### Example: Each player has a dominant strategy

Example of dominant strategy ( when each player has a dominant strategy)

Dominant strategy is the strategy that is optimal for the firm irrespective of the behavior of the other firm.

What is the dominant strategy for firm A and firm B?

 Firm B Firm A Start a new campaign Don’t Start Start a new campaign 10,5 15,0 Don’t Start 6,8 10,2

Steps:

1. Study Firm A’s Payoff
2.Find out the maximum payoff from 2 of the strategies, no matter what the other firm does.
3. In above example, firm A earns max when it chooses to advertise.
(15,0) – A will earn 15, if it chooses to advertise and B does not advertise.
(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.
(10,2) – A will earn 10, if it chooses not to advertise and B also does not advertise.
A's maximum payoff = 15 ( and strategy = to adverise)
So, Starting a new campaign is dominant for firm A, whether firm B choses or not choses to advertise.

4. Study Firm B’s Payoff
5.Find out the maximum payoff from 2 of the strategies, no matter what the other firm does.
6. In above example, firm B earns max when it chooses to advertise.
(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 to not to advertise and A advertises.
(10,2) - – Bwill earn 2, if it chooses not to advertise and A also does not advertise.
B's maximum payoff = 8 ( and strategy = to adverise)
So, Starting a new campaign is dominant for firm B, whether firm A choses or not choses to advertise.

7. Both firms have same dominant strategies and both firms will advertise.
And this situation is called Equilibrium in dominant strategies.(ie the outcome of a game in which each firm is doing the best, regardless of what the other person is doing.)

#### 3 comments:

Anonymous said...

this is a very good explanation. thanks

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