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QUESTION 3 You won $200M ($200,000,000) playing the lottery. Two charities have approached you for a donation. You summoned the directors of the two charities and informed them that they will play the following sequential game: First, the director of Charity 1 (call her D, ) will make a public request, which can be any integer dollar amount, starting from $1 and up to $200M. Then the director of Charity 2 (call him D, ) - having heard D, 's request - will announce his own request, which, again, can be any integer dollar amount starting from $1 and up to $200M. You inform them that one of your objectives is to punish greed and thus you will proceed as follows: Let d, denote the amount requested by D, and d, the amount requested by D, . If d, > d, then D, - being the greedy one - will get nothing, while D, will be rewarded with two times what he asked for, up to $200M; that is, D, will get min (2d,, 200M} . Symmetrically, if d, 0. Vm -c if she exerts effort The individual has an initial wealth of W and faces a potential loss of /. The probability of her incurring a loss is p, if she exerts effort and p,, if she chooses no effort, with 0