Nash equilibrium(s)

1. Julie and Mark are on a newlyweds game show. They make it to the final round and get to play for the biggest prize. Both of them are given two cards, one that says Paris and one that says Australia. The host of the game show counts to three, at which point both of them has to show one of the cards. If they both choose the same card they get an all expenses paid vacation to the destination on the card. If the choose different cards they walk away with nothing. Julie prefers Paris and Mark prefers Australia. If they go to Paris Julie receives 100 utils and Mark receives 50 utils. If they go to Australia Julie gets 50 utils and Mark gets 100 utils. a. Assuming complete information, represent the game in normal form where the payoffs are in utils. b. What is the Nash equilibrium(s)?
2. Kim and Kanye are playing a single game of Rock-Paper-Scissors. They have complete information. The winner must pay the loser $1,000. If they make the same choice they each get nothing. What is the Nash equilibrium for the game.
3. There is small restaurant operating in the town of Farmingville. The small restaurant currently makes $5,000 in profit and sells only dishes using the local corn. There is a larger restaurant that currently makes $5,000 in profit operating in a nearby city, and also uses only the Farmingville corn.
The larger restaurant is considering opening a new location in Farmingville. If the larger restaurant does open in Farmingville it will make a total profit of $10,000. However, the smaller restaurant will have its profits reduced to $2,000. If the larger restaurant does open in Farmingville the smaller restaurant can choose to shutdown the local corn production leaving both restaurants with $0 in total profit.
a. Represent the game in extensive form. b. What is the subgame perfect Nash equilibrium?

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