Bargaining via Weber's law

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.