You searched for: “vied
vie (VIGH) (verb), vies; vied; vying
1. To compete; to strive for superiority; to put forth great effort to outdo others: Playing their hardest, the two teams vied for the championship.

These students are always vying for the highest grades.

2. Etymology: from Old French envier, "to invite, to challenge."
This entry is located in the following unit: English Words in Action, Group V (page 1)