Show the steps and take a like Find all Nash equilibria using the table method. Use / for column dominance andfor row dominance. Put both and \ if both apply: i.e. check every cell for bothrow and column elimination. After using algebra to resolve any surviving cells,plug your strategies back into the game and compute payoffs to verify yoursolutions. Show all your work. NO CALCULATORS or decimal answers - usefractions!121.20.32.13-1,-2 2.-2-3.012131,11.0-1.-1231231 231213 23 123

Step 3: Solve for Nash EquilibriaIn the reduced matrix, we look for cells where neither player has…

Answered: Find all Nash equilibria using the…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

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Find all Nash equilibria using the table method. Use / for column dominance and \ for row dominance. Put both / and \ if both apply; i.e. check every cell for both row and column elimination. After using algebra to resolve any surviving cells, plug your strategies back into the game and compute payoffs to verify your solutions. Show all your work. NO CALCULATORS or decimal answers - use fractions! 1,2 0,3 -1,-2 2₁-2 1,1 1,0 2,1 -3,0 -1,-1 1 2 3 12 13 23 123 1 2 3 12 13 23 123
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a) Return to the two-player game tree in part (a) of Exercise U2 in Chapter 3. (a) (b) Write the game in strategic form, making Albus the Row player and Minerva the Column player. Find all Nash equilibria. For those equilibria you found in part (a) of this exercise that are not subgame-perfect, identify the reason. 13,0 a MINERVA 12,1 N 1,1 a MINERVA ALBUS E S MINERVA 15,0 20 a 4,4 b 1,5
1
6
Consider the following simultaneous game: Player 1 U D Player 2 L 30,20 -10, -10 R -10, -10 20,30 Suppose player 1 plays a mixed strategy in which she plays U 25% of the time and D 75% of the time, and player 2 plays a mixed strategy in which she plays L 25% of the time and R 75% of the time. This pair of strategies ✓a Nash equilibrium. Player 1's expected payoff from playing U (when player 2 plays the mixed strategy above) is
(a) Design a two-player game with the property that "the payoff for Player1 is Playerl plays a strategy Sl and Player2 plays a strategy S2 is the same as the payoff for Player2 if Player2 plays Sl and Playerl plays S2". Express your game in terms of payoff matrices. Show the above property holds in your given payoff matrices. Give a case to show that there is one Nash equilibrium and such an equilibrium is also a Pareto efficient (justify your answers) in your given payoff matrices. Prove or disprove the above case that is unique. Give another example to show that there are two Nash equilibria in your given payoff matrices.
For the following simultaneous move game, we want to find a mixed strategy Nash equilibrium. ROWENA Safe 4*q + 4*(1-q) = Risky Safe 1 4,4 1,4 COLIN Risky 4,1 We denote Colin's mixture probability on Safe by q.. To find q in Colin's mixed strategy Nash equilibrium, we apply indifference property to player Rowena 's expected payoffs from pure strategies in mixture: 6,6 +q+6 *(1-q)
1. Consider the following two player 2x2, normal form game: (Payoffs are starting from northwest and moving clockwise are (10,5), (2,30), (5,5), and (40,10). Player 1 strategies are A and B, Player 2 strategies are C and D. Identify all Nash equilibria in pure strategies. a) 2. Using the normal form game, represent a two-player Rock-Paper-Scissors-Game where Player 1's losses and gains are triple that of Player 2.
2. Army 1 of country 1 must decide whether to attack army 2 of country 2 which is occupying an island between the two countries (i.e. army 1 moves first). In the event of an attack, army 2 may fight or retreat over a bridge to its mainland. Each army prefers to occupy the island than not to occupy it; a fight is the worst outcome for both armies. (a) Model the situation as an extensive form game with perfect information. Find a Nash Equilibrium of this game which is not subgame perfect. (b) Find the only Subgame Perfect Nash Equilibrium and compare with the equilibrium in the previous question. (c) Assume now that army 2 has the possibility of burning the bridge to its mainland. If it does, army 2 would then not be able to retreat if army 1 attacked. i. Write down the extensive form of this game. Show that army 2 can increase its payoff in a Subgame Perfect Nash equilibrium in the new game. Interpret what this fact illustrates. ii. iii. Now assume that the attacking army cannot observe…
Consider the game with the payoffs below. Which of the possible outcomes are MORE efficient than the Nash Equilibrium (NE)? Note, they do NOT need to be Nash equilibria themselves, they just need to be more efficient than the NE. Multiple answers are possible, but not necessary. You need to check ALL correct answers for full credit. JILL High Medium LowMAGGIE Left 3,4 2,3 2,2Center 4,8 9,7 8,7Right 7,6 8,5 9,4Group of answer choices (Left, Low) There is no strategy combination that is more efficient than the Nash equilibrium for this game. (Right, Medium) (Left, High) (Center, Medium) (Center, High) (Center, Low) (Left, Medium) (Right, Low) (Right, High)
Consider the game with the payoffs below. Check ALL the Nash equilibria (if any), multiple answers are possible, but not necessary. You need to check ALL correct answers for full credit, no partial credit. JILL High Medium Low 13,4 MAGGIECenter 4,8 21,3 9,17 8,5 2,21 31,7 Left Right 17,4 19,4 O (Center, High) O (Left, Medium) O (Left, High) O (Right, Medium) O (Center, Low) O There is no Nash equilibrium for this game. O (Right, High) O (Left, Low) O (Center, Medium) O (Right, Low)

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