The emergence of collective cooperation within competitive environments is well-documented in biology, economics, and social systems. Traditional evolutionary game models primarily investigate the evolution of strategies within fixed games, neglecting the simultaneous coevolution of strategies and the environment. Here, we introduce a game selection model where both the strategies employed by agents and the games themselves evolve dynamically through evolutionary processes. Our results demonstrate that these coevolutionary dynamics foster novel collective phenomena, including changed cooperative interactions. When applied to structured populations, the network’s architecture, and agent properties such as risk-aversion and bounded rationality significantly influences outcomes. By exploring the interplay between these factors, our model provides novel insights into the persistent social dilemmas observable in real-world systems.