Hi , please answer the following questions thanks.

1. Consider the following games, how many strategies (complete plan of action) are available to each player? List all possible strategies for each player. (a) MINERVA a MINERVA E b 'l, 1 ALBUS 5,0 4.4 (I!) ALSO S 2. For games described in question 1, find the rollback equilibrium outcome and optimal strategy for each player. 3. Two players, Amy and Beth, play the following game with a jar containing 100 pennies. The players take turns; Amy goes rst. Each time it is a player's turn, she takes between 1 and 10 pennies out of the jar. The player whose move empties the jar wins. a. If both players play optimally, who will win the game? Does this game have a first-mover advantage? Explain your reasoning. b. What are the optimal strategies? Explain your reasoning. 4. Consider a slight variant to the game in above question. Now the player whose move empties the jar loses. a. Does this game have a rstmover advantage? b. What are the optimal strategies for each player