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....

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.

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.