  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.
