Hobby hunter Jack decides what to do the next weekend. He can either stay at home and watch movies (Movies), or call his friend Katherine to go hunting (Hunt). If he stays in, both Jack and Katherine get a payoff of 2. If he decides to hunt, he knows the situation with his friend will resemble a classic stag hunt game with simultaneous moves: Hunting a stag is better than hunting a rabbit, but it only works if they cooperate. The hunting subgame is captured as:     Katherine       Stag Rabbit Jack Stag 3 , 3 0 , 1   Rabbit 1 , 0 1 , 1 Are the Nash Equilibria of the full game credible? Comment on any Nash equilibria of the full game which are not credible. Find all subgame perfect equilibria in pure strategies.

Suppose Antonio and Trinity are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Antonio chooses Up and Trinity chooses Down, Antonio will receive a payoff of 7 and Trinity will receive a payoff of 5. Trinity Up Down Up 4,8 7,5 Antonio Down 3,2 5,6 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses, and Trinity chooses Grade It Now Save & Continue Continue without saving @ 2 F2 #3 80 Q F3 MacBook Air 44 F7 Dll F8 44 F10 74 $ 4 05 Λ & % 5 6 7 8 * 0 Q W E R T Y U 1 A N S X 9 0 -O O D F G H J K L on را H command C > B N M Λ - - P [ H Λ command opti

In 'the dictator' game, one player (the dictator) chooses how to divide a pot of $10 between herself and another player (the recipient). The recipient does not have an opportunity to reject the proposed distribution. As such, if the dictator only cares about how much money she makes, she should keep all $10 for herself and give the recipient nothing. However, when economists conduct experiments with the dictator game, they find that dictators often offer strictly positive amounts to the recipients. Are dictators behaving irrationally in these experiments? Whether you think they are or not, your response should try to provide an explanation for the behavior.

Jane is interested in buying a car from a used car dealer. Her maximum willingness to pay for thecar is 12 ($12,000). Bo, the dealer, is willing to sell the car as long as he receives at least 9($9,000). What is the Nash bargaining solution to this game?

(The Beckhams' dilemma) Victoria and David are husband and wife. They both prefer ciean to dirty house but neither likes to clean the house. Their payoffs are given in the table below. Victoria Clean Don't clean 0,8 Clean 5,5 David Don't clean 8,0 1,1 a) Let say they play the clean house game only once, what is the Nash equilibrium? b) Let say Victoria and David has to decide whether to clean or not every day for indefinite number of days. How grim-trigger strategy will be our subgame perfect Nash equilibrium? In other words, what is the patience rate that ensure Victoria and David maintain the cleanliness of the house?

Part 1 Sam and Ray do not like each other and will be miserable if they attend the same event. Both are going out Friday night to either the bar or a concert; and Sam will publicly tweet where he is going before Ray makes his plans. Each  will get 6 payoff from going to a concert and 2 benefit from going to the bar if the other is not there. If both go to the same venue, they will get a payoff of zero. Write a game tree for this game and find the equilibrium strategy and equilibrium payoffs clearly labeling both. Part 2 Take the game from the question above and switch the order of the decisions. Write a game tree for this game and find the equilibrium strategy and equilibrium payoffs clearly labeling both. Has the equilibrium strategies and payoffs changed from the question above? Explain why.

QUESTION 4 Suppose there are 2 players in a non- cooperative game theory situation. Player A can move Up or Down while Player B can choose Left or Right. The following matrix contains the payoffs that each player receives under 4 scenarios. The first number in each cell refers to the payoffs for Player A. Player A Up Down A. B. C. 10, 60 D. 20, 80 Player B Suppose Player A moves first and Player B moves second. There is one equilibrium, Up, Left Left There is one equilibrium: Down, Right. 50, 90 40, 50 There are two equilibria, (Down, Left) and (Up, Right) Right There is one equilibrium in this game, Up Right

“To be or not to be, that is the question.” Imagine that in answering this question Hamlet had the following data to consider. Hamlet must choose either “To Be” or “Not to Be.” If Hamlet chooses “To Be” then his enemy the King will make a decision to either “Kill” Hamlet or let him “Live.” If Hamlet is killed by the King his payoff in this game is 200 since he will have been killed by the King who is his uncle and who also killed Hamlet’s father, the King’s brother, who was the prior king. If the King decides to let Hamlet Live then Hamlet will be able to avenge his father’s death and his payoff will be +300. Hamlet also considers suicide an option but given the uncertainty of the afterlife if he chooses not to be then his payoff is +100 since his doesn’t what the afterlife holds for one who kills himself. Draw the complete game tree for this situation. Be sure to accurately label the tree and include the payoffs. Assume Hamlet will choose the course of action that offers the highest…

Consider the following static, single-shot game played between two cyclists, Chico and Loco, who find themselves riding towards each other down a narrow lane. Chico wants to pass by safely, and he can only do this by cycling on the opposite side of the lane to Loco. So, he has two options: to cycle on the Right of the lane, or to cycle on the Left. Loco meanwhile is having a bad day and wants to crash into Chico, and the way he can achieve this is by cycling on the same side of the lane as Chico. So again, he has two options: to cycle on the Right of the lane, or to cycle on the Left. He does not care at all about hurting himself if they collide. (c) By constructing the best response lines of both players, identify all Nash equilibrium outcomes in the above game i.e., in pure and mixed strategies. (d) Provide an intuitive interpretation of the equilibrium outcome(s) identified in part (c) above.

Write the game below in normal form and find all Nash equilibria. C 2. Write the game below in normal form and find all Nash equilibria. जल P = 1/1535 Nature ताल P = 1/3 P1 A (3,6) P1 B P2 B C2 P2 Pz Pz (0,3) ✓ (9,0) (3,3) ✓ (0, 6) (-3,3) ✓ (9,6) Х (3,0) (-3, 12)