For the following simultaneous move game, we want to find a mixed strategy Nash equilibrium. ROWENA Safe Risky Safe 4*q + 4*(1-q) = 1 4,4 1,4 COLIN Risky 4,1 6,6 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: *q + 6 *(1-q)

For the following simultaneous move game, we want to find a mixed strategy Nash equilibrium. ROWENA Safe Risky Safe 4q + 4(1-q) = 1 4,4 1,4 COLIN Risky 4,1 6,6 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: q + 6 (1-q)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The bimatrix represents a simultaneous move game between Rowena and Colin. Rowena's payoff is the left number in each cell. ROWENA O O 2 Calculate Rowena 's expected payoff in the mixed strategy Nash equilibrium. 3.5 2.5 Up Down 3 Left 1,16 2,20 COLIN Right 4,6 3,40
Consider the following constant sum game: 5 2 4 4 9 8 6 Assume that the value of x is known to both players. Assume that the Row Player chooses randomly between strategies 1, 2, and 3 (hence, she chooses each strategy with probability 1/3). Under what conditions will the Column Player always play Strategy 2 (Column 2)? Provide an explanation. a) The Column Player will never commit to a pure strategy. b) Only when x 3. e) Only when x 6.
help please. please be detailed please. i think we also need to draw some diagrams
2. Suppose we have 2 players in a first price auction. More specifically, suppose player i values the object being auctioned at v, where v > vz > 0. These valuations are known to both players. They simultaneously choose bids b;. Whoever bids the most gets the object and pays what she bid. In case of a tie, each player has probability of receiving the good and paying her bid and probability of a payoff of 0. Suppose the strategy set (set of all possible bids) for each player is [0, 0). Show that there is no pure strategy Nash equilibrium.
The action set of player 1 is {1,2, 3, 4, 5} (not considering the $ sign). When both players are rational, the theoretical SPNE is (5, 1). Now answer the following problems. What is the dollar equivalent of utility of happiness to ensure player 2 to accept the 2$ offer of player 1? Just write the number, no need to put the $ sign. 5| 5 What is the dollar equivalent of utility of happiness to ensure player 2 to accept the 4$ offer of player 1? Just write the number, no need to put the $ sign. 100 100
a) Write out the extensive form of a game between a farmer (playing in the first round) and nature (playing a mixed strategy in the second round). Assume that the farmer can either pay a cash rent of $1500 for land (English system) or 1/2 of crop production to the landlord (sharecropping). Assume the farmer is planting corn and will produce 2 tons of corn. Assume that nature has a 50% chance of playing a strategy in which the price of corn is $3500/ton and a 50% chance of playing a strategy in which the price of corn is $500/ton. The farmer keeps any money left after paying cash rent and sells any corn left after paying the landlord in sharecropping. b)What is the most that a risk neutral farmer would be willing to pay for an accurate prediction of the price of corn in problem 1 before choosing whether to pay cash rent or sharecrop?
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I need question 3, question 2 is only for background informati
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This payoff matrix shows a two-player variant of the sushi game, but where B really loves sushi, so her payoffs from getting to eat sushi are higher than A's, and her payoffs from there not being enough sushi are lower than A's. Payoffs are ordered A, B. В A 10, 15 10, 25 20, 15 0, -5 A. Find and state all of the mixed strategy Nash equilibria of the game. If there are multiple equilibria, number them in preparation for answering part "c." B. (From the week 6 lectures) Draw a graph of the expected payoffs for each player. Use these graphs to formulate the decision rule for each player. C. (From the week 6 lectures) Draw a graph of the best replies of the two players. Carefully label each Nash equilibrium.
Derive all Nash equilibria of the following game. a1 b1 a1 2,7 3,2 b1 0,0 4,1
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