{":/(*1 +12 1. Consider two individuals {1,2} potentially in conflict with each other. Hence, these individuals may engage in costly actions for grabbing the production of the other or defending what they themselves have produced. Individual {1,2}'s payoff from peace is her income yi > 0, where y > 42. Conflict is initiated if and only if at least one individual prefers so, where for each individual i e{1,2} such preference is determined by the comparison of her income yi with the expected payoff from conflict, denoted by Ti. So, conflict occurs if and only if yi 0 used to mobilise conflict. (You can think of this as how much time and energy the individual spends on competing with the other, or hurting the other etc.) Mobilisation efforts jointly determine the probabilities of winning the conflict, 2/21 +22) if x1 + x2 > 0, Pi(21, 22) = 1/2 otherwise for each i E {1,2}. In the aftermath of the conflict, incomes are scaled down by a factor a (0, 1) due to disruption of economic activity, and the winner gets ay (the share of the larger income) and the loser gets ayz. (You can interpret it as follows: if individual 1 wins the conflict, she gets to keep a fraction of her income while if individual 2 wins the conflict, he swaps positions with individual 1.) Assuming risk neutrality and perfect substitutability of income and effort, indi- vidual i E {1, 2}'s expected payoff from conflict is Thi = -1; + p;ay + (1 - Piay2 (a) Find the optimal level of effort x; for each individual i E {1, 2} in the event of conflict. (b) Using the optimal levels of effort you have found in (a), compute the equi- librium expected payoffs from conflict for each individual. Under which condition does the conflict occur? Interpret the condition. (c) Suppose there is no conflict between the two individuals. How will increas- ing income inequality affect the possibility of conflict