Consider the following game (anachronistically) called the battle of the sexes. Two brothers, Shahid and Jamil are spending their weekend in Philadelphia, but they have lost communication with each other and Shahid is coming from New York where Jamil is coming from Washington DC. They are trying to find out where they should meet when they arrive in Philadelphia: they want to meet up, and both know that Shahid prefers meeting at Reading Terminal Market (he's a foodie!) and Jamil prefers meeting at the Rocky Steps (he's a movie buff!). Not meeting up though would be the worst outcome as it's the city of brotherly love. Suppose the game is represented by the following payoff matrix with Jamil the row player: Rocky Steps Reading Terminal Market Rocky Steps 2,1 1,2 Reading Terminal Market 0,0 What is the expected value for each player in the mixed strategy Nash equilibria? 4/3 1.5 2 1 1/3 0,0

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Consider the following game (anachronistically) called the battle of the sexes. Two brothers, Shahid
and Jamil are spending their weekend in Philadelphia, but they have lost communication with each
other and Shahid is coming from New York where Jamil is coming from Washington DC. They are
trying to find out where they should meet when they arrive in Philadelphia: they want to meet up,
and both know that Shahid prefers meeting at Reading Terminal Market (he's a foodie!) and Jamil
prefers meeting at the Rocky Steps (he's a movie buff!). Not meeting up though would be the worst
outcome as it's the city of brotherly love. Suppose the game is represented by the following payoff
matrix with Jamil the row player:
Rocky Steps Reading Terminal Market
Rocky Steps
2,1
0,0
Reading Terminal Market 0,0
1,2
What is the expected value for each player in the mixed strategy Nash equilibria?
4/3
1.5
2
1
1/3
Transcribed Image Text:Consider the following game (anachronistically) called the battle of the sexes. Two brothers, Shahid and Jamil are spending their weekend in Philadelphia, but they have lost communication with each other and Shahid is coming from New York where Jamil is coming from Washington DC. They are trying to find out where they should meet when they arrive in Philadelphia: they want to meet up, and both know that Shahid prefers meeting at Reading Terminal Market (he's a foodie!) and Jamil prefers meeting at the Rocky Steps (he's a movie buff!). Not meeting up though would be the worst outcome as it's the city of brotherly love. Suppose the game is represented by the following payoff matrix with Jamil the row player: Rocky Steps Reading Terminal Market Rocky Steps 2,1 0,0 Reading Terminal Market 0,0 1,2 What is the expected value for each player in the mixed strategy Nash equilibria? 4/3 1.5 2 1 1/3
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