Player A B1 Player B B2 A1 7,13 15, 10 A2 3,8 9,16 A3 5,8 4,7 In Game Z (see table above), assuming players move simultaneously. Which of the following is true?
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- GAME UUU B1 Player B B2 A1 7,13 5, 10 A2 3,8 9,16 Player A A3 5,8 4,7 In Game UUU (see table above), assuming players move simultaneously, Player A choosing A1 and Player B choosing B3 is a Nash equilibrium. Player A choosing A3 and Player B choosing B2 is a Nash equilibrium. Both Player A choosing A1 and Player B choosing B1 and Player A choosing A2 and player B choosing B2 are Nash equilibria in pure strategies Player A choosing A1 and Player B choosing B2 is a Nash equilibrium.GAME 5 Player B B1 B2 Player A A1 7,3 | 5, 10 A2 3, 8| 9, 6 In Game 5 above, O Neither player has a dominant strategy. O Player B has a dominant strategy. O Player A has a dominant strategy. O Both players have dominant strategies.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.
- 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 following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff ofIn equilibrium, what is the probability that player 1 will use the pure strategy E in this game?
- 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?ALBUS MINERVA N S Z MINERVA لی a C a b 3,3 ALBUS b 0,4 2,2 4 N S 15,2 1,3 13,1 For the above sequential game, both Albus and Minerva make moves in two possible situations. A number in purple indicates which node of the two for each of Albus and Minerva. Albus' strategy NS indicates a strategy of taking action N at node 1 and action 5 at node 4. Minerva's strategy ab indicates a strategy of taking action a at node 2 and action b at node 3. Adopt this format of writing strategies, find the subgame perfect Nash equilibrium. Fill in the blanks: The subgame perfect Nash equilibrium of this game is "Albus" Minvera"Consider 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
- Consider the following simultaneous game: Player 1 U D Player 2 L 30,20 -10, -10 R -10, -10 20,30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.In the following simultaneous-move game, what is player 1's maximin strategy? Player 2 OL OR OU OD Player 1 L R U 50, 50 0, -10 D -10, 0 0,0Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.
