Consider the two player game described by the payoff matrix below. L RU -1,5 2,1D -1,1 1,0How many outcomes survive the iterative elimination of strongly dominated strategies? Write your answer as an integer (e.g. 5). [Note that a strategy profile is an outcome, for example (D,R) is an outcome.]
Question
Consider the two player game described by the payoff matrix below. L RU -1,5 2,1D -1,1 1,0How many outcomes survive the iterative elimination of strongly dominated strategies? Write your answer as an integer (e.g. 5). [Note that a strategy profile is an outcome, for example (D,R) is an outcome.]
Solution
To solve this problem, we need to identify if there are any strongly dominated strategies for each player. A strategy is strongly dominated if there is another strategy that always results in a higher payoff, regardless of what the other player does.
- For Player 1 (the row player), compare the payoffs of strategy U and D:
- Against strategy L of Player 2, U gives -1 and D gives -1. There is no domination here.
- Against strategy R of Player 2, U gives 2 and D gives 1. So, U dominates D.
So, we can eliminate strategy D for Player 1.
- For Player 2 (the column player), compare the payoffs of strategy L and R:
- Against strategy U of Player 1, L gives 5 and R gives 1. So, L dominates R.
- Against strategy D of Player 1, L gives 1 and R gives 0. So, L dominates R.
So, we can eliminate strategy R for Player 2.
After eliminating these strongly dominated strategies, we are left with one outcome: (U,L).
So, the answer is 1.
Similar Questions
Consider the two player game described by the payoff matric below. L R U 3,3 2,4 D 2,3 1,2 After eliminating strongly dominated strategies, how many outcomes are left? Write your answer as an integer (e.g. 5). [Note that a strategy profile is an outcome, for example (D,R) is an outcome.]
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(In this and all other questions in which a game matrix is given, Player 1 chooses the row, Player 2 chooses the column, and if there is a Player 3, she chooses the matrix.) A Bc 2,1 -2,-1d -1,-1 1,3In the 2 player game above, what is Player 1's expected payoff given the mixed strategy profile ((1/4, 3/4), (2/3, 1/3))? Round your answer to two decimal places (e.g. 2.15).
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