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    Nash equilibrium and dominant strategies

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     Consider the following strategic form game. 
      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 Preview

    Consider the following strategic form game.
    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 ...

    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.