# Two person cooperative non-zero sum game

This a two person cooperative non-zero sum game. The shaded area is the negotiation set. $s_a$ and $s_b$ are the security levels for $A$ and $B$ respectively. I do not understand the part I have highighted in green.

$B$ can ensure a payoff of $8$ for herself by defecting. Thus any cooperative solution must yield a payoff of at least $8$ for $B$. The line connecting $(36,36)$ and $(39,0)$ represents the expected payoffs if $B$ cooperates and $A$'s strategy is a mixture of the two options. Since $B$ will not cooperate unless her expected payoff is at least $8$, $A$ cannot expect to get more than his expected payoff at the rightmost point that lies above $y=8$. This is $M'$. The same argument holds analogously with roles reversed.