Cooperation in spatial public good games depends on the locality effects of game, adaptation, and punishment.

Despite intensive studies on the evolution of cooperation in spatial public goods games, there have been few investigations into locality effects in interaction games, adaptation, and punishment. Here we analyze locality effects using an agent-based model of a regular graph. Our simulation shows that a situation containing a local game, local punishment, and global adaptation leads to the most robustly cooperative regime. Further, we show an interesting feature in local punishment. Previous studies showed that a local game and global adaptation are likely to generate cooperation. However, they did not consider punishment. We show that if local punishment is introduced in spatial public goods games, a situation satisfying either local game or local adaptation is likely to generate cooperation. We thus propose two principles. One is if interactions in games can be restricted locally, it is likely to generate cooperation independent of the interaction situations on punishment and adaptation. The other is if the games must be played globally, a cooperative regime requires both local punishment and local adaptation.