Bargaining via Weber's law

TL;DR

This paper introduces a novel bargaining solution based on Weber's law, which models utility perception and leads to a unique, affine-covariant solution that aligns with the Nash solution and explains empirical features of the ultimatum game.

Contribution

It applies Weber's law to bargaining, deriving a new solution method that does not rely on inter-personal utility comparisons and explains empirical observations.

Findings

The solution converges to the Nash solution for susceptible players.

It applies to the ultimatum game, reproducing its empirical features.

The solution is covariant under affine transformations of utilities.

Abstract

We solve the two-player bargaining problem employing Weber's law in psychophysics, which is applied to the perception of utility changes. Using this law, the players define the jointly acceptable range of utilities on the Pareto line, which narrows down the range of possible solutions. Choosing a unique solution can be achieved by applying the Weber approach iteratively. The solution is covariant to independent affine transformations of utilities. We provide a behavioral interpretation of this solution, where the players negotiate via Weber's law. For susceptible players, iterations are unnecessary, so they converge in one stage toward the (axiomatic) asymmetric Nash solution of the bargaining problem, 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. We also show that our solution applies to the ultimatum game (which is not bargaining but still involves offer formation) and leads to an affine-covariant solution of this game that can reproduce its empirical features. Unlike previous solutions (e.g. the one based on fairness), ours does not involve comparing inter-personal utilities and is based on a partial symmetry between the proposer and respondent.