I’ve actually done something like that several times. The first time was at work, to raise money for a charity. Their idea was to do a weigh-in once a week, & for everyone to put in a dollar each week, plus an additional dollar from those who’d gained, instead of lost, weight. This was for a period of 6 weeks - the money put in to go to a charity. I took it a step farther, & got some friends & family members to pledge to donate a certain amount for each pound I lost (like a dime or a quarter a pound). At the end of the 6 weeks, I had lost a total of 33 pounds (& got $48 in donations). Everyone else had dropped out after 3 weeks, & had just paid $2 for each remaining week.
A couple of years later, at a different job, 2 of my female co-workers & I decided to have a friendly weight-loss competition. We decided we’d each put in $2 a week, & at the end of 6 weeks there’d be $36 to go to the one who’d lost the most (& of course we had a wkly weigh-in to check our progress). I warned them at the beginning that I would win, & I did. I seem to get quite competitive about this! I lost 30 lbs. that time, they only lost 9 lbs. & 6 lbs.
I did the same thing at another job, 3 yrs. after that, only this time it was with only one other woman, & she insisted we each put in $5 a week (& she knew me & knew how I'd done before). So, after 6 weeks, I had lost 31 lbs., & ended up with the $60. I think she lost about 12 lbs.
So, the competitive thing works for me for losing weight, but not for keeping it off. Each time, the 30-something pounds that I lost, were the same ones I’d lost before & gained back!