a Question 4. (25 pts.) Consider the following normal form game, a shoot-out for a prize of K amounts of consumption goo

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A Question 4 25 Pts Consider The Following Normal Form Game A Shoot Out For A Prize Of K Amounts Of Consumption Goo 1 (59.32 KiB) Viewed 31 times

a Question 4. (25 pts.) Consider the following normal form game, a shoot-out for a prize of K amounts of consumption good (where K stands for kapital). There are N > 2 players, each of whom has a gun а with only one bullet. Each of the players decides whom to shoot if they choose to do so. (The shot agent leaves the game with certainty.) A player has the option to shoot any one of the other players, himself, and nobody at all. An agent wants to survive but gets more utility when the number of survivors gets smaller. This is captured by the following model for preferences. Each player gets a utility of zero if that player is shot by somebody (including himself). Meanwhile, if he is one of the s < N survivors, then he gets a utility of a. (10 pts.) Formulate this situation as a normal form game and provide its formal definition. b. (5 pts.) Consider a player who is shooting himself. Is that action weakly dominated for that player? Justify your answer by explaining your reasoning regardless of your affirmative or negative answer. c. (10 pts.) Suppose N = 3 and K = 12. Formulate this situation using a matrix form game.