In a two-player zero sum game, the matrix below shows the value to Player 1. Player...
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In a two-player zero sum game, the matrix below shows the value to Player 1. Player 1's strategies are labelled I to VI, where Player 2's strategies are labelled A to F. (i) I II III IV V VI A 13 18 18 11 18 23 B 29 22 22 22 16 22 a B Y C 8 a 13 18 23 21 31 12 19 19 b 29 22 D 12 Show, by eliminating dominated strategies, that the game can be reduced to the following 3 x 3 matrix. [3] 22 22 31 21 14 23 E 16 29 27 21 19 30 c 8 31 19 F 23 31 37 26 28 34 (ii) Explain whether or not this new 3 x 3 matrix has any saddle points. [2] Now consider a randomised strategy for Player 2, denoted X, whereby strategy 'a' is chosen with probability p and strategy 'e' is chosen with probability 1-p, 0<p<1. (iii) Find the range of values for p such that X dominates strategy 'b'. (iv) Solve the game and determine the value to Player 1 given that 'b' is dominated. [3] [3] A bear spread is an option strategy that produces the following payoff graph: (i) Payoff Determine TWO derivative portfolios that could produce the payoff graph above. A butterfly spread is an option strategy that produces the following payoff graph: (ii) Share price at expiry Payoff Share price at expiry [6] Determine how the payoff graph above may be achieved using a portfolio of calls. [5] (iii) Discuss the aims of the two strategies in parts (i) and (ii). [2] In a two-player zero sum game, the matrix below shows the value to Player 1. Player 1's strategies are labelled I to VI, where Player 2's strategies are labelled A to F. (i) I II III IV V VI A 13 18 18 11 18 23 B 29 22 22 22 16 22 a B Y C 8 a 13 18 23 21 31 12 19 19 b 29 22 D 12 Show, by eliminating dominated strategies, that the game can be reduced to the following 3 x 3 matrix. [3] 22 22 31 21 14 23 E 16 29 27 21 19 30 c 8 31 19 F 23 31 37 26 28 34 (ii) Explain whether or not this new 3 x 3 matrix has any saddle points. [2] Now consider a randomised strategy for Player 2, denoted X, whereby strategy 'a' is chosen with probability p and strategy 'e' is chosen with probability 1-p, 0<p<1. (iii) Find the range of values for p such that X dominates strategy 'b'. (iv) Solve the game and determine the value to Player 1 given that 'b' is dominated. [3] [3] A bear spread is an option strategy that produces the following payoff graph: (i) Payoff Determine TWO derivative portfolios that could produce the payoff graph above. A butterfly spread is an option strategy that produces the following payoff graph: (ii) Share price at expiry Payoff Share price at expiry [6] Determine how the payoff graph above may be achieved using a portfolio of calls. [5] (iii) Discuss the aims of the two strategies in parts (i) and (ii). [2]
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TwoPlayer ZeroSum Game Analysis i Eliminating Dominated Strategies We can eliminate dominated strategies in the original matrix by comparing each row Player 1s strategies Strategy II Dominated by Stra... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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