2. Consider the following game: 1 u 6,0 0,6 d 3,2 6,0 Are there any Nash equilibria in pure strategies for this game? Find the mixed strategy Nash equilibrium.
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- Consider the following simultaneous move game: Player 1 U M D Player 2 L 2,10 2,5 8,7 C 5,2 11,8 8,4 R 5,4 2,9 8,3 In the Nash equilibrium of this game, player 1 receives a payoff of ✓ and player 2 receives a payoff ofConsider 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.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.
- 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 of16. Consider a game with two players, each with three strategies. Given the payoff matrix shown below, determine which pair of strategies is a Nash equilibrium. Player One X Y 1 3. X' 3 1 4 Player Two Y 5 0. 3 Z' 4 (a) X, X' 21 1.2: Provide a definition for a Nash equilibrium and then find all pure-strategy Nash equilibria of the following game: Left Center Right Up Middle 1,3 2,7 6,3 2,9 4,4 7,10 Down 3,8 2,5 3,4
- Aedri Quick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No esc The Ice Cream Guys $3.99 $4.99 + Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 tab Treats CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. %3D caps lo 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information hift 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would…2. Brad and Angelina have agreed to meet up for their first date. Neither of them can remember the exact location where they arranged to meet up and have forgotten their phones at home. Their payoff matrix can be described as follows: Brad The Hive Le Monde a) What is the Nash equilibrium in this game? Angelina The Hive 5; 5 0; 0 Le Monde 0; 0 5; 5(b) ROWENA up Answer 1: up Answer 2: In this simultaneous move game, the iterated dominance equilibrium is (Rowena's . Colin's left left Answer 3: ). This game has two Nash equilibria one of which is the iterated dominance equilibrium. The other Nash equilibrium, which is not the IDE, is (Rowena's down Colin's right down Up Down Answer 4: Left right 0,0 0,0 COLIN Right 0,0 1,1
- one two X, 14 three four Firm B Low Firm A Sell High 6, Y Buy Low Let X = 9, Y = 15 and Z=10. This game has 10, Z Firm B High 8,8 Nash equilibrium.3. Write a normal form representation of the game shown in the figure below and derive all pure strategy Nash equilibria. P1 L R P2 P2 L R R l's Payoff 1 2's Payoff 2Quick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No The Ice Cream Guys $3.99 $4.99 Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 Treats The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would they agree upon, if any? a) Both…
