Re: Econ assignment question
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I might be way off, but isn't A's utility if he goes 'y' only 5.5, since B is indifferent between his two choices, one of which gives A utility of 4 and one which gives A a utility of 7?
Therefore, since going 'x' has a utility of 6 for A, wouldn't the only equilibrium be AxBz for (6,3,5)?
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For pure strategies, you assume that the indifferent player does one or the other, and then find the equilibrium in accordance with this (so there will be two if B is indifferent between two choices).
If you are allowing mixed (i.e. randomization between choices), then you will have the same two equilibrium as in pure strategies, but they will each apply for a given value of p, where p is the probability B assigns to playing a certain choice. So p is on the interval [0,1] which is subdivided for the two equilibrium.
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