1. The popular British gaming game show Love Island places a group of contestants (dubbed, 'Islanders')...
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1. The popular British gaming game show Love Island places a group of contestants (dubbed, 'Islanders') on an island as they search for "love" and compete for a shot at £50,000. a. In order to remain on the island, contestants must be coupled up with another Islander (i.e., you're kicked off if you end up spending your nights alone). On the first day, Islanders couple up for the first time based on first impressions, but over the duration of the game they are given opportunities to recouple. Consider a couple, Gabby and Marcel. Halfway through the season, Marcel and the other men are moved to a separate mansion with a new set of female contestants, while Gabby and the other women remain at the original villa with a new set of men. Both Gabby and Marcel find new partners during their time apart, but they really miss each other. After a week in their separate houses, Gabby and Marcel are brought back under one roof and must simultaneously choose whether to recouple with their new partner or stay loyal to each other. If Gabby and Marcel both choose each other, they are really happy and also keep their chance at the prize money. On the other hand, if Gabby chooses Marcel but Marcel picks his new partner, Gabby is sent home heartbroken, while Marcel remains in the game. Similarly, if Marcel chooses Gabby and Gabby picks her new partner, Marcel is sent home heartbroken, while Gabby remains on the island. Finally, if they both pick their new partners, they both remain on the island, but their chance at any long-term relationship is dashed. Assume that both Gabby and Marcel most prefer staying together, then staying on the island with someone else, and least prefer being dumped/kicked off the island. Formalize this strategic interaction as a simultaneous game with an appropriate payoff table (ordered payoffs are fine, as in if there are three unique outcomes, assign payoffs of 3>2 > 1). Find all pure strategy Nash equilibria. b. Love Island concludes with a couple voted as the winner by an audience vote. This couple is awarded £50,000-with a catch. Each member of the couple must simultaneously choose whether to split the cash down the middle (both get £25,000) with their partner or steal the entire pot for themselves (leaving their partner with nothing). If both partners select steal, they are each awarded only £1,000. Suppose Gabby and Marcel win the audience vote and are faced with the prize-money scenario. Formalize this strategic interaction as a simultaneous game with an appropriate payoff table based on their monetary. Find all pure strategy Nash equilibria. What common game from class does this represent? c. What strategic action (commitment, threat, or promise) could Gabby take to improve her outcome? Discuss issues surrounding credibility of the action. d. Finally, the above game only considers payoffs as the personal monetary reward each player takes home. Consider the fact that either or both players selecting steal will result in the other partner (or both) feeling betrayed, ending the relationship. Suppose that Gabby and Marcel both consider the loss of their relationship as the equivalent of losing £ A, no matter who ends it. What value of A (if any) would change the outcome of the game by adding a new and/or removing an old pure strategy Nash Equilibrium? 1. The popular British gaming game show Love Island places a group of contestants (dubbed, 'Islanders') on an island as they search for "love" and compete for a shot at £50,000. a. In order to remain on the island, contestants must be coupled up with another Islander (i.e., you're kicked off if you end up spending your nights alone). On the first day, Islanders couple up for the first time based on first impressions, but over the duration of the game they are given opportunities to recouple. Consider a couple, Gabby and Marcel. Halfway through the season, Marcel and the other men are moved to a separate mansion with a new set of female contestants, while Gabby and the other women remain at the original villa with a new set of men. Both Gabby and Marcel find new partners during their time apart, but they really miss each other. After a week in their separate houses, Gabby and Marcel are brought back under one roof and must simultaneously choose whether to recouple with their new partner or stay loyal to each other. If Gabby and Marcel both choose each other, they are really happy and also keep their chance at the prize money. On the other hand, if Gabby chooses Marcel but Marcel picks his new partner, Gabby is sent home heartbroken, while Marcel remains in the game. Similarly, if Marcel chooses Gabby and Gabby picks her new partner, Marcel is sent home heartbroken, while Gabby remains on the island. Finally, if they both pick their new partners, they both remain on the island, but their chance at any long-term relationship is dashed. Assume that both Gabby and Marcel most prefer staying together, then staying on the island with someone else, and least prefer being dumped/kicked off the island. Formalize this strategic interaction as a simultaneous game with an appropriate payoff table (ordered payoffs are fine, as in if there are three unique outcomes, assign payoffs of 3>2 > 1). Find all pure strategy Nash equilibria. b. Love Island concludes with a couple voted as the winner by an audience vote. This couple is awarded £50,000-with a catch. Each member of the couple must simultaneously choose whether to split the cash down the middle (both get £25,000) with their partner or steal the entire pot for themselves (leaving their partner with nothing). If both partners select steal, they are each awarded only £1,000. Suppose Gabby and Marcel win the audience vote and are faced with the prize-money scenario. Formalize this strategic interaction as a simultaneous game with an appropriate payoff table based on their monetary. Find all pure strategy Nash equilibria. What common game from class does this represent? c. What strategic action (commitment, threat, or promise) could Gabby take to improve her outcome? Discuss issues surrounding credibility of the action. d. Finally, the above game only considers payoffs as the personal monetary reward each player takes home. Consider the fact that either or both players selecting steal will result in the other partner (or both) feeling betrayed, ending the relationship. Suppose that Gabby and Marcel both consider the loss of their relationship as the equivalent of losing £ A, no matter who ends it. What value of A (if any) would change the outcome of the game by adding a new and/or removing an old pure strategy Nash Equilibrium?
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1 The game has two pure strategy Nash equilibria Gabby chooses Marcel Marcel chooses Gabby and G... View the full answer
Related Book For
Introduction to Probability and Statistics
ISBN: 978-1133103752
14th edition
Authors: William Mendenhall, Robert Beaver, Barbara Beaver
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