Final answer:
The statement is true; using a competing style in conflict management makes future cooperation more challenging due to decrease in trust. In conflict scenarios like the prisoner's dilemma, rebuilding trust is difficult once one party defects, often necessitating a third party to enforce cooperation and rebuild trust.
Step-by-step explanation:
The statement that once you have used the competing style of managing conflict, it is much more difficult to cooperate with the other is true. The competing style, also known as the win-lose approach, can lead to a decrease in trust and increase in hostility, making future cooperation challenging. In situations such as the prisoner's dilemma, once trust is broken, the parties involved may find it difficult to trust each other again, hence making cooperation even more unlikely. The need for a mediator or a third party becomes crucial to enforce cooperation or to provide sanctions to discourage defection and encourage future cooperation. This is because rebuilding trust is often much harder than losing it, especially in long-standing conflicts.