What do researchers say about the relation between a firm's productivity and exposure to global competition?

The thing that researchers have to say about the relation between a firm's productivity and exposure to global competition is that they had found out that sports is the best comparison of global competitiveness since from their observation, the firms or companies that were exposed to fierce global competition are inclined to be more productive than those who are not because just like in sports, you get better if you play against people who are much better than you.