This table shows a game played between two players, A and B. The payoffs are given in the table as (Payoff to A, Payoff to B). B LeftCenterRight Up(8, 4)(4, 10)(6, 6)AMiddle(6, 2)(10, 6)(10, 4) Down(2, 6)(8, 8)(12, 2)Refer to Table 17-16. Which of the following outcomes represents a Nash equilibrium in the game?Group of answer choicesMiddle-CenterDown-CenterUp-LeftMore than one of the above is a Nash equilibrium in this game.
Question
This table shows a game played between two players, A and B. The payoffs are given in the table as (Payoff to A, Payoff to B). B LeftCenterRight Up(8, 4)(4, 10)(6, 6)AMiddle(6, 2)(10, 6)(10, 4) Down(2, 6)(8, 8)(12, 2)Refer to Table 17-16. Which of the following outcomes represents a Nash equilibrium in the game?Group of answer choicesMiddle-CenterDown-CenterUp-LeftMore than one of the above is a Nash equilibrium in this game.
Solution
To find the Nash equilibrium, we need to look for a situation where neither player A nor player B would want to unilaterally change their strategy, given the strategy of the other player.
Let's go through each of the options:
-
Middle-Center: If player A chooses Middle and player B chooses Center, the payoffs are (10, 6). If player A deviates to Up, the payoff becomes (4, 10), which is worse for player A. If player A deviates to Down, the payoff becomes (8, 8), which is also worse for player A. If player B deviates to Left, the payoff becomes (6, 2), which is worse for player B. If player B deviates to Right, the payoff becomes (10, 4), which is also worse for player B. Therefore, Middle-Center is a Nash equilibrium.
-
Down-Center: If player A chooses Down and player B chooses Center, the payoffs are (8, 8). If player A deviates to Up, the payoff becomes (4, 10), which is worse for player A. If player A deviates to Middle, the payoff becomes (10, 6), which is better for player A. Therefore, Down-Center is not a Nash equilibrium.
-
Up-Left: If player A chooses Up and player B chooses Left, the payoffs are (8, 4). If player A deviates to Middle, the payoff becomes (6, 2), which is worse for player A. If player A deviates to Down, the payoff becomes (2, 6), which is also worse for player A. If player B deviates to Center, the payoff becomes (4, 10), which is better for player B. Therefore, Up-Left is not a Nash equilibrium.
So, the only Nash equilibrium in this game is Middle-Center.
Similar Questions
Table 17-16This table shows a game played between two players, A and B. The payoffs are given in the table as (Payoff to A, Payoff to B). B LeftCenterRight Up(8, 4)(4, 10)(6, 6)AMiddle(6, 2)(10, 6)(10, 4) Down(2, 6)(8, 8)(12, 2)Refer to Table 17-16. Which of the following statements is true regarding this game?Group of answer choicesBoth players have a dominant strategy.Neither player has a dominant strategy.A has a dominant strategy, but B does not have a dominant strategy.B has a dominant strategy, but A does not have a dominant strategy.
Find the Nash Equilibrium/ Equilibria of the game below (the first payoff is for player 1): Player 2 Player 1 Left RightUp (30, 40) (25, 30)Down (60, 10) (35, 45) Group of answer choices(Up, Right)(Up, Left)(Down, Right)(Down, Left)None of the other answers are correct
Consider the following game represented in normal form. Terry and Kerry are roommates who must make decisions about cleaning. Terry’s payoff is the first number in each cell and a higher number is a better outcome. Assume that Terry makes his decision first, if so what is the Nash Equilibrium of this game: Kerry CleanDon’t cleanTerryClean( 8, 2 )( 3, 5 )Don’t clean( 10, 3 )( 4, 1 )Group of answer choicesTerry will clean and Kerry will not clean.Terry will not clean and Kerry will not clean.Terry will not clean and Kerry will clean.Terry will clean and Kerry will clean.More information is required to answer this question.
Consider the following game in which Sally can play T or B and John chooses between L or R. Each player makes their choice simultaneously. If Sally chooses T and John chooses L ,Sally gets a payoff of 3 and John has a payoff of 7. If Sally plays T and John R, Sally’s payoff is 2 and John gets 1. If Sally Chooses B and John L, the payoffs are 1 to Sally and 2 to John. Finally, if Sally chooses B and John R, the payoffs are 4 to Sally and 3 to John. What are the Nash equilibria of the game?Group of answer choices(T,R)(B,R)(T,L) and (B,R)(T,L)None of the above
Consider the following game. Player A and B simultaneously choose to work on either Project 1 (P1) or Project 2 (P2). The payoffs are as follows: if both players choose P1 the payoffs are 6 to A and 2 to B; if A chooses P1 and B chooses P2 the payoffs are 0 to each party; likewise, if A chooses P2 and B chooses P1 the payoffs are 0 to each party; and, finally, if A chooses P2 and B P2 the payoffs are 3 to both players. What are all of the Nash equilibria of this game? a. (P1, P1) b. (P1, P1), (P2, P2) c. (P1, P1), (P2, P2) and (Player A plays P1 with probability 1/3, Player B plays P1 with probability 1/2) d. (P1, P1), (P2, P2) and (Player A plays P1 with probability 3/5, Player B plays P1 with probability 1/3) e. (P1, P2), (P2, P2) and (Player A plays P1 with probability 1/2, Player B plays P1 with probability 2/3)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.