Suppose there is a game between two players where each can choose either 'A' or 'B'. If the strategy 'B' is strictly dominant for Player 1 and the strategy 'A' is strictly dominant for Player 2 then which of the following is true? O There could be an interior mixed strategy Nash equilibrium O There could be multiple pure strategy Nash equilibria O There is no Nash equilibrium O There is a Nash equilibrium at (B,A) O More than one of the above
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- Which 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.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. O
- Which of the following statements about Nash Equilibria in a two-player one-shot simultaneous game is FALSE? 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. A Nash Equilibrium is conditional on at least one player having a dominant strategy. Click SoConsider the following price game: Firm 1 Firm 2 High Low High 20, 20 12, 24 Low 24, 12 14, 14 Remark: In simultaneous move games (games with rows and columns) theconvention is to write the row player’s payoff first and the column player’spayoff second. (a) What is the Nash equilibrium of this game? Recall that for each playeryou should find the best response to each of the opponents’ strategies andunderline the associated payoff. Then look for a cell where both strategiesare best responses to each other. This is a Nash equilibrium. (b) Does either firm have a dominate strategy (a strategy that is always abest response)?A Nash equilibrium occurs when O no player has an incentive to unilaterally change strategies. each player has an incentive to unilaterally change strategies. O both players can cooperate to increase their payoffs. O no player can earn a higher payoff from any other strategy.
- Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?Consider a repeated game with the following stage game: Player 1 O O O Cooperate Not Cooperate This game is repeated T-120 times, and t each period both players must choose their actions simultaneously. The players are deciding whether or not to cooperate specifically, whether or not to follow this cooperation strategy: r≤ 3 S|S|AW|N N|H "Each player will play cooperate as long as no one has played Not Cooperate before. If someone has played Not Cooperate before, then each player will play Not Cooperate forever." rs 5 rs Player 2 In this case, cooperation will be possible if the interest rate r is Not Cooperate 5,15 10, 10 None of the above Cooperate 12, 12 15,5Consider this as a simultaneous-move (static) game: Player A Top Bottom Player B Left Right ETEL UU 1.b) Does any player have a dominant strategy in this game? Explain. 1.a) Write down the Best Response Correspondence for each of the two players. Molimonsbestich Quinit 1.c) Find all Nash Equilibria in pure strategies of this game. 1.d) Is there any Nash Equilibria in mixed strategies? If so, find it. Elekt
- 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.The payoff matrix below describes a one-shot game in which two farmers ("Player A" and "Player B") choose between planting corn or planting wheat. The payoffs in this matrix represent thousands of dollars of income, so more is better. Pla yer A Plant Corn Plant Wheat What kind of equilibrium is this? Plant Corn Dominant Strategy Equilibrium Nash equilibrium 3, 3 Player B 5,0 Both a Nash and a Dominant Strategy Equilibrium O No equilibrium Plant Wheat 0,5 1, 1Consider 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 left