Question

**Problem 1:**

*For the following, please answer "True" or "False" and
explain why.*

- In simultaneous move game where one player has a dominant strategy, then he is sure that he will get the best possible payoff in a Nash equilibrium.
- In a simultaneous game where both players prefer doing the opposite of what the opponent does, a Nash equilibrium does not exist.
- If neither firm has a dominant strategy, a Nash equilibrium cannot exist.

Answer #1

A.

False

Playing dominant strategy doesnt yield Nash equilibrium. The best
outcome of each player depends on the best response of the other
one.

Nash equilibrium occurs when both players defect. The best solution
is to defect and other player to coperate. But this is not a Nash
Equilibrium.

B. False

In this situation there a two Nash Equilibria.

In each situation player A and Player B doing the opposite strategy
of one another. It is not easy to analyse which equilibrium
situation is achieved without the cooperative moves from
players.

C.

False

If both players have no dominant strategy, still they have
strategy that can attain nash equilibrium. When both firms played
the same strategy without cooperation, a Nash equilibrium can
exist.

Any dominant strategy can always be nash equilibrium but not all
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Column
L
M
N
P
Row
U
(1,1)
(2,2)
(3,4)
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D
(2,5)
(3,3)
(1,2)
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