MATH 331 HOMEWORK 5
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MATH 331 HOMEWORK 5
1. Solve the following 4 × 2 zero-sum game (for player A’s payoffs).
(
4 
).
(Hints: a) eliminate any dominated strategies, b) find the maximin and minimax and
look for a Nash Equilibrium over the pure strategies, and c) if none exists plot the appropriate gain functions and find the maximin (or minimax) as appropriate.)
2. Find the optimal strategies and the values of the following 3 × 3 zero-sum games, with A’s payoffmatrices
i) (
2 
)
ii) ( 5
3 
3)
7 
).
(Hints: a) Check for any dominated strategies, b) check the maximin and minimax are not equal giving a Nash Equilibrium over the pure strategies, c) otherwise solve the primal problem of maximising ∑
=1 
subject to the constraints ∑
=1 
≤ 1 for 
= 1,2 and 3. Make sure all your entries in the matrix are non negative and check all the possible solutions for feasibility - that is 
≥ 0 and that none of the constraints are violated. If you are employing c) there is no need to find player A’s optimum strategy, just player B’s will do.)
2022-03-19