Question One Assume a lake has been overrun by algae and two resort owners-Owner One and Owner Two-are considering cleaning up the algae. If they both fail to clean up the algae there is no gain to them in cleaning up the lake and no cost. If the lake is cleaned up then each resort owner gains $400,000. Assume that the total cost of cleaning up the lake is $500,000. Assume both resort owners must decide simultaneously. Finally assume that if both owners agree to clean up the lake that the cost of cleaning up the lake is split equally. Set up the matrix and determine the equilibrium. Question Two Now assume that everything is the same as in Question One except that each resort owner gains $700,000 from cleaning up the lake. Prove that there are two equilibriums. Question Three Assume that the benefit to each resort owner is $700,000. Now assume that we are looking at sequential behavior. One resort owner must make a binding commitment to either clean up the lake or not clean up the lake. Prove that whichever resort owner gets to go first will have an advantage-the resort owner that goes first will be better off than the resort owner that does not go first. (NOTE: you only have to set up the tree for one resort owner because things are symmetrical.) Question Four Consider the equilibrium that you generated in Question Three. Explain why in the real world the resort owner who goes second may decide to 'burn down the house