Consider a two-person guessing game. Player 1's lower limit is 100, upper limit is 500, and target is 0.5. Player 2's lower limit is 100, upper limit is 900, and target is 1.5. That is, Player 1 wants to guess a number between 100 and 500 that is closest to 0.5x Player 2's guess, and Player 2 wants to guess a number between 100 and 900 that is 1.53: Player 1's guess. Show your work in the answers. 1. 1What is the Nash Equilibrium guess for Player 1'? 2. Consider the Level-k model. Suppose L0 Player 2s randomly guess any number in their range with equal probability. 'What is the L1 guess for Player 1'? 3. 'What is the L2 guess for Player 1? 4. 'What is the L3 guess for Player 1? 5. Consider the Cognitive Hierarchy model instead. Instead of L2 Player ls thinking they are playing against L1 Player 2s only, L2 Player 1s think they are playing against a mixture of L1 and L0 Player 2s; If the ratio of L0 to L1 Player 2s is 1 to 1, what is the L2 guess for Player 1