We extend public goods game and design transboundary public goods game which players receive more information from the local group, and marginal return per capital (MPCR) is heterogeneous across local groups that high MPCR among local groups and low MPCR among counter groups. We experimentally investigate the relationship between the equilibrium selection and cognitive ability in infinitely repeated transboundary public goods game under the increasing probability of continuations. We also study the relationship between cognitive ability and strategy profile. We use two methods to investigate the types of strategies employed by the subjects: the strategy frequency estimation method and one period ahead strategy method. We find that fully cooperative strategies are mostly lenient and forgiving. We find that subjects with higher cognitive ability tend to be more cooperative, forgiving and lenient when the cooperative strategy is supported as risk dominance. However, we cannot find the same trend among low cognitive ability groups. They behave similarly even the probability of continuations increase. These results show that subjects with high cognitive ability behave according to risk dominance, but not subjects with low cognitive ability.