Behavioral Traps and the Equilibrium Problem on Hadamard Manifolds

TL;DR

This paper establishes conditions for solving equilibrium problems on Hadamard manifolds, proposes a convergence framework for a proximal point algorithm, and applies it to behavioral traps in human decision-making.

Contribution

It introduces a new convergence analysis framework for equilibrium problems on Hadamard manifolds and applies it to behavioral traps using variational rationality.

Findings

Proposed a sufficient condition for equilibrium solutions on Hadamard manifolds.

Developed a convergence analysis framework for proximal point algorithms.

Applied the framework to behavioral traps in human behavior.

Abstract

In this paper we present a sufficient condition for the existence of a solution for an equilibrium problem on an Hadamard manifold and under suitable assumptions on the sectional curvature, we propose a framework for the convergence analysis of a proximal point algorithm to solve this equilibrium problem in finite time. Finally we offer an application to personal equilibrum problems as behavioral traps problems, using a recent "variational rationality" approach of human behavior.