A mathematical framework for dynamical social interactions with dissimulation

TL;DR

This paper develops a comprehensive mathematical framework to analyze social interactions involving dissimulation and external influences, addressing a gap in existing models by considering honest, persuasive, and conforming agents.

Contribution

It introduces a novel framework that captures dissimulation and externalities in social interactions, analyzing both non-cooperative and cooperative scenarios with theoretical and computational methods.

Findings

Existence and uniqueness of Nash equilibria established.

Identification of optimal strategies within the Pareto front.

Development of numerical algorithms for model assessment.

Abstract

Modeling social interactions is a challenging task that requires flexible frameworks. For instance, dissimulation and externalities are relevant features influencing such systems -- elements that are often neglected in popular models. This paper is devoted to investigating general mathematical frameworks for understanding social situations where agents dissimulate, and may be sensitive to exogenous objective information. Our model comprises a population where the participants can be honest, persuasive, or conforming. Firstly, we consider a non-cooperative setting, where we establish existence, uniqueness and some properties of the Nash equilibria of the game. Secondly, we analyze a cooperative setting, identifying optimal strategies within the Pareto front. In both cases, we develop numerical algorithms allowing us to computationally assess the behavior of our models under various settings.