Please show all necessary steps

Question 4(10 marks) Two people are fighting over an object and they each have a dollar which can be allocated towards the fight either entirely or partially. They each face the following decision: How much of the dollar to allocate towards the fight and how much of the dollar they should use productively. Person 1 can denote amount x (out of the dollar he has) towards the fight and person 2 can denote the amount y (out of the dollar) towards the fight. Production is determined by the following equation: Output produced= 2-x-y Production is shared according to the following rules: 1. The player who will allocate a larger proportion of the dollar towards the fight will obtain the entire produce and the other player does not get anything. 2. If they allocate equal amounts, the entire produce is split equally amongst them Each player wants to maximize their share of output. Model this as a strategic game and solve for all pure strategy Nash equilibria. What are the payoffs to player 1 and 2 in equilibrium