Consider a game with two players making sequential decisions, Player 1 going fir
ID: 3149126 • Letter: C
Question
Consider a game with two players making sequential decisions, Player 1 going first and Player 2 going second, with the following Payoff Matrix:
Player 1Player 2
High
Medium
Low
High
0, 1
4, 0
3, 2
Medium
1, 5
2, 3
4, 4
Low
2, 3
3, 1
5, 2
A. Are there any Nash equilibria? If so, what are the strategies and payoffs?
B. If no information is shared, how many information sets do we have? What do we expect to happen? Why?
C. If we have perfect information, how many information sets do we have? What do we expect to happen? Why?
Player 1Player 2
High
Medium
Low
High
0, 1
4, 0
3, 2
Medium
1, 5
2, 3
4, 4
Low
2, 3
3, 1
5, 2
Explanation / Answer
A.There is one Nash equilibria:
{ Medium,Medium),(high,low)}
Player 1 strategy: (high,low)
Player2 strategy :(medium,medium)
B. If no information is shared ,there are 5 information sets .The information will be passed to the player 1 and player to very rarely,without subgames.
C. If we have perfect information , 3 information sets we will have ,and the player1 passes information to player2 frequently with Nash equilibria and moreover
Every node in the set belongs to one player.
If the information set contains more than one node ,the player to the set belongs doesnot know which node is set has been reached.
we expect that
both use the mixed strategy with player 1 and player 2.
both use three aspects (high ,medium,low).
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