12.3 Armed Conflict: Consider the following strategic situation: Two rival armies plan to seize a disputed territory. Each army's general can choose either to attack (A) or to not attack (N). In addition, each army is either strong (S) or weak (W) with equal probability, and the realizations for each army are independent. Furthermore the type of each army is known only to that army's general. An army can capture the territory if either (i) it attacks and its rival does not or (ii) it and its rival attack, but it is strong and the rival is weak. If both attack and are of equal strength then neither captures the territory. As for payoffs, the territory is worth m if captured and each army has a cost of fighting equal to s if it is strong and w if it is weak, where s

12.3 Armed Conflict: Consider the following strategic situation: Two rival armies plan to seize a disputed territory. Each army's general can choose either to attack (A) or to not attack (N). In addition, each army is either strong (S) or weak (W) with equal probability, and the realizations for each army are independent. Furthermore the type of each army is known only to that army's general. An army can capture the territory if either (i) it attacks and its rival does not or (ii) it and its rival attack, but it is strong and the rival is weak. If both attack and are of equal strength then neither captures the territory. As for payoffs, the territory is worth m if captured and each army has a cost of fighting equal to s if it is strong and w if it is weak, where s

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter15A: Auction Design And Information Economics

Section: Chapter Questions

Problem 10E

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12.3 Armed Conflict: Consider the following strategic situation: Two rival armies plan to seize a disputed territory. Each army's general can choose either to attack (A) or to not attack (N). In addition, each army is either strong (S) or weak (W) with equal probability, and the realizations for each army are independent. Furthermore the type of each army is known only to that army's general. An army can capture the territory if either (i) it attacks and its rival does not or (ii) it and its rival attack, but it is strong and the rival is weak. If both attack and are of equal strength then neither captures the territory. As for payoffs, the territory is worth m if captured and each army has a cost of fighting equal to s if it is strong and w if it is weak, where s <w. If an army attacks but its rival does not, no costs are borne by either side. Identify all 12.7 Exercises • 267 the pure-strategy Bayesian Nash equilibria of this game for the following two cases, and briefly describe…
Consider the following two-player game.First, player 1 selects a number x≥0. Player 2 observes x. Then, simultaneously andindependently, player 1 selects a number y1 and player 2 selects a number y2, at which pointthe game ends.Player 1’s payoff is: u1(x; y1) = −3y21 + 6y1y2 −13x2 + 8xPlayer 2’s payoff is: u2(y2) = 6y1y2 −6y22 + 12xy2Draw the game tree of this game and identify its Subgame Perfect Nash Equilibrium.
Q14. Do players have perfect information in the above game? Yes, all of them have perfect information No, player 2 has imperfect information No, player 3 has imperfect information No, no player has perfect information Q15. If we want to describe the above game with a strategic form representation, what would the strategy sets for the three players be? Player 1={a, b, c} ; Player 2={x, y}; Player 3={r, s} Player 1={a, b, c} ; Player 2={xx, xy, yx, yy}; Player 3={r, s}
The following is a payoff matrix showing profit in millions of dollars when two companies simultaneously decide on various advertising budgets ($1 million, $2 million, or $3 million): Pizza Hut $1 mill $2 mill $3 mill $1 mill $120 / $175 110 / 160 100 / 170 Papa Johns $2 mill 130 / 150 115 / 145 110 / 155 $3 mill 140 / 125 120 / 120 105 / 130 a. In the first round of strategy elimination (when all three possible budgets are under consideration), which ad budget would the companies exclude? b. After the first round of elimination (previous question), would either company make a second-round elimination? c. What would be the likely outcome of this simultaneous advertising decision (i.e. what ad budget would each company end up choosing)?
