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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.
Why might an oligopoly be reluctant to change its price? When some large firms have high total market share and are non-collusive, there is a strong element of interdependency.
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