### Example: one player dominant strategy

We know that the dominant strategy is the strategy that is optimal for the firm irrespective of the behavior of the other firm.
Example of dominant strategy (when Only one player has a dominant strategy)

Steps
1. Study Firm A’s Payoff
2.Find out the maximum payoff from 2 of the strategies
3.Lets see the payoffs
(10,5) – A will earn 10, if it chooses to advertise and B also advertises.
(6.8)- – A will earn 6, if it chooses not to advertise and B advertises.
(15,0) – A will earn 15, if it chooses to advertise and B does not advertise.
(20,2) - – A will earn 20, if it chooses not to advertise and B also does not advertise.
So, here choosing advertise or not to advertise depends on B’s decision. If B decides to advertise, A will choose advertise and if B decides not to advertise, the firm A will also not advertises.
4. So, here Firm A doesn’t have a dominant strategy. Its decision depends on firm B’s decision.
5. Now, Study Firm B’s Payoff
6.Find out the maximum payoff from 2 of the strategies
7. lets study B’s payoffs
(10,5) – B will earn 5, if it chooses to advertise and A also advertises.
(6.8)- – B will earn 8, if it chooses to advertise and A does not advertise.
(15,0) – B will earn 0, if it chooses not to advertise and A advertises.
(20,2) - – B will earn 2, if it chooses not to advertise and A also does not advertise.
8.Here firm B has a dominant startegy. B is earning maximum profits when it chooses to advertise whether A advertises or not.

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