Fractional punishment with imitate the better dynamic

A Public Goods Game is an experiment widely used in economics to analyze the behavior of individuals when facing the decision to cooperate or not to a common project. The primary barrier to achieving cooperation in a group of individuals is the temptation to act as a free-rider. To mitigate defection, incentives, rewards or punishments, are typically applied. One strategy is to sanction only a subset d of the defectors in the population. This mechanism, known as fractional punishment , reduces the associated costs while effectively promoting cooperation. When the Public Goods Games is applied with an evolutionary perspective to study the frequencies’ behavior evolution in a population, a new element must be taken into account, the dynamic that defines the way in which strategies are reproduced. Replicator dynamics and Imitate the better ar imitative dynamics, where the individual copy an existing strategy, in the other hand, best-reply dynamics optimizes the response with a strategy that may be new. In this ongoing work, we study the fractional punishment with Imitate the better dynamics. While the general behavior is similar, the results show differences in the trajectories near the homogeneous population of cooperators and loners.