Which of the following statements about Nash Equilibria in a two-player one-shot simultaneous game is FALSE? O f one player has a dominant strategy, a Nash Equilibrium is guaranteed. If both players have a dominant strategy, a Nash Equilibrium is guaranteed. O A Nash Equilibrium is conditional on at least one player having a dominant strategy.
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- Which of the following statements about Nash Equilibria in a two-player one-shot simultaneous game is FALSE? O If one player has a dominant strategy, a Nash Equilibrium is guaranteed. O If both players have a dominant strategy, a Nash Equilibrium is guaranteed. O A Nash Equilibrium is conditional on at least one player having a dominant strategy. O It is possible for a game in pure strategies to not have a Nash Equilibrium. It is possible for a two-person game to have more than two Nash Equilibria.Consider the following simultaneous move game: Player 1 \ Player 2 Top Bottom Select one: Left Right 5,3 4,1 2,0 0,2 Player 2 has a dominant strategy in this game. Player 1 has a dominant strategy in this game. O This game has a Nash equilibrium in dominant strategies. This game does not have a Nash equilibrium in pure strategies. None of the statements is correct. OWhich of the following accurately describes a player's strictly dominant strategy? O It is a strategy that is better than all the player's other strategies, no matter what the other players do. There is always at least one player who has one in every game.. O It is the strategy a player uses in the Nash equilibrium of a game. Since a Nash equilibrium always exists, players always have a strictly dominant strategy. O It is a strategy that is better than all the player's other strategies, no matter what the other players do. A player may or may not have one. O It is a strategy that is better than all the player's other strategies, no matter what the other players do. Every player has a dominant strategy in every game.. O It is the strategy a player uses in the Nash equilibrium of a game. Since a Nash equilibrium may not exist, players may not always have a strictly dominant strategy.
- GAME 5 Player B B2 B1 Player A A1 7, 3 5, 10 A2 3, 8 9, 6 In Game 5 above, O there are no Nash equilibria in pure strategies. Player A choosing A1 and Player B choosing B2 is a Nash equilibrium. O Player A choosing A1 and Player B choosing B1 is a Nash equilibrium. O Player A choosing A2 and Player B choosing B1 is a Nash equilibrium.Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.Normal Form Game: The table below provides a normal form, 2 x 2 game. The players are Column and Row. Column can choose either LEFT or RIGHT, and Row can choose either UP or DOWN. Their payoffs for each combination of moves are provided in the four boxes. Column Row UP DOWN The combination of moves (UP, LEFT) is a Nash-Equilibrium. A. False O B. True 2 LEFT -1 -7 3 6 RIGHT -5 -10
- Consider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column. Up Down Left 0,-1 2,3 Right 1,2 0,1 What is (are) the Nash equilibrium (equilibria)? Select one or more: □ a. Player 1 plays right; Player 2 plays up O b. Player 1 plays up; Player 2 plays right Oc. Player 1 plays up; Player 2 plays left O d. Player 1 plays left; Player 2 plays up Oe. Player 1 plays left; Player 2 plays down Of. Player 1 plays down; Player 2 plays right Og. Player 1 plays right; Player 2 plays down Oh. Player 1 plays down; Player 2 plays leftWhich of the following DOES NOT accurately describe a Nash equilibrium? O It is the set of strategies which provides the players with the highest possible combined payoffs. All of these choices accurately describe a Nash equilibrium. O It is a set of strategies such that no player can receive a higher payoff by changing only their own strategy. It is a set of strategies such that no player, after seeing what the other players' strategies were, regrets their choice of strategy. It is a set of strategies such that every player, after seeing what the other players' strategies were, is satisfied (if not actually happy) with their choice of strategy.Refer to the accompanying figure. What is the Nash equilibrium of this game? Player A O Multiple Choice O Up O Down Player B Left 5 for A 30 for B -2 for A 10 for B A chooses Up, B chooses Right A chooses Up, B chooses Left Right 10 for A 12 for B 8 for A 15 for B A chooses Down, B chooses Right A chooses Down, B chooses Left
- Consider the following simultaneous game: Player 1 U D Player 2 L 20,-10 -10, 20 R -10, 20 20,-10 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has a Nash equilibrium. This game has a Nash equilibrium in pure strategies. Player 1's best response is D if player 2 plays R.Mark and Bevis play a static game. Mark chooses x and Bevis chooses y. Mark's payoff is 16 - (x- y)2, and Bevis' payoff is 16 - (x-0.5)2 - (y-0.5)2. Then O a. both Mark and Bevis have dominant strategies O b. Mark has a dominant strategy, but Bevis does not O c. Bevis has a dominant strategy, but Mark does not O d. neither Mark or Bevis have dominant strategiesOne of the following statements about the theory of economic games is not correct. Select the one answer that is false. Select one: O Each player's most preferred scenario in a prisoners' dilemma game is to free ride. O Looking for dominant strategies will identify all equilibria in a game. In a dominant strategy equilibrium, no player has an incentive to unilaterally change their strategy. O In a Nash equilibrium, no player has an incentive to unilaterally change their strategy.