How do I solve this Game Theory Bargaining problem?
So, we have to solve this game by Backward induction. We know if $P_1$ rejects the offer at the end note, both will get $P_1=P_2=\delta $. So, to make $P_1$ better off and make the proposal accepted,$P_2$ will offer $P_1$ an amount of $(\delta +\epsilon ) $, where $\epsilon \rightarrow 0$.(I'm considering the case of continuous prices or you can think of a $\epsilon =0.001$ i.e. a very small amount which just makes the $P_1$ strictly better off in accepting the proposal. So, $P_2$ will get $3\delta -(\delta +\epsilon )$ or $3\delta -\delta +0.001=2\delta +0.001$. Now, $P_1$ knows that if $P_1$ offers any amount $&lt; 2\delta +\epsilon $( strictly less than), then $P_2$ will reject the offer. So, to make $P_2$ strictly better off, he'll offer $P_2$ an amount of $(2\delta +\epsilon + \theta )$, where $\epsilon \to 0,\theta \to 0 $ i.e. infinitesimal changes such as $\epsilon =\theta =0.001$. So, $P_1$ will get an amount of $(3-2\delta -\epsilon -\theta )$ where, $\epsilon ,\theta &gt; 0$