Problem 2. Five political parties, A, 3,0,1), E take part in the following cooperative game. The number of votes controlled by individual parties are a=1+X, b=1+X, c=2+X, d=40+Y, e=40+Y, where X refers to the month of your birth, expressed as a number (i.e. a whole number between 1 and 12), and Y is the day of your birth (Le. a whole number between 1 and 31). Any coalition that controls a majority of the votes will be able to form a government, receiving a payoH of 1. Other coalitions' payoffs are zero. Games and Decisions: Home Assignment Jan Zouhar 3) Write down the characteristic function of the game. 2 points b) Find the core of the game. 3 points c) Calculate the Shapley value of the game. 3 points d) What would be the Shapley value of the game in which the three smaller parties (A, B, and C} merged into a single party? Is it in their interest to merge? 2 points