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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 eA into conict, then the probability of its winning the contest is m' for B, the correSpond- 1+e +6 ' ing probability is en. Thus, group A has an iiahareat advantage in the contest function invtilig grease that even if it invests 6,4 = 0, it has some chance of winning, while B has none if it chooses 83 = O. [In the model done in class, 7 = 0-] Whoever wins the contest 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 11),; per unit of time worked for group A, and ma for group B. (a) Determine the equilibrium of this game. Can it happen that in equilib- rium, group A chooses peace i.e. 6A = 0? What about group B? How does an increase in 7, group A's inherent advantage, impact the total investment in conict eA + 63