PLEASE HELP ME SOLVE THIS WITH EXPLANATION EXERCISE 5 Consider the Rock-Paper-Sc
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PLEASE HELP ME SOLVE THIS WITH EXPLANATION
EXERCISE 5 Consider the Rock-Paper-Scissors game. Two players simultaneously show to each other either of the three signs. The rules are standard: Paper beats Rock, Rock beats Scissors, and Scissors beat Paper. If both players show the same sing, the game ends in a draw. The winner then receives $1 from the loser and in case of a draw, nobody pays anything to anyone. The players play this game simultaneously and only once. 1. What kind of game is this? What is the set of possible actions for each of the players? 2. Express this game in its normal form (draw the matrix of the game with the payoffs for each outcome assuming that the money the players win corresponds to their utility) 3. Find all Nash equilibria of this game (including those in mixed strategies).Explanation / Answer
1. Rock- Paper - Scissor game is also known as stone paper scissor is a type of hand game that is been usually played by the two members in which each of the player simultenously form one of the three shapes i.e. either rock, paper, or scissor with an outstreched hands.
Now, set possible actions for each player is as follows:
If player one choose rock, the other player should play paper.
If player one choose paper, other player respond with scissors.
If player one choose scissor, other player choose rock.
2, The game in its normal form is shown in the matrix is as below:
PLAYER TWO
PLAYER ONE
ROCK
PAPER
SCISSOR
ROCK
0 0
-1 1
1 -1
PAPER
1 -1
0 0
-1 1
SCISSOR
-1 1
1 -1
0 0
3. Alll the nash equilibria of this game will includes:
If player one choose rock, the player two should also choose rock.
If player one choose paper, the player two should respond with rock (or paper).
If player one choose scissor, player two respond with rock.
Notice that in this case the player playing with the rock is in dominant strategy. So that the equilibrium for this game is unique. And the Nash equilibrium for this is given below:
PLAYER TWO
PLAYER ONE
ROCK
PAPER
SCISSOR
ROCK
0 0
1 -1
1 -1
PAPER
-1 1
0 0
-1 1
SCISSOR
-1 1
1 -1
0 0
PLAYER TWO
PLAYER ONE
ROCK
PAPER
SCISSOR
ROCK
0 0
-1 1
1 -1
PAPER
1 -1
0 0
-1 1
SCISSOR
-1 1
1 -1
0 0
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