Consider a two-stage game of complete but imperfect information where players 1 and 2 simultaneously choose actions a₁ and a₂ in stage 1 and players 3 and 4 simultaneously choose actions a3 and a4 in stage 2. Provide the notation for the Nash equilibrium in stage 2. How come players 1 and 2 can anticipate this outcome in stage 2?

Consider a two-stage game of complete but imperfect information where players 1 and 2 simultaneously choose actions a₁ and a₂ in stage 1 and players 3 and 4 simultaneously choose actions a3 and a4 in stage 2. Provide the notation for the Nash equilibrium in stage 2. How come players 1 and 2 can anticipate this outcome in stage 2?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

See similar textbooks

Similar questions

Game Theory and Strategic Choices – End of Chapter Problem The Old Familiar and The Beehive are the only two bistros in town. Each is trying to decide whether or not it should advertise in the local newspaper. The accompanying payoff table gives their weekly profits under each possible outcome. The Beehive The Beehive does advertise does not advertise The Old Familiar The Old Familiar earns $X in profits. earns $3,500 in profits. The Old Familiar does advertise The Beehive The Beehive earns $Y in profits. earns $2,250 in profits. The Old Familiar The Old Familiar earns $2,000 in profits. earns $2,500 in profits. The Old Familiar does not advertise The Beehive The Beehive earns $4,000 in profits. earns $3,500 in profits. a. Which combination or combinations of X and Y would make a situation in which The Old Familiar does not advertise and The Beehive advertises a Nash equilibrium?
i. ii. QUESTION ONE A. A Nash equilibrium is a strategy profile such that every player's strategy is the best response to all the other players. It requires that each player makes a best response and that expectations regarding the play of other players are correct. Below is the table showing strategies and payoff for Player 1 and Player 2. PLAYER 1 R1 R2 R3 R4 C1 0,7 5,2 7,0 6,6 C2 2,5 3,3 2,5 2,2 PLAYER 2 C3 7,0 5,2 0,7 4,4 CA 6,6 2,2 4,4 10,4 REQUIRED; Transform the normal form game above into an imperfect extensive game form Find the Nash equilibrium for the game above using iterative deletion of strictly dominated strategies. Find the Nash equilibrium using brute force or cell by cell inspection.
1. Consider the game where initially She chooses between "Stay Home" and "Go Out". If She chooses "Stay Home" then She gets 2 and He gets 0. If She chooses "Go Out" then they each simultaneously choose "Movie" or "Concert" where the payoffs are 0,1 or 3 as in the Battle of the Sexes Game. What are the subgame perfect Nash Equilibria of this game ?
Consider the following game : Stag Rabbit Stag 9, 9 0, 8 Rabbit 8, 0 7, 7 The first payoff is that of player 1 and the second that of player 2. a. ) Draw the extensive form of the simultaneous game. Find all the Nash equilibrium. p. Suppose player 1 moves first or we are in a sequential game now. Draw the extensive form in the sequential version. c. What is the subgame perfect Nash Equilibrium (SPNE) in the sequential version? d. ) Explain why it is an SPNE.
Suppose that you are a manager. You are considering whether or not to monitor employees with the payoffs in the normal-form accompanying game. Worker Work Shirk Manager Monitor -1,1 1,-1 Don't Monitor 1,-1 -1,1 Which of the following pairs of strategies constitutes a Nash equilibrium? Multiple Choice Manager monitors and worker shirks. Manager does not monitor and worker works. Manager monitors and worker works. O None of the answers is correct.
5. Consider a simultaneous game in which player A chooses one of two actions (Up or Down), and B chooses one of two actions (Left or Right). The game has the following payoff matrix, where the first payoff in each entry is for A and the second for B.(8 points) B Right Left 3,3 5,1 Down 2,2 4,4 a. Find the Nash equilibrium or equilibria. b. Which player, if any, has a dominant strategy? A Up
Consider the following game. Which one of the following statements is TRUE? 1. There are 8 subgames for this extensive-form game. 2. There are 8 proper subgames for this extensive-form game. 3. There is no Subgame Nash Equilibrium for this game. 4. There exists some Subgame Nash Equilibrium that gives the payoff 7 to Player 1 and 3 to Player 2.
on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.
1.a) If the three executives of a fraudulent organization report nothing to the authorities, each gets a payoff of 100. If at least one of them blows the whistle, then those who reported the fraud get 28, while those who didn’t get -100. Suppose they play a symmetric mixed-strategy Nash equilibrium where each is silent (does not report fraud) with probability p. What is p?A, 0.1B, 0.28C, 0.5D, 0.8 b) In a two-player game, with strategies and (some known and some unknown) payoffs as shown below, suppose a mixed-strategy equilibrium exists where 1 plays C with probability 3/4, and Player 2 randomizes over X, Y, and Z with equal probabilities. What are the pure-strategy equilibria of this game? A, (A, Y) and (B, X)B, (A, Z) and (C, Y)C, (B, X) and (C, X)D, (C, X) and (C, Y)
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.
3. Two individuals are planning to start a business. The earnings from a grocery store business would be $30,000 for each, but the business requires two people (one to watch over the stock and the other to act as a cashier). Each individual could instead start an mpesa business. The take from mpesa business is only $3000 but can be done with one person acting alone. i) Write down the payoff matrix for this game ( ii) Solve the Nash equilibrium
3. Solving for dominant strategies and the Nash equilibrium Suppose Charles and Dina are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Charles chooses Right and Dina chooses Right, Charles will receive a payoff of 3 and Dina will receive a payoff of 8. Dina Left Right Left 3,7 2,6 Charles Right 4,5 3,8 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Charles chooses and Dina chooses