In this common-knowledge, simultaneous move game there are two players. The players have two strategies available, abbreviated as U and D. The payoffs for the strategies are as follows: • If both players select U, they each get a payoff of 0. • If both players select D, they each get a payoff of 0. • If player 1 selects D and player 2 selects U, player 1 gets a payoff of 3 and player 2 gets a payoff of 1. • If player 1 selects U and player 2 selects D, player 1 gets a payoff of 1 and player 2 gets a payoff of 3. The pure Nash equilibria for this game are (D,U) and (U,D) + Let p be the probability Player 1 plays U and let q be the probability Player 2 plays U. In the mixed Nash Equilibriump will be and q will be (Hint: the payoffs in the game are symmetric)
In this common-knowledge, simultaneous move game there are two players. The players have two strategies available, abbreviated as U and D. The payoffs for the strategies are as follows: • If both players select U, they each get a payoff of 0. • If both players select D, they each get a payoff of 0. • If player 1 selects D and player 2 selects U, player 1 gets a payoff of 3 and player 2 gets a payoff of 1. • If player 1 selects U and player 2 selects D, player 1 gets a payoff of 1 and player 2 gets a payoff of 3. The pure Nash equilibria for this game are (D,U) and (U,D) + Let p be the probability Player 1 plays U and let q be the probability Player 2 plays U. In the mixed Nash Equilibriump will be and q will be (Hint: the payoffs in the game are symmetric)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:In this common-knowledge, simultaneous move game there are two players. The players have two strategies
available, abbreviated as U and D.
The payoffs for the strategies are as follows:
• If both players select U, they each get a payoff of 0.
• If both players select D, they each get a payoff of 0.
• If player 1 selects D and player 2 selects U, player 1 gets a payoff of 3 and player 2 gets a payoff of 1.
• If player 1 selects U and player 2 selects D, player 1 gets a payoff of 1 and player 2 gets a payoff of 3.
The pure Nash equilibria for this game are (D,U) and (U,D) :
Let p be the probability Player 1 plays U and let q be the probability Player 2 plays U.
In the mixed Nash Equilibrium p will be
and q will be
(Hint: the payoffs in the game are symmetric)
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