Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A's payoff, and the second entry is Animal B's payoff: Hawk Dove Animal A (rows)/Animal B (columns) Hawk Dove (-5,-5) (0,10) (10,0) (4,4) An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share. Explain why there cannot be an equilibrium where all animals act as Doves. Explore whether there are any Nash equilibria in pure strategies and explain which these are and why. Derive a mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawks and Doves? If the proportion of Hawks in the population of animas is greater than the mixed strategy equilibrium proportion you calculated, which strategy does better, Hawks of Doves? Explain your answer.

Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A's payoff, and the second entry is Animal B's payoff: Hawk Dove Animal A (rows)/Animal B (columns) Hawk Dove (-5,-5) (0,10) (10,0) (4,4) An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share. Explain why there cannot be an equilibrium where all animals act as Doves. Explore whether there are any Nash equilibria in pure strategies and explain which these are and why. Derive a mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawks and Doves? If the proportion of Hawks in the population of animas is greater than the mixed strategy equilibrium proportion you calculated, which strategy does better, Hawks of Doves? Explain your answer.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.5P

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Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A’s payoff, and the second entry is Animal B’s payoff: Animal A (rows)/Animal B (columns) Hawk Dove Hawk (-5,-5) (10,0) Dove (0,10) (4,4) An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share. Explain why there cannot be an equilibrium where all animals act as Doves. Explore whether there are any Nash equilibria in pure strategies and explain which these are and why. Derive a mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawks and Doves? If the proportion of Hawks in the population of animals is greater than the mixed strategy equilibrium proportion you calculated, which strategy does better, Hawks of Doves? Explain your answer. Draw the best response functions and show in the…
Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A’s payoff, and the second entry is Animal B’s payoff: Animal A (rows)/Animal B (columns) Hawk Dove Hawk (-5,-5) (10,0) Dove (0,10) (4,4) An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share. Explain why there cannot be an equilibrium where all animals act as Doves. Explore whether there are any Nash equilibria in pure strategies and explain which these are and why. Derive a mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawks and Doves? If the proportion of Hawks in the population of animals is greater than the mixed strategy equilibrium proportion you calculated, which strategy does better, Hawks of Doves?
2. Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A's payoff, and the second entry is Animal B's payoff: Animal A Hawk Dove (rows)/Animal B (columns) (-5,-5) (0,10) (10,0) (4,4) Hawk Dove An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share. (a) Explain why there cannot be an equilibrium where all animals act as Doves. (b) Explore whether there are any Nash equilibria in pure strategies and explain which these are and why. (c) Derive a mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawks and Doves? If the proportion of Hawks in the population of animals is greater than the mixed strategy equilibrium proportion you calculated, which strategy does better, Hawks of Doves? Explain your answer. (d) Draw the best response functions and show in the diagram all pure and mixed…
4. Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A's payoff and the second entry is Animal B's payoff: Animal A Hawk (rows)/Animal B (columns) Hawk Dove (-10,-10) (0,20) Dove (20,0) (8,8) An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share. (a) Explain why there cannot be an equilibrium where all animals act as Doves. (b) Explore whether there are any Nash equilibria in pure strategies and explain which these are and why they are equilibria.
Consider the following game. Firm 1 can implement one of two actions, A or B. Firm 2 observes the action chosen by Firm 1 and then decides whether to fight it or not. (-10, 20) F2 Fight A Don't fight -(30, 10) Firm 1 (-10, 0) Fight B Don't fight -(20, 15) (a) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses fight if A, and fight if B. • this strategy profile is [Select] (b) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses fight if A, and don't fight if B. • this strategy profile is [Select] O (c) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses don't fight if A and don't fight if B. • this strategy profile is [Select] 00 F2 ()
2. Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A's payoff, and the second entry is Animal B's payoff: Animal A Hawk Dove (rows)/Animal B (columns) (-5,-5) (0,10) (10,0) (4,4) Hawk Dove An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share. (a) Explain why there cannot be an equilibrium where all animals act as Doves. (b) Explore whether there are any Nash equilibria in pure strategies and explain which these are and why. (c) Derive a mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawks and Doves? If the proportion of Hawks in the population of animals is greater than the mixed strategy equilibrium proportion you calculated, which strategy does better, Hawks of Doves? Explain your answer.
Consider a game in which there is $4 to be divided, and the first mover is only permitted to make one of three proposals: (a) $3 for the first mover and $1 for the second mover, (b) $2 for each, or (c) $1 for the first movier and $3 for the second mover. The second mover is shown the proposal and can either accept, in which case it is implemented, or reject and cause each to earn $0. Show this game in extensive (tree) form. Be sure to show the payoffs for each person, with the first mover listed on the left, for each of the six terminal nodes.
(a) Consider a ROCK PAPER SCISSOR game. Two players indicate either Rock, Paper or Scissor simultaneously. The winner is determined by: Rock crushes Scissors, Paper covers Rock, and Scissor cut Paper. In the case of a tie, there is no payoff. In the case of a win, the winner collects 5 dollars. Write the payoff matrix for this game. (b) Find the optimal row and column strategies and the value of the matrix game. 3 2 4 -2 1 -4 5
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?
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
Convert into Normal-Form Game and Find out the subgame-Nash Equi- libria? OUT (0, 2) Small Entrant Small IN Entrant Incumbent Large Large Small Large (−6, −6) (−1,1) (1,−1) What does the Information set imply in this game? (-3,-3)
The payoff matrix below shows the payoffs for Firm A and Firm B, each of whom can either "cooperate" or "cheat." The numbers in parentheses are (payoff for A, payoff for B). Firm B Cooperate Cooperate (30, 30) (x, 10) Cheat (10, X) (20, 20) Firm A Chent If x = 40, the Nash equilibrium is. O a. (Firm A: cheat, Firm B: cheat) O b. (Firm A: cooperate, Firm B: cheat) O c. (Firm A: cheat, Firm B: cooperate) O d. (Firm A: cooperate, Firm B: cooperate) O e. There is no Nash equilibrium for this value of x.