Assume a Hawk -Dove game with the following payoff matrix, where the first entry is nimal 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) n animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays ove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet ey share. (a) Explain why there cannot be an equilibrium where all animals act as Doves.

Assume a Hawk -Dove game with the following payoff matrix, where the first entry is nimal 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) n animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays ove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet ey share. (a) Explain why there cannot be an equilibrium where all animals act as Doves.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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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.
16. Consider a stag-hunt game with payoffs Bob Bob stag rabbit Alice, stag 5, 5 0,4 Alice, rabbit 4,0 4,4 The most likely experimental outcome in this game should be (A) (stag, stag); (B) (rabbit, rabbit); (C) (stag, rabbit); (D) (rabbit, stag).
3.Students A and B decide whether to clean the dormitory. Regardless of whether the other party participates, the cleaning cost for each student to clean the dormitory is $ 8; and the benefit for each student from cleaning is $5 times the number of participants. (hint: if both of them clean the dormitory together, A and B benefit. If one cleans while the other does not, A and B benefit too) (a) Please use a game theory to briefly describe the above scenario, (that is to calculate the revenue for different strategies) (b) Draw the payoff matrix, find the Nash equilibrium.
Table 8. This table shows a game played between two players, A and B. The payoffs are given in the table as (Payoff to A, Payoff to B). A Select one: Up Middle Down Left (4,2) a. Middle-Center O b. Down-Center (3, 1) (1,3) B Center (2,5) (5, 3) (4,4) Refer to Table 8. This table shows a game played between two players, A and B. The payoffs in the table are shown as (Payoff to A, Payoff to B). Which of the following outcomes represents a Nash equilibrium in the game? Right (3, 3) (5,2) (6, 1) O c. Up-Left O d. More than one of the above is a Nash equilibrium in this game.
Consider a two-player game in which a father chooses between actions yes, no, and maybe. His daughter moves second and chooses between stay home and go to the mall. The payoffs are as follows : (given) Write down the extensive form game for this strategic situation.
Costco Spend $1B on advertising Spend $1.5B on advertising Spend $1B on advertising $3.5B; $2.7B $4.2; $2.2B Target Spend $1.5B on advertising $3.2B; $3.4B $4B; $3B
16) Convert the following extensive form game into a normal form game. Solve the game to find all pure strategy Nash equilibria. 1 A B 2 W X Y 3, 3 1, 2 2, 1 4, 4
16. 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.
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5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…
5. Aaron and Betty play the following one-shot game. Aaron Up Middle Down Left 10,0 5,10 1,1 Betty Right 0,5 1,0 2,2 a. Does the game above have any (pure strategy) Nash equilibria? Find any equilibria or explain why an equilibrium doesn't exist. b. Suppose instead that Aaron moves first and Betty moves second. Represent this situation with a game tree and find the subgame perfect Nash equilibrium. Are Aaron and Betty better off playing a simultaneous game or a sequential game in which Aaron moves first? Explain. c.
17) Convert the following extensive form game into a normal form game. Solve the game to find all pure strategy Nash equilibria. 1 A 2 2 W X W 4,3 1, 2 2, 4 3, 1