If a player has a dominant strategy in a simultaneous-move game, then she is sure to get her best…

If a player has a dominant strategy in a
simultaneous-move game, then she is sure to get her best possible outcome.” True
or false? Explain and give an example of a game that illustrates your answer.

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An old lady is looking for help crossing the street. Only
one person is needed to help her; if more people help her, this is no better.
You and I are the two people in the vicinity who can help; we have to choose
simultaneously whether to do so. Each of us will get pleasure worth a 3 from
her success (no matter who helps her). But each one who goes to help will bear
a cost of 1, this being the value of our time taken up in helping. If neither
player helps, the payoff for each player is zero. Set this up as a game. Write
the payoff table, and find all pure-strategy Nash equilibria.

 

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