Two players are fighting over some resource worth v. Now, instead of simply choosing whether to play dove or hawk, the players must choose for how long to fight before giving up. Let be the time player 1 devotes to the fight and to be the time player 2 devotes to the fight. Fighting is still costly: fighting costs both players c > 0 per unit of time. The payoffs of the game are thus: -ct1 if ti to -ct2 if to t1 For this problem we will consider that each player can choose a pure strategy, but not a mixed strategy, i.e. players are forbidden to randomize. (a) Often, the easiest way to solve problems with a continuous strategy space, is to solve for players' best response (BR) function. The BR function tells you, for any t ; that the other player chooses, what choice of t; would maximize player i's payoffs? Le. BRi(t_;) = t, where u (t;, t_,) > u(ti, t_;), Vti. Let's solve for player 1's BR function. i. Suppose to t2}