Game Theory Caterpillar Game

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Homework Assignment #5 Due Friday, November 4th 1. The following is a version of a famous game known as the “Caterpillar Game” because of the shape of its game tree. In the game, there are two players competing over a prize. Every round, one of the two players gets to decide whether to claim the prize or let it ride. If a player claims the prize, he or she will receive the value of the prize in that round, the other player will receive nothing, and the game will end. If the player chooses to let it ride, the game will move on to the next round and the other player will have the option of claiming the prize or letting it ride. The value of the prize increases every time it is not claimed. In the first round the prize is worth one dollar, and every round afterward the prize increases by one dollar. If no one has claimed the prize by the end of the fourth round, the game ends and both players receive two dollars. a. Put the game into extensive form by drawing a game tree in which the moves available at every decision node are C (claim) and R (let it ride). b. How many information sets does each player have? Is the game one of perfect or imperfect information, why? c. Put the game into normal form. Use the strategy notation from class, reading information sets from top to bottom and left to right. d. Find two ways to put the game back into extensive form by drawing two new, distinct game trees. (Hint: the only way to do this is to represent the game as a dynamic game of imperfect information). e. Solve the game by backward induction. How would the solution differ if the game would only self-terminate with both players splitting the prize at the end of the 100th round (instead of the fourth)? 2. The number of strategies available to a given player in a finite game is always equal to the product of the number of moves available to the player at each of his or her

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