(d) Suppose the game is repeated indefinitely, and each player discounts his/her payoff with a discount factor & € (0,1). Find a subgame perfect equilibrium in which (H,T) and (L,T) are played alternately on the equilibrium path. Compute the discount factor 8 needed for this equilibrium. (e) Suppose the game is repeated indefinitely. Player 1 (the row player) discounts her payoff with a discount factor d₁ € (0,1). Player 2 discounts his payoff with a discount factor d₂ = 0. That is, in any given period, player 2 only cares about his payoff in that period. Can you find a subgame perfect equilibrium in which (H,T) is played in every period on the equilibrium path. If no, explain. If yes, compute the discount factor d₁ needed for this equilibrium.

(d) Suppose the game is repeated indefinitely, and each player discounts his/her payoff with a discount factor & € (0,1). Find a subgame perfect equilibrium in which (H,T) and (L,T) are played alternately on the equilibrium path. Compute the discount factor 8 needed for this equilibrium. (e) Suppose the game is repeated indefinitely. Player 1 (the row player) discounts her payoff with a discount factor d₁ € (0,1). Player 2 discounts his payoff with a discount factor d₂ = 0. That is, in any given period, player 2 only cares about his payoff in that period. Can you find a subgame perfect equilibrium in which (H,T) is played in every period on the equilibrium path. If no, explain. If yes, compute the discount factor d₁ needed for this equilibrium.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter16: Bargaining

Section: Chapter Questions

Problem 3MC

See similar textbooks

Similar questions

Consider the Normal Form Game characterized in the following figure: P1 \ P2 A1 A2 A3 A4 B1 B2 B3 B4 (-1,1) (0,0) (1,-1) (2,0) (-2,-2) (2,7) (-1,-1) (-1,1) (5,7) (3,5) (0,0) (0,8) (0,3) (-1,-1) (10,2) (0,0) Which is the set of rationalizable actions? O (A2, A4)x(B2, B3) O (A1, A2)x(B1, B2, B4) O (A1, A3)x(B1, B4) O (A1, A3, A4}x{B1, B3)
Consider the Normal Form Game characterized in the following figure: P1 \ P2 b1 b2 b3 a1 (1,2) (0,1) (0,3) a2 (3,-1) (1,1) (-1,0) a3 (2,2) (1,-1) (3,0) a4 (-5,1) (-1,0) (-3,-2) a5 (-3,3) (3,0) (2,4) What is the set of actions of player 1? O la 1, a2, a3, a4, a5) O (b1,b2, b3} O {a2, a3, a4) O (bl, b2}
asap
A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?
1.9. What is a mixed strategy in a normal-form game? What is a mixed-strategy Nash equilibrium in a normal-form game?
Consider the following game represented in normal form. Terry and Kerry are roommates who must make decisions about cleaning. Terry's payoff is the fiırst number in each cell and a higher number is a better outcome. Assume that Terry and Kerry make their decisions simultaneously. Kerry Clean Don't clean Terry Clean ( 8, 2 ) ( 3, 5 ) Don't ( 10, 3) ( 4, 1 ) clean The Nash equilibrium of this game is Terry will [ Select ] v and Kerry will [ [ Select ]
Consider the following simultaneous move game: Player 1 U M D Player 2 L 2,10 2,5 8,7 C 5,2 11,8 8,4 R 5,4 2,9 8,3 In the Nash equilibrium of this game, player 1 receives a payoff of ✓ and player 2 receives a payoff of
2. Consider the following two-player game with two players: Adam and Eve. Adam A1 A2 A3 A4 E1 6,3 5, 3 5, 0 2,0 E2 4,4 5, 4 3, 2 2, 3 Eve E3 4, 1 0,2 6, 1 3, 4 E4 3,0 5, 1 4,0 6₂ 1 a. Find the Iterated Elimination of Dominant Strategies Equilibrium for this game. Explain.
Let G₁, G₂ and G3 be the following games. Colin A Rose B A (10,3) (7,5) B (6,6) (8.4) G₁ Rose Rose Colin A B A (4,4) (3,6) B (5,3) (2,7) G3 Colin A B A (5,8) (4,2) B (9,2) (3,5) G₂ Rose and Colin play the following dynamic game with Rose moving first. In her first move, Rose has a choice of either 0 or 3. If she chooses 3, then Rose and Colin play G3 with Colin moving first. If Rose chooses 0 in her first move, then Colin can play either 1 or 2 in his first move. If he plays 1, then Rose and Colin play G₁ with Rose moving first, and if he plays 2, then Rose and Colin play G₂ with Rose moving first. Draw the game tree associated with this game, and find the backwards induction solution.
Consider the following game. Firm 1 can implement one of two actions, A or B. Firm 2 observes the action chosen by Firm 1 and then decides whether to fight it or not. (-10, 20) F2 Fight A Don't fight -(30, 10) Firm 1 (-10, 0) Fight B Don't fight -(20, 15) (a) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses fight if A, and fight if B. • this strategy profile is [Select] (b) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses fight if A, and don't fight if B. • this strategy profile is [Select] O (c) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses don't fight if A and don't fight if B. • this strategy profile is [Select] 00 F2 ()
1. Consider the following normal form game: Player 2 Player 1 U (2,2) (1,6) Find the mixed-strategy Nash equilibrium, supposing that this is a simultaneous non- repeated game.
Consider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Player 2 C D Player 1 A 12,9 3,6 B 6,0 6,9 C D A 0,9 3,6 B 6,0 6,9 Type a Player 1 Prob = 2/3 Type b Player 1 Prob = 1/3 Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.