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A "properly mixed strategy" means a mixed strategy that does not assign all the probability to one pure strategy. In other words, it is not a pure strategy. Consider a simultaneous move game with the following payoff matrix:
Player 2
L
R
Player 1
A
4, 0
0, 3
B
2.5, 0
C
1, 1
a) Is pure strategy C strictly dominated by any other pure strategy of player 1? If so, write one out. If not, explain.
b) Is pure strategy C strictly dominated by any proper mixed strategy for player 1? If so, write one out. If not, explain.
c) Is pure strategy C a best response to some mixed strategy of player 2? If so, write one out. If not, explain.
Demonstrate mathematically that the equilibrium condition MRS PB PA is the equivalent of the utility-maximizing rule MU AP A MU B PB .
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