2. Consider the same game poker, except that the deck now has aces, kings, and queens. The new matrix is 8 x 8. If you are energetic, write it and solve it by iterated dominance. If you are less energetic, you may take my word that only three strategies for each player need to be considered (the others are dominated): betting (or calling) always, with ace only, or with ace or king only. Write and solve the 3 X 3 matrix. The solution should involve mixed strategies. Interpret the solution as advice to the players.

2. Consider the same game poker, except that the deck now has aces, kings, and queens. The new matrix is 8 x 8. If you are energetic, write it and solve it by iterated dominance. If you are less energetic, you may take my word that only three strategies for each player need to be considered (the others are dominated): betting (or calling) always, with ace only, or with ace or king only. Write and solve the 3 X 3 matrix. The solution should involve mixed strategies. Interpret the solution as advice to the players.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.3P

See similar textbooks

Similar questions

please solve it in 30 minute please Consider an infinitely repeated game where the stage game is the game of chicken: Swerve Straight Swerve 0,0 -1,1 Straight 1, –1 -10, -10 Assume that the discount factor is very close to one. For concreteness, you can assume that d = 0.99. (a) Is there an SPE in which player l's payoff is 1/(1 – 6)? Explain. (b) Is there an SPE in which each player gets a payoff of 0? Explain. (c) Is there an SPE in which player l's payoff is -2/(1 – 8)? Explain.
Game theory Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Player 2 7. Player 1 A B C D -3, -3 0, -11 -4, 3 -11, E 0 -7, -7 -12, 0 (a) Identify any dominated strategies in this game. If there are none, state this clearly. (b) Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly
1. Consider the odds and evens game introduced in Sec. 15.1 (Week 7, second video) and whose payoff table is shown as below. Strategy Player 1 (even player) 1 (finger) 2 (fingers) 1 (finger) Player 2 (odd player) 2 (fingers) 3 -4 −4 3 (a) Show that this game does not have a saddle point. (b) Write an expression for the expected payoff for player 1 (the evens player) in terms of the probabilities of the two players using their respective pure strategies. (c) Show what this expression in part (b) reduces to for the following three cases: (i) Player 2 definitely uses his first strategy, (ii) player 2 definitely uses his second strategy, (iii) player 2 assigns equal probabilities to using his two strategies. (Your answer should be like the bottom table on sec 15.3's notes Page 7: each reduced expression only has x₁.)
6. Players 1 and 2 are leaving the house and need to decide whether or not to bring an umbrella. They know there's a 75% chance that it will rain (thanks AccuWeather). If they don't bring an umbrella and it rains they receive a payoff of -7. If they do bring an umbrella and it rains, they receive a payoff of -4. If it doesn't rain, but they bring an umbrella they receive a payoff of -2. Finally, if it doesn't rain and they don't bring an umbrella they receive a payoff of 2. Player 1 learns the weather before they leave the house, but player 2 does not. Player 2 can, however, observe player 1s choice. (a) Represent this game in the extensive form. i. Use backwards induction to solve for the Nash equilibrium (b) Represent this game in the normal form i. Solve for the Nash equilibrium (c) Are the equilibrium strategy profiles the same in a) and b)? Explain why or why not.
2. Consider the following Bayesian game with two players. Both players move simultaneously and player 1 can choose either H or L, while player 2's options are G, M, and D. With probability 1/2 the payoffs are given by "Game 1" : GMD H 1,2 1,0 1,3 L 2,4 0,0 0,5 and with probability 1/2 the payoffs are according to "Game 2" : G |M|D H 1,2 1,3 1,0 L 2,4 0,5 0,0 (a) Find the Nash Equilibria when neither player knows which game is actually played. (b) Assume now that player 2 knows which one among the two games is actually being played. Check that the game has a unique Bayesian Nash Equilibrium.
QUESTION (1) Consider the following game tree of a two-stage dynamic game. Write the players' information sets and their associated pure strategies. Also, show all the subgames. Find all subgame perfect Nash equilibria of the game. (a) (b) (c) Find all perfect Bayesian equilibria of the two games below by specifying the beliefs. (d) Compare outcomes in (b) and (c). Player 1 + 2 A 3 L Player 2 D U 3 0 R 0 8 0 D Player 2 U 2
1. Each of two players simultaneously announces either Rock, Paper, or Scissors. Paper beats Rock, Rock beats Scissors, and Scissors beats Paper. The player who names the winning object receives $1 from her opponent. If both players make the same choice, no payment is made. Each players's preferences are represented by by the expected amount of money she receives. a) Formulate the situation as a strategic game and find all its mixed strategy equilibria. Make sure that you consider all different supports. b) Find all the mixed strategy equilibria of the modified game in which player 2 is prohibited from announcing Rock.
Consider the following payoff matrix. -1 5 P = 0 -1 (a) Find the optimal mixed row strategy. (b) Find the optimal mixed column strategy. (c) Find the expected value of the game in the event that each player uses his or her optimal mixed strategy. PLease advise with any ideas
Player 1 Cooperate (C) Defect (D) If the game has a dominant strategy, what is it? There is none. If the game has a Nash equilibrium in pure strategies, what is it? There is none. Cooperate (C) 3,3 8,0 Cooperate (C) is a dominant strategy for both players. Defect (D) is a dominant strategy for both players. Cooperate (C) is a dominant strategy for 1, and Defect (D) is a dominant strategy for 2. C, C is the only Nash equilibrium. D, D is the only Nash equilibrium. C, C and D, D are both Nash equilibria. Player 2 Defect (D) 0,8 1,1
E3 Bayesian Game]. Consider a Bayesian game described by a following payoff matrix. Please solve (show your solution). 1. Enumerate all pure strategies for each player. 2. Suppose that player 1 observes his type ?1 = 3. How does player 1 think of the probability of ?2? 3. Find a (pure strategy) Bayesian Nash equilibrium.
38. Consider the following game. There are ten churches in town: nine are Catholic and one is Eastern Orthodox. All churches conduct their divine services at 10am on Sunday morning. You and your friend, without communication, agree to meet at a church service. If you fail to meet at the same church, then you are sad and become a Doomer. What is this game's focal point? Remember that you cannot communicate about this. (A) You meet at any of the Catholic churches. (B) You meet at any of the churches – denomination does not matter. We're all the same bro. (C) You meet at the Orthodox church. (D) There is no focal point. 39. Consider a fractional-reserve banking system in which an initial deposit of $1,000 can generate up to $4,000 in money. What is the reserve ratio? (A) 4 percent. (B) 5 percent. (C) 25 percent. (D) 75 percent.
EXERCISE 3.a. Show that if G; has value v; for i = 1, 2, then their series-sum game has value v₁ + v₂.