In the game "War of attrition NE", three players are fighting for one good worth $v_i$ for each player $v_1>v_2>v_3>0$. Each player decides the time it wants to spend on fighting: $t_1,t_2,t_3$. Until they both fight they loose 1 per time unit. Whoever fights longer than an enemy gets the good they are fighting for (if $t_1=t_2=t_3$ they split equally). Find best response correspondence and find Nash equilibrium.
I know how this works for two players (simply find $u_1(t_1,t_2)$ and $u_2(t_1,t_2)$, combining those two i can easily find best response correspondence ). But how to compute those functions when we have to deal with three players?
Any hints how to construct those functions and/or find Nash equilibrium? Any ideas?
EDIT: question unanswered....