is invariant to
affine-transformations of utilities. For susceptible players, iterations are
unnecessary, so they converge in one stage toward the (axiomatic) Nash solution
of the bargaining problem. This situation also accounts for the asymmetric Nash
solution, where the weights of each player are expressed via their Weber
constants. Thus the Nash solution is reached without external arbiters and
without requiring the independence of irrelevant alternatives. For
non-susceptible players our approach leads to different results.
