Emergence of Cooperation in Heterogeneous Population: A Discrete-Time Replicator Dynamics Analysis

The emergence of cooperation is analyzed in heterogeneous populations where individuals can be classified in two groups according to their phenotypic appearance. Phenotype recognition is assumed for all individuals: individuals are able to identify the type of every other individual, but fail to recognize their own type, and thus behave under partial information conditions. The interactions between individuals are described by 2 × 2 symmetric games where individuals can either cooperate or defect. The evolution of such populations is studied in the framework of evolutionary game by means of the replicator dynamics. Overlapping generations are considered, so the replicator equations are formulated in discrete-time form. The well-posedness conditions of the system are derived. Depending on the parameters of the game, a restriction may exist for the generation length. The stability analysis of the dynamical system is carried out and a detailed description of the behavior of trajectories starting from the interior of the state-space is given. We find that, provided the conditions of well-posedness are verified, the linear stability of monomorphic states in the discrete-time replicator coincides with the one of the continuous case. Specific from the discrete-time case, a relaxed restriction for the generation length is derived, for which larger time-steps can be used without compromising the well-posedness of the replicator system.

Intercultural Management and Leadership in the Context of Language Academies

Throughout this undergraduate thesis, a study of intercultural management and leadership will be carried out with a special focus on language academies. We begin by analyzing the importance of cultural values and their effects on the perception of a leader. We then study the role of Strategic Human Resources Management in an intercultural environment. Finally, as an original contribution to this thesis, an investigation is performed that examines three local language academies and their management practices. After reviewing the findings, we hope to propose a sort of ‘best practices’ for language academies that could lead to a more harmonious relationship between teachers and their managers.