1. Consider the following two-person parlor game, which starts with $ n $ counters on the table in front of the two players. Players 1 and 2 move sequentially, player 1 moving first. When it is his turn to move, a player must remove either 1 or 2 counters from the table. The game ends when all the counters are removed, and the player who moves last wins the game. a) Suppose that $ n = 15 $. Solve the game by backwards induction. (Hint: let $ k $ be the number of counters left on the table. Focus on the winning positions – the value of $ k $ where a player wins – and losing positions for a player. Start with small values of $ k $, i.e., $ k = 1 $ and $ k = 2 $.) b) How would you generalize your answer in (a), so that for any $ n $, you can determine which player wins the game in the backwards induction solution?

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Answered: 1. Consider the following two person…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Consider a new card game between 2 players: Jim (player 1) and Angella (player 2) Jim is dealt two cards : ♡8 and ♠️9 . Angella is also dealt two cards: ♢6 and ♣️6 . Now, each of the players will play 1 card both at the same time. The payoff of Jim is 4 points if he plays a card of opposite color (red/black) than Angella, and otherwise his payoff is 10 points. The payoff of Angella is 3 points if the difference of the already played card numbers is greater than 4, otherwise her payoff is 2 points. 1. Find the Best Responses for Angella.2. Find all the Nash Equilibriums of the game (if any).
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