10. Your little brothers Sonic and Shadow are rolling around at the speed of sound and...

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10. Your little brothers Sonic and Shadow are rolling around at the speed of sound and driving you nuts! You've baked them a lovely emerald shaped cake, but they won't stop fighting over who gets the biggest slice. To settle the dispute, you draw on a time-honored ritual: You ask Sonic to cut the cake, and Shadow to choose which piece he wants. a. Draw the extensive form of this game. Let Sonic's strategies be "Cut Evenly" or "Cut Unevenly"; depending on what's on the platter, Shadow's strategies might include "Take Big Slice," "Take Small Slice," or "Take Equal Slice." Assign payoffs to Sonic and Shadow that grow with the size of the slice they receive. b. Use backward induction to find the equilibrium outcome for this game. Is the equilibrium consistent with your experience? C. After the rules are announced, Shadow says, "It's not fair! I want to be the one who gets to cut the cake, not the one that chooses the slice!" Is Shadow's complaint valid in other words, is there a first-mover advantage in this game? 10. Your little brothers Sonic and Shadow are rolling around at the speed of sound and driving you nuts! You've baked them a lovely emerald shaped cake, but they won't stop fighting over who gets the biggest slice. To settle the dispute, you draw on a time-honored ritual: You ask Sonic to cut the cake, and Shadow to choose which piece he wants. a. Draw the extensive form of this game. Let Sonic's strategies be "Cut Evenly" or "Cut Unevenly"; depending on what's on the platter, Shadow's strategies might include "Take Big Slice," "Take Small Slice," or "Take Equal Slice." Assign payoffs to Sonic and Shadow that grow with the size of the slice they receive. b. Use backward induction to find the equilibrium outcome for this game. Is the equilibrium consistent with your experience? C. After the rules are announced, Shadow says, "It's not fair! I want to be the one who gets to cut the cake, not the one that chooses the slice!" Is Shadow's complaint valid in other words, is there a first-mover advantage in this game?