The term used to describe cooperation by competitors who want to achieve a strategic objective is Coopetition.
Coopetition is a corporate philosophy directly borrows on game theory's principles. Coopetition games are statistical models that take into account the manner in which collaboration between rivals may produce synergy.
There are several motivations for rivals for coopetition. It can be a strategy to cut expenses and prevent duplication of work on the most basic level. Collaboration could be the only solution if a project is too large or hazardous for one firm to handle alone. Other times, two parties can exchange talents if one is better at doing A and the other is better at B.
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