Two old friends plan to meet at a conference in San Francisco, and they agree to

Question

Two old friends plan to meet at a conference in San Francisco, and they agree to meet by “the tower.” After arriving in town, each realizes that there are two natural choices: Sutro Tower or Coit Tower. Not having cell phones, each must choose independently which tower to go to. Each player prefers meeting up to not meeting up, and neither cares where this would happen. Write down the formal description of the game and the normal form representation of the game. Also, find all the best responses and the Nash equilibrium of this game.

Explanation / Answer

Let's assume both players get utility of "x" if they meet up and utility of "y" if they don't meet up

Friend2

Sutro Tower Coir Tower

Friend 1 Sutro Tower (x,x) (y,y)

Coir Tower (y,y) (x,x)

Now we know they prefer meeting up than not meeting up therefore x>y

BR1(Sutro Tower)=Sutro Tower ,BR1(Coir Tower)= Coir Tower

Nash equilibrium is (Sutro,Sutro) and (Coir,Coir)

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