Consider the following lottery game played by Pam (consider her as player 1) and Dwight (consider him as player 2). They have two boxes and each box has three papers inside. On each paper one of three numbers 3,12 and 24 is written. Pam picks up a paper randomly from one box and Dwight picks up a paper randomly from another box at the same time on the count of 3. Who gets the greater number is the winner of that match. If the numbers are equal, the lottery is declared as a tie. Winner of this game will get 20 Taka from the loser. When a lottery is tie, no money is exchanged. The actions of this game are the number picked by a player and the utility is winning money (+20) or losing money (-20) or nothing (0). Winning of one player means losing of another. For example if in a particular pick up, Pam gets greater number than Dwight then the utility pair for that action pair is (20,-20). Now answer the following questions. 4. Is this a pure competition game, or a pure cooperation game, or a mixed game? Why? 5. Find the best response of Pam given Dwight to is going to pick a. 3 b. 12 C. 24 6. Find the best response of Dwight given Pam is going to pick a. 3 b. 12 c. 24 7. Find the pure strategy Nash Equilibrium of this game, if any.
Consider the following lottery game played by Pam (consider her as player 1) and Dwight (consider him as player 2). They have two boxes and each box has three papers inside. On each paper one of three numbers 3,12 and 24 is written. Pam picks up a paper randomly from one box and Dwight picks up a paper randomly from another box at the same time on the count of 3. Who gets the greater number is the winner of that match. If the numbers are equal, the lottery is declared as a tie. Winner of this game will get 20 Taka from the loser. When a lottery is tie, no money is exchanged. The actions of this game are the number picked by a player and the utility is winning money (+20) or losing money (-20) or nothing (0). Winning of one player means losing of another. For example if in a particular pick up, Pam gets greater number than Dwight then the utility pair for that action pair is (20,-20). Now answer the following questions. 4. Is this a pure competition game, or a pure cooperation game, or a mixed game? Why? 5. Find the best response of Pam given Dwight to is going to pick a. 3 b. 12 C. 24 6. Find the best response of Dwight given Pam is going to pick a. 3 b. 12 c. 24 7. Find the pure strategy Nash Equilibrium of this game, if any.
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 74E: Lottery Powerball is a lottery game that is operated by the Multi-State Lottery Association and is...
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Transcribed Image Text:Consider the following lottery game played by Pam (consider her as player 1) and Dwight (consider him as player 2). They have two boxes and each box
has three papers inside. On each paper one of three numbers 3,12 and 24 is written. Pam picks up a paper randomly from one box and Dwight picks up
a paper randomly from another box at the same time on the count of 3. Who gets the greater number is the winner of that match. If the numbers are
equal, the lottery is declared as a tie.
Winner of this game will get 20 Taka from the loser. When a lottery is tie, no money is exchanged.
The actions of this game are the number picked by a player and the utility is winning money (+20) or losing money (-20) or nothing (0). Winning of
one player means losing of another.
For example if in a particular pick up, Pam gets greater number than Dwight, then the utility pair for that action pair is (20,-20).
Now answer the following questions.
4. Is this a pure competition game, or a pure cooperation game, or a mixed game? Why?
5. Find the best response of Pam given Dwight to is going to pick
а. 3
b. 12
C. 24
6. Find the best response of Dwight given Pam is going to pick
а. 3
b. 12
C. 24
7. Find the pure strategy Nash Equilibrium of this game, if any.
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