A projected gradient dynamical system modeling the dynamics of bargaining

TL;DR

This paper introduces a projected gradient dynamical system model for bargaining, capturing how agents update their beliefs to reach an agreement with minimal deviation, using convex dynamics and Lyapunov methods.

Contribution

It presents a novel dynamical system framework for modeling belief updates in bargaining, ensuring convergence to agreement with minimal belief deviation.

Findings

Model guarantees convergence to agreement

Beliefs evolve under subjective probability updates

Uses convex dynamics and Lyapunov functions for analysis

Abstract

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.