I need help with problem 2 - problem 3. This is managerial economics game theory.
Homework 2 is due on March 29th, 2018 (at the beginning of class).
If they both go to any event by themselves, they both get 0. Assume they make their decisions simultaneously. Write the game in its normal form representation and find all the Nash equilibria (both in pure and mixed strategies). NE = {Football, Football}, NE = {Opera, Opera}, NE = {Bob: Football = 3/4, Opera = 1/4}.
Now assume the game is played sequentially. Assume Jessica can leave a note on Bob's desk asking him to meet her at the football game or at the opera house. Later, during the outcome in this case? How about if things are reversed and Bob is the one who leaves the note.
Problem III: Consider the following dynamic game: An entrant chooses whether to enter the market or stay out. If he chooses to stay out, he will get $0, while the incumbent gets $20. If he enters the market, the entrant and the incumbent play the following simultaneous pricing game: they both choose whether to price high or low. If they both price low, they each get $5. If they both price high, they each get $10. If one prices low while the other one prices high, the one who prices low gets $15 and the one who prices high gets $0.
a) Find the subgame perfect Nash equilibrium of this game (SPNE = {Enter; Low Low}).
b) Find the equilibrium of a modified game where the entrant's outside option is no longer $0, but $10 (SPNE = {Stay Out; Low Low}).
Problem IV: Write the rock-paper-scissors game in its normal form representation and find its Nash Equilibrium (in mixed strategies, since there is no equilibrium in pure strategies for this game. All probabilities should be 1/3).
Problem V: The US is engaged in a military dispute with North Korea. Model this as a dynamic game with the US being the leader and NK being the follower (NK observes the US action and then acts). The US has the option to attack NK or not to attack NK. After observing the US choice, NK has the option to attack or not. Assume any kind of retaliation infuriates the NK.
