Please help me

1. Consider the contest model for conict done in class: two parties, A and B, compete over a prize V. If party A invests time e A into conict, then the probability of its winning the contest is J-L' for B, the correspond- T+8A +68 ' ing probability is . Thus, group A has an inherent advantage in the contest function in the sense that even if it invests e A = 0, it has some chance of winning, while B has none if it chooses eB = 0. [In the model done in class, 7 = 0.] Whoever wins the centest gets access to the entire prize V. Both parties possess 1 unit of time each, which they can split between ghting and working in the market. The latter activity earns a wage an; per unit of time worked for group A, and 103 for group B. (a) Determine the equilibrium of this game. Can it happen that in equilib- rium, group A chooses peace i.e. e A = 0? What about group B? How does an increase in 7, group A's inherent advantage, impact the total investment in conict eA + 63'? (b) Let us return to the model done in class by taking 7 = 0. So far, we fOCussed On a One-shot interactiOn between the two parties and saw that \"peace\" is never an equilibrium of the one-shot game. Suppose the interaction between the two parties is innitely repeated. Each party discounts future payoffs at the rate 5 6 (O, 1). When none of them engage in conict (i.e. 6,4 = e B = 0), then peace reigns, and A gets a share 3 of the prize while B gets share 1 s of the prize. But if either of them deviate from this by choosing even a little bit of conict, they win the prize for this period for sure; but then from next period onwards conict breaks out and they return to the equilibrium of the one-shot game. When can \"peace\" be sustained as an equilibrium of this innitely repeated game? If so, characterize the conditions that .3 must satisfy for this equilibrium. Give the intuition behind these conditions. [In characterizing equitibria for the innitely repeated game, be sane to specify what exactly are the strategies for the two parties]