9. Consider the following parlor game to be played between two players. Each player begins with three chips: one red, one white, and one blue. Each chip can be used only once. To begin, each player selects one of her chips and places it on the table, concealed. Both players then uncover the chips and determine the payoff to the winning player. In particular, if both players play the same kind of chip, it is a draw; otherwise, the following table indicates the winner and how much she receives from the other player. Next, each player selects one of her two remaining chips and repeats the procedure, resulting in another payoff according to the following table. Finally, each player plays her one remaining chip, resulting in the third and final payoff. Winning Chip Red beats white White beats blue Blue beats red Matching colors Payoff ($) 90 70 50 0 Formulate this problem as a two-person, zero-sum game by constructing a payoff table for Player 1. Do not need to solve this problem.

9. Consider the following parlor game to be played between two players. Each player begins with three chips: one red, one white, and one blue. Each chip can be used only once. To begin, each player selects one of her chips and places it on the table, concealed. Both players then uncover the chips and determine the payoff to the winning player. In particular, if both players play the same kind of chip, it is a draw; otherwise, the following table indicates the winner and how much she receives from the other player. Next, each player selects one of her two remaining chips and repeats the procedure, resulting in another payoff according to the following table. Finally, each player plays her one remaining chip, resulting in the third and final payoff. Winning Chip Red beats white White beats blue Blue beats red Matching colors Payoff ($) 90 70 50 0 Formulate this problem as a two-person, zero-sum game by constructing a payoff table for Player 1. Do not need to solve this problem.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

7. Solving for dominant strategies and the Nash equilibrium Suppose Carlos and Deborah 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 Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 5 and Deborah will receive a payoff of 1. Carlos Deborah Left Left 4,4 Right 2,4 Right 6,7 5,1 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses and Deborah chooses
5
2. Consider the two-player strategic form game represented in the following payoff table: t 1 m b 7,2 1,2 3,7 2 M 2,4 3,4 1,6 R 1,3 7,1 4,2 Player 1 chooses between rows, S₁ = {t, m, b), and receives the first listed payoff in each cell. Player 2 chooses between columns, S₂ = {L, M, R), and receives the second listed payoff in each cell. a. Does either player have a strictly dominant strategy? Explain. b. Explaining your steps carefully, identify the set of rationalizable strategies in this game. c. Making sure to explain your solution method, solve for all pure strategy Nash equilibria in this game.
The options for the last 3 fill-in-the-blanks are "Up" or "Down." Thank you!
None
8.8
Once again, two ice cream truck vendors, A and B, are playing a simultaneous pricing game. If only one of the vendors prices low, he gets all the customers for a payoff of 12, while the other vendor gets no customers and a payoff of zero. If both vendors price high, they each get a payoff of 6. If both price low, they each get a payoff of 5. Suppose that the above game is repeated indefinitely, and together the vendors adopt a trigger strategy such that they would start charging the low price only if the other vendor charged a low price last time. Provided that the vendors stick to their new strategy, what would be the Nash equilibrium going forward? a) Both the vendors price high b) Both the vendors price low c) Vendor A prices high, vendor B prices low d) Vendor B prices high, vendor A prices low
Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain two units of utility from a vote for their positions (and lose two units of utility from a vote against their positions). However, the bother of actually voting costs each one unit of utility. Diagram a game in which they choose whether to vote or not to vote.
2. Consider the following "centipede game." The game starts with player 1 choosing be- tween terminate (T) and continue (C). If player 1 chooses C, the game proceeds with player 2 choosing between terminate (t) and continue (c). The two players choose be- tween terminate and continue in turn if the other player chooses continue until the terminal nodes with (player l's payoff, player 2's payoff) are reached as shown below. TTTT Player 1 Player 2 Player 1 Player 2 (3, 3) t (1, 1) (0, 3) (2, 2) (1, 4) (a) List all possible strategies of each player. (b) Transform the game tree into a normal-form matrix representation. (c) Find all pure-strategy Nash equilibria. (d) Find the unique pure-strategy subgame-perfect equilibrium.
Please help with #1
Please help with #2
Keith and Blake play a simultaneous one-shot game. Keith chooses between Top and Bottom, whereas Blake chooses between left and right. Payoffs are given by (Keith's payoffs are listed first and Blake's payoffs second): Top+left: 3,-6. Top+right:0,-7 Bottom+left:4,0. Bottom+right:-2,6. In a mixed strategy equilibria, Keith will play Top with what probability? 1. 6/7 2. 1/4 3. 1/2 4. 1/7 5. 0 6. 3/4