1. Suppose there is a group of individuals, say 11: III] of them, who are being ranked on the basis of their performance. A rank 1 is better than a rank 2, which is better than 3 and so on. If two players get the same rank, say 3, because of equal performanoe, then the next best rank is 5 and so on. It is common knowledge that the innate abilities o,- of the individuals are as follows: vi :- vi+1,but 1.5.4 2 on. That is, the last two candidates in the ranking have the same innate ability That is, player 1 has a higher performance than player 2, player 2 than player 3 and so on, except [for 143 players] player 9 and 1|] have the same abilities. Each player, however, can put in extra effort a at a cost c. If player i puts in this effort and the next better ranked player, i 1, does not, then player i overtakes i 1 in performance. Suppose the cost of eort and the benets are such that there is a net prot from overtaking i 1 but not i 2, that is, going up two ranks involves too high a cost of eort for the resulting benet. If both 1' and i 1 put in effort, then is rank relative to t' 1 does not change, though both performances get better. For the last two players, n 1 and n, if both put in effort (and all players above them put in effort] each maintains rank n 1. If one of them does not, he drops to rank 11. If, say Players 1 and 4 put in effort but Players 2 and 3 do not, Player sl replaces Player 3 in rank but is still below Player 2. A player's payoff is his or her nal mat: based on her performance. Show that each player putting in effort is a Nash equilibrium