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You and your friend play a game with pennies and nickels. Each of you puts down a coin. If the coins match, you take both,

You and your friend play a game with pennies and nickels. Each of you puts down a coin. If the coins match, you take both, and if they do not match, your friend takes both. Write the payoff matrix for this game. What is your optimal mixed strategy and what is your corresponding expected payoff for this game?

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