A Moves First and Can Go L, M or R

Essay

A moves first and can go L, M or R. B moves second and can go R, M or L. If both of them end up at L or at R, A gets $ 1 and B get $ 0. If one ends up at L and the other at R then B gets $ 1 and A gets $ 0. If B ends up in M while A does not, then A gets $ -1 while B gets $ 2. If both of them end up in M then both get $ 0. Show that A has no first mover advantage in this game.B. When it is B's turn to move, she will go M regardless of what A does. Since A knows this, the best she can do is to go M. Hence, A gets $ 0 in this game. There is really no advantage in going first.