Best Response and other Alternative Dynamics for Optional Public Goods Games with Punishment

The Optional Public Goods Game has been studied extensively by many works since its conception in the works of C. Hauert in 2002. Some of these have included different ways to punish free-riders and increase cooperation while discussing the costs associated with it [Grau J. 2022, Botta R. 2021], yet a discussion of how different dynamics may affect said results has not been done until now.
This work focuses on implementing the Best Response dynamics applyed to the Optional Public Goods game using fractional punishment to modify the expected payoffs of defectors, similarly to what is implemented in R. Botta's work of 2021.