Keith and Blake play a simultaneous one-shot game. Keith chooses between Top and Bottom, whereas Blake chooses between left and right. Payoffs are given by (Keith's payoffs are listed first and Blake's payoffs second): Top+left: 3,-6. Top+right:0,-7 Bottom+left:4,0. Bottom+right:-2,6. In a mixed strategy equilibria, Keith will play Top with what probability? 1. 6/7 2. 1/4 3. 1/2 4. 1/7 5. 0 6. 3/4
Consider the following dynamic game. There are two players (P1, P2). Player 2 tries to rob Player 1. If Player 1 pays $100, the game is over with Player 1 (victim) paying $100 to Player 2 (robber) (P1: -$100, P2: +$100). If Player 1 refuses to pay $100, then Player 2 has two choices: one is to hurt Player 1 (P1: -$5,000, P2: -$1,000) and the other is to walk away (P1: 0, P2: 0). Explain how to find an equilibrium in this game.
Suppose O2 and Vodafone are the only two telecommunicationscompanies in UK. Both companies are considering whether ornot to stop offering unlimited data plans. Each company has twostrategies: stop or don’t stop. The first entry in the brackets is the payoffsof O2 and the second entry is the payoffs of Vodafone, both in $million.What will be the dominant strategies of O2 and Vodafone and what willbe the Nash equilibrium? Explain your answers.
UNIT 9 CHAPTER 5 In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. Is there a pure strategy? Why or why not? Determine the optimal strategies and the value of this game. Does the game favor one player over the other? Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy.
please discuss the separation eqilibrium in details 1. Assume that two players play the Tinder game. There are two types of potential boyfriends: the gentleman (25% of the population) and the douchebag (75% of the population), and they can decide on the different level of effort: low, medium, and high. For the first type, the respective costs are 30, 50, and 80. For the second type, the respective costs are 50, 75, and 120. For the potential boyfriend, the payoff from being in relationship is 130, and the payoff associated with being dumped is 70. The girl can get 60 if she stays single, 100 if she is in relationship with the gentleman, and 25 if she dates the douchebag (credits to Owen Sims) a) Present the game in the extensive form b) Calculate the expected pay-off for the girl. Should she date at all? c) Discuss whether the game has a separating equilibrium
14. Company A and Company B are each telecommunications manufacturers. Both companies manufacture the same products, and they make their decisions based on the other's actions. Both companies are considering opening retail outlets to increase their profits. The payoff matrix shows the profits of the companies in millions of dollars if they choose to open retail outlets. The government imposes a new $5 million tax to open retail outlets. What is the expected outcome of the new payoff matrix, given the tax? The Nash equilibrium is for Company A to not open retail outlets and for Company B to open retail outlets. The Nash equilibrium is for Company A to open retail outlets and for Company B to not open retail outlets. The Nash equilibrium is for both Company A and Company B to open retail outlets. The Nash equilibrium is for both Company A and Company B to not open retail outlets. There is no Nash equilibrium after the change given in the scenario.…
Alice and Betsy are playing a game in which each can play either of two strategies, leave or stay. If both play the strategy leave, then each gets a payoff of $400. If both play the strategy stay, then each gets a payoff of $800. If one plays stay and the other plays leave, then the one who plays stay gets a payoff of $C and the one who plays leave gets a payoff of $D. When is the outcome where both play leave a Nash equilibrium? a) never, since 800 > 400 b) when 400 > C and D > 800 but not when 800 > D c) whenever 400 > C d) when D > C and C > 400 e) whenever d < 800
John and Paul are walking in the woods one day when suddenly an angry bear emerges from the underbrush. They each can do one of two things: run away or stand and fight. If one of them runs away and the other fights, then the one who ran will get away unharmed (payoff of 0) while the one who fights will be killed (payoff -200). If they both run, then the bear will chase down one of them and eat them to death but the other one will get away unharmed. Assuming they don't know which one will escape we will call this a payoff of -100 for both. If they BOTH fight, then they will successfully drive off the bear but they may be injured in the process (payoff -20). Construct a payoff matrix for this game and identify the pure strategy Nash equilibrium. (Indicate it with words not with a circle!)