The researchers conducted an experiment to see how auctioning the right to play a public goods game affects efficiency. They found that when players were given the right to play, they tended to reach an inefficient outcome. However, auctioning off this right to more players led to a more efficient outcome. Once the best outcome was reached, the auction price increased, ensuring all players benefited from providing the public good. Overall, the full contribution equilibrium was very stable, with players sticking to the best strategy and not affecting the provision of the public good.