Consider the p-beauty contest game. a group of people wrote down a number between 1 and 100. 2/3rd of the average of all the numbers was calculated. Whoever's answer was closest to the value wins. (a)...

Extracted text: Consider the p-beauty contest game. a group of people wrote down a number between 1 and 100. 2/3rd of the average of all the numbers was calculated. Whoever's answer was closest to the value wins. (a) Write down a game representing this situation. You will have to make some assumptions about the utility of the players. Make sure you state your assumptions explicitly. (b) Which actions are strictly dominated? (c) Which actions are weakly dominated? (d) Suppose that Jim is a student in the class. Jim is rational and thinks that all of his classmates are cautious and will not play weakly dominated actions. Based on this information alone, what can you conclude about Jim's choice?