Brett and Oliver are both going surfing. Each can choose between "North Beach" (N) and "South Beach" (S). North beach is better, but they both also prefer havingthe beach to themselves rather than sharing it with the other person. If Brett chooses N and Oliver N, the payoffs are (60, 60). If Brett chooses N and Oliver ChoosesS, the payoffs are (70,30). If Brett chooses S and Oliver N the payoffs are (30,70). If they both choose S the payoffs are (20,20). Brett gets to choose first and tellsOliver, who then makes a decision. Which of the following is true?O The number of nash equillibrium in this game is less than the number of subgame perfect equillibriumO The number of nash equillibrium in this game is the same as the number of subgame perfect equillibriumO The number of nash equillibrium in this game is more than the number of subgame perfect equillibriumO There is no subgame perfect equilibrium in this game

Sub game perfect equilibrium is a type of dynamic game , in which one player starts and other one…

Answered: Brett and Oliver are both going…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Two neighborhood kids can play at home or walk to a nearby park. Playing with their toys yields some happiness. However, they would enjoy playing with the other kid at the park even more at the park. But each has a concern that if they go the park the other will not show up. This is an interesting game or situation because neither kid has an incentive to betray the other and not show up, but each kid fears walking to the park and having no one to play with. They also have to fear that if the other kid thinks they won't show up, that other kid will won't show up. All this strategic thinking is a lot for kids to take in. Here is the payoff matrix: Kid 1 Toys at Home Park Toys at Home Kid 2 Park How many Nash equilbria are there? 1,2,3 or 4 There is an option to let Kid 1 move first, but no option for Kid 2 to move first. Should Kid 2 let Kid 1 move first. Yes or No Blank # 1 Blank # 2
Consider a sequential-move version of a rock-paper-scissor game. Players sequentially form one of three shapes with an outstretched hand. These shapes are "rock", "paper", and "scissors". A player playing rock will beat another player playing chosen scissors, but will lose to one playing paper; a play of paper will lose to a play of scissors. If both players choose the same shape, the game is tied. Suppose the winner receives a payoff of 1 and the loser receives the payoff of -1. Both players receive zero payoff under a tie. Suppose Player 1 moves first and Player 2 moves afterwards. In this game, what is the subgame perfect Nash equilibrium payoff of Player 1? 1 00 0-1
Two friends are deciding where to go for dinner. There are three choices, which we label A, B, and C. Max prefers A to B to C. Sally prefers B to A to C. To decide which restaurant to go to, the friends adopt the following procedure: First, Max eliminates one of three choices. Then, Sally decides among the two remaining choices. Thus, Max has three strategies (eliminate A, eliminate B, and eliminate C). For each of those strategies, Sally has two choices (choose among the two remaining). a.Write down the extensive form (game tree) to represent this game. b.If Max acts non-strategically, and makes a decision in the first period to eliminate his least desirable choice, what will the final decision be? c.What is the subgame-perfect equilibrium of the above game? d. Does your answer in b. differ from your answer in c.? Explain why or why not. Only typed Answer
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3. Two individuals are involved in a synergistic relationship. If both individuals devote more effort to the relationship, they are both better off. Specifically, an effort level is a nonnegative number, and player 1's payoff function is e₁(1+€₂-e₁), where ei is player i's effort level. For player 2 the cost of effort is either the same as that of player 1, and hence her payoff function is given by e2(1+e₁ - e₂), or effort is very costly for her in which case her payoff function is given by e₂(1 + e₁ — 2e2). 1 Player 2 knows player 1's payoff function and whether the cost of effort is high for herself or not. Player 1, however, is uncertain about player 2's cost of effort. He believes that the cost of effort is low with probability p, and high with probability 1 - p, where 0 < p < 1. Find the Bayesian Nash equilibrium of this game as a function of p.
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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!)
An auditor and a taxpayer play the following strategic game. The auditor must choose whether to Audit (A) the taxpayer or not (N). The taxpayer independently decides whether to be Honest (H) in reporting her income or to Cheat (C). Since auditing is costly, the auditor prefers not to audit the taxpayer if she reports honestly, but prefers to audit if the axpayer cheats. If the taxpayer is caught cheating (i.e. if she cheats and is audited), then she receives a severe punishment. If she is not caught, she prefers cheating to being honest. Suppose that payoffs are as in the following matrix: Auditor Taxpayer C 4, -10 0,4 H A 2,0 N 4,0 (a) Find all (mixed strategy) Nash equilibria of this game. Solution: There is no NE in pure strategies. Moreover, since each pure strategy has a unique best response, there is no NE in which either player plays a pure strategy. If the Auditor chooses A with probability p and the Taxpayer chooses H with probability q, then the condition for the Auditor to…
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
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