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ECON 485
Problem Set 3
Note: In one of the first classes, we argued that a strictly dominated strategy can be eliminated from the game. However, we showed this only in the case where the other player was restricted to using pure strategies.
It turns out that even when the other player can play mixed strategies, a player will never want to play a strictly dominated strategy. You can use this result to simplify the games below,but you could try and prove the following in a 3x3 game for your own satisfaction:
If a (pure) strategy of the Row player is strictly dominated when the Column player can only play pure strategies, it is also strictly dominated if the Column player can play mixed strategies.
Use this result in the following even if you cannot prove it!
1. Show that there are no mixed-strategy equilibria in the following games:
(a) Prisoners ’ dilemma
(b)
2. Find all the NE in the following game:
3. Find all the NE in the following game:
