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Cooperation in evolutionary biology means paying a cost, c, to enjoy benefits, b. A defector is one who does not pay any cost but enjoys the benefits of cooperators. Human societies, especially, have evolved a strategy to discourage defection, punishment. Costly punishment is a type of punishment where an agent in a biological network or some cooperative scheme pays a cost to ensure another agent incurs some cost. A previous study shows how parameters like diversity in neighbors across games, density of connectivity, and costly punishment influence the evolution of cooperation in non-regular networks. In this study, evolution in regular networks due to the influence of costly punishment is also considered, specifically spatial lattices. This study compares observations between non-regular and regular networks as these parameters change and brings a clearer understanding of interactions that occur in these networks. The models, results and analysis bring a new understanding to game theory and punishment. The results show that costly punishment never arises as a sole evolutionary strategy. However, in evolutionary games where costly punishers could evolve more favorable strategies, the initial presence of costly punishers would bring about high average payoffs in all types of regular networks and heterogeneous networks. In regular networks, every node has the same degree, k. Although punishment is conventionally thought to be anti-progressive, in the presence of diversity in neighbors, it magnifies the payoff of a group for all heterogeneous networks. In regular networks however, diversity in neighbors is not required for costly punishment to boost average payoff. This suggests an answer to the question on why costly punishment has been favored by natural selection, which is particularly obvious in human populations.