Hello Tutors.

Please help me with the following questions.

They relate to game theory;

1. A normal form Game is depicted below. Player 1 chooses the row (T or B), Player 2 chooses the column (L.M, or R), and Player 3 chooses the matrix (W,X,Y, or Z). W X L M R L M R T 1,1,10 1,0,10 5,-5,0 T 1,1,-10 1,0,10 5,-5,0 B 0,1,10 0,0,-10 5,-5,0 B 0,1,10 0,0,10 5,-5,0 L M R L M R T 20,15,2 12,20,2 5,-5,40 T 8,8,-20 8,8,-20 5,40,-20 B 16,20,2 20,15,2 5,-5,40 B 8,8,-20 8,8,-20 5,40,-20 Z (a) (5 points) Write a strategic form game tree for this game, and indicate the payoffs on any two terminal nodes of your choice. You don't need to write the payoffs at any other terminal nodes.(h) [5 points] Find utilities that player 1 can get by playing each of his actions are: RT = Ep+12[1p]=12+8p lp+ZU[1p]=2G4p HE (c) (10 points) Find all of the rationalizable strategies in the full 3 player game. Show your reasoning.(a) (REQUIRED; 15 points) If Bob, Sue and May are rational voters with strict preferences given in the table to the right, with top being better, and all this is common knowledge, what outcome do you expect the binary agenda at left to produce? Bob Sue May X1 Xo X3 X3 X2 Xo Strictly Worse X2 X1 X1 XO Xo X3 X23. In this question you are asked to compute the rationalizable strategies in a linear Bertrand-duopoly with discrete prices and fixed "startup" costs. We consider a world where the prices must be an odd multiple of 10 cents, i.e., P = {0.1, 0.3, 0.5, ...,0.1 + 0.2n, ...} is the set of feasible prices. For each price p, the demand is: Q(p) = max {1 - p, 0}. We have two firms / = {1, 2}, each with 0 marginal cost, but each with a fixed "start- up" cost k. That is, if the firm produces a positive amount, it must bear the cost k. If it produces 0, it does not have to pay k. Simultaneously, each firm sets a price p; C P. Observing prices p, and pa, consumers buy from the firm with the lowest price. When prices are equal, they divide the demand equally between the two firms. Each firm i wishes to maximize its profit. p:Q(pi) - k if pi 0) "(PI, P2) = 0 otherwise (a) If k = 0.1 : 1. (5 points) Show that p; = 0.1 is strictly dominated.4. There are three "dates", f = 1, 2,3, and two players: Government and Worker. . At t = 1, Worker expends effort to build K E [0, co) units of capital. . At t = 2, Government sets tax rates Tx ( [0, 1] and 7. E [0, 1] on capital-holdings and on labor income. . At t = 3, Worker chooses effort ez ( [0, co) to produce output Kez. The payoffs of Government and Worker are: UG = TKK + TeKe2 and Uw = (1 -Te)Ke2 + (1 - TK)K - K2/2 - e3/2. (a) (20 points) Solve the game by backwards induction