Kobe Bryant's basketball team the Lakers are have a game on against the Miami heat on Friday. He believes that they will lose the game, so he tells his girlfriend Vanessa to place a bet on the Miami heat. She bets $x, that she will lose if the Lakers win, but will get her original bet back and an extra $mx if the lakers do not win.

Kobe is risk adverse and his receives utility u(w) from wealth w. The lakers will win with probability p, and for him, winning is the same as receiving $W. His girlfriend Vanessa has the exact preferences as Kobe, and places an optimal bet believing that Kobe will try his hardest.

What are all values of m that Kobe has an incentive to purposefully throw his game.