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Sagot :
The Nash equilibrium of the game is $8000 , $6000 (Dresses , shirts). The player 1 chooses dresses & the player 2 chooses shirts .
Give a brief account on Nash Equilibrium.
The most popular technique to determine the outcome of a non-cooperative game involving two or more participants in game theory is the Nash equilibrium, which bears the name of the mathematician John Nash. In a Nash equilibrium, each player is supposed to be aware of the equilibrium strategies of the other players, and changing one's own strategy offers no advantages. The concept of Nash equilibrium has been around since Cournot used it to explain how rival enterprises choose their outputs in 1838.
To solve the question :
Step 1
Player 1 always picks dresses because he has a dominant strategy for them throughout the game. Player 2 has two choices if Player 1 picks dresses. He has the option of receiving $5000 for pants or $6000 for shirts.
He will therefore choose the shirt because it offers a better return. Therefore, the Nash equilibrium will include dresses, shirts, player 1 getting paid $8000, and player 2 getting paid $6000.
Coats and pants would be the strategies if dry cleaners collude.
The downtown cleaners will have the incentive to switch their strategy to dresses .
Step 2
Coats and pants will be the plan if the dry cleaners collude.
As a result, the uptown cleaners will receive a bigger payoff than the Nash equilibrium while the cleaners in the downtown will receive the same payoff as the Nash equilibrium.
Downtown cleaners will be encouraged to switch to dresses since they will benefit more financially from doing so. By upgrading to dresses, they may increase their present strategy's $8000 profit to $9000.
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The complete question is mentioned below :
Two dry cleaners are considering what special offer to do this week. their payoff's in the form of profits are given in the game matrix below.
What is Nash Equilibrium?
O {$8,000 ; $6,000}
O This game has multiple NE
O ($9,000 ; $5,000}
O ($8,000 ; $7,000}
O (dresses; shirts)
O (dresses; pants)
O {$6,000 ; $5,000}
O (coats ; pants)
O (coats ; shirts)
O This game has no NE
If the dry cleaners collude, the strategies would be
O (dresses ; shirts)
O (coats; pants)
O (dresses ; pants)
O (coats ; shirts)
However, even if collusion wasn't illegal, this outcome is not an equilibrium because Downtown Cleaners would have the incentive to switch their strategy to
O coats
O dresses
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