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mosors Question 2: Nash Equilibrium in Mixed Strategies 2a) Solve for all Nash equilibria in pure and mixed strategies. Include

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, and each player's expected payoff for the mixed strategy equilibrium. \table[[,Player 2,],[,,Left,Right],[Player 1,Up,63,84],[Down,86,52]] 2b) In which of the following games would a Nash equilibrium in mixed strategies exist? Check all that apply:

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Prisoner's Dilemma

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Games with 2 Nash Equilibria in pure strategies

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Leadership Games

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`2\times 2`

game with a dominated strategy by both players

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Battle of the 2 Cultures

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`3\times 3`

game with a dominant strategy by only 1 player

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Chicken Games

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Coordination Games Question 3: Repeated Games 3a) For the following game table, solve for the Nash equilibrium if it is played only once. Then, explain whether the Nash equilibrium would change if it is played exactly three times in a repeated game. Finally, explain how the outcome might change if the game is repeated indefinitely with no known ending. \table[[,,,,],[,,Le,,Righ],[,Up,,5,],[,Down,3,8,5]] 3b) Suppose a tit-for-tat strategy is used in the above game. One player chooses to defect for only one round, and then the other player responds by defecting in the following round, and then cooperation resumes. Based the numbers in the table, explain whether the strategy to defect first and then face one round of retaliation by other player is a worthwhile strategy to pursue by either player.