While there has been some research that has looked at the ethical behavior of contestants before and during a competition, not much has been written about the behavior of the contestants after a competition.
Amos Schurr at Ben-Gurion University of the Negev and Ilana Ritov at The Hebrew University of Jerusalem looked at such behavior by conducting five experiments which revealed that after a competition has taken place winners behave more dishonestly than competition losers.
Studies one and two demonstrated that winning a competition increased the likelihood of winners to steal money from their counterparts in a subsequent unrelated task. Studies three (a) and three (b) demonstrated that the effect holds only when winning means performing better than others (i.e., determined in reference to others) but not when success is determined by chance or in reference to a personal goal. Finally, study four demonstrates that a possible mechanism underlying the effect was an enhanced sense of entitlement among competition winners.
The authors did note that sometimes a person may have multiple goals, such as winning a competition and setting a personal record. In such cases, the personal record goal may affect future conduct more than beating the opponent in the competition, thus decreasing subsequent ethical misconduct.
The authors concluded that while it is important to acknowledge the value of competition in advancing economic growth, technological progress, wealth creation, social mobility, and greater equality, it is also important to recognize the role of competition in eliciting future unethical behavior. A greater tendency toward such behavior on the part of winners, as their findings indicate, is likely to impede social mobility and equality, exacerbating disparities in society rather than alleviating them.
I think the study suggests the importance of teaching children at a young age that while competing against others is a useful way to measure their progress, it is just as important, if not more, to set personal goals that they would like to achieve in the competition.
It seems such an approach will lead to all of the benefits of competition noted above, but at the same time decrease the likelihood of future unethical behavior if they were to win the competition.
So Vince Lombardi was close to getting it right:
Winning Isn’t the Only Thing, It’s How You Behave Afterwards That Matters.
Borden's Blather 