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Construct a two person game G with finitely many actions for both players with the following properties. (Each part is independent) The game G has

Construct a two person game G with finitely many actions for both players with the following properties. (Each part is independent)

  1. The game G has a pure strategy Nash equilibrium. Increase some of the payoffs of the row-player to get a new game G that has a Nash equilibrium in which the row player payoff is strictly worse. (The payoffs of the column player should not change.)
  2. The game G has a pure strategy Nash equilibrium. Eliminate one of the actions of the row-player to get a new game G that has a Nash equilibrium in which the row player's payoff is strictly better.

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