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- 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.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.A R1 R2 C1 5,4 6,4 B C2 11,5 9, 2 In this game between players A and B, Only A has a dominant strategy O Only B has a dominant strategy Both players have a dominant strategy O Neither player has a dominant strategy
- 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 0,0Player 2 E F H A 6, 5 6, 7 9, 6 7,6 В Player 1 C 6, 7 6, 9 8, 5 9, 7 5, 8 5, 6 7,5 7,5 7,9 8, 7 11, 6 5, 6 (1) In the Unique Nash equilibrium of this game, which strategy does Player1 play? And why? (2) In the Unique Nash equilibrium of this game, which strategy does Player2 play? And why? (3) Is this game dominance solvable? And Why? (4) Does this game have at least one inadmissible Nash equilibrium? And Why?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 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 Z Player A B1 A1 7, 13 A2 3,8 Player B B2 15, 10 9,16 A3 5,8 4,7 In Game Z (see table above), assuming players move simultaneously. Which of the following is true? Player A has a dominant strategy Player B has a dominant strategy Both players have dominant strategies O Neither player has a dominant strategyes Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. C 23, 5 27, 5 a. What is player 1's optimal strategy? Player 1 Strategy O Strategy B O Player 1 does not have an optimal strategy. Strategy A b. Determine player T's equilibrium payoff. 21 D 10, 16 4,9 Player 2 E 18, 18
- 11. The following payoff table involves two players each of whom has three possible moves. L M N L 30,15 45,35 55,25 M 25,35 20,20 30,50 N 15,35 35,40 15,15 a. Are there any dominant strategies in this game?1. Find all of the pure strategy Nash Equilibrium to the following simultaneous move game. Show all of your work. Row a b C d e A 9,4 14,8 7,8 15,0 20,18 B 12,10 3,10 6,8 7,4 2,9 Column C 15,7 12,18 20,10 14.2 10,14 D 2,8 4,7 3,12 5.3 3,7 E 15,5 20,12 15,9 9,1 19,20Consider 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.