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Nash equilibrium and dominant strategies

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 Consider the following strategic form game. 
B            
  sell not sell
A new    3, 1          3, 2 
old      12, 8          1, 3 
 

(a.) Determine whether A and/or B have a dominant strategy.   
(b.) Find any Nash equilibrium.   
(c.) Suppose that B will play sell with probability p and not sell with probability 1‐p.  For what values of p  does it make sense for A to choose new? 

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Solution Summary

Strategic game with explanation of dominant strategy, Nash equilibrium and probability equation is examined. The expert determines whether A and/or B has a dominant strategy.

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Consider the following strategic form game.
B
sell not sell
A new 3, 1 *3, 2*
old *12, 8* 1, 3

To find the dominant strategy, we compare each player's payoffs, given the strategy of the other player. For example, if B chooses "not sell" then A's best option is new. We place and asterisk on this higher payoff. From this we see that ...

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