Identify any pure strategy equilibria of this game. Choose one or more: OA. (wrestling, wrestling) OB. (wrestling, opera) OC. (opera, wrestling) OD. (opera, opera) O E. There are no pure strategy equilibria.
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- 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 equilibriumThe game of Chicken is played by two teens who speed toward each other on a single-lane road. The first to veer off is branded the chicken, whereas the one who does not veer gains peer-group esteem. Of course, if neither veers, both die in the resulting crash. Payoffs to the Chicken game are provided in the following table. Team 2 Veer Does not veer Team 1 Veer 2, 2 1, 3 Does not veer 3, 1 0, 0 The first payoff number is for Teen 1 and the second number is for Teen 2. a) Does any of the players has a dominant strategy? b) Find the pure-strategy Nash equilibrium or equilibria. c) Suppose the game is played sequentially. Find the Nash equilibrium.The following game is played by 2 playerse 田 Jacke Lefte Middlee Righte Adame Upe 1,2e 3,5e 2,1e 0,4- -1,1e 2,1e 4,3 Middlee 3,0e Downe 0,2e a) Determine all dominant strategies for Adam and Jack. b) Solve the equilibrium for this game.
- 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.Return to the game between Monica and Nancy in Exercise U10 in Chapter 5. Assume that Monica and Nancy choose their effort levels sequentially instead of simultaneously. Monica commits to her choice of effort level first. On observing this decision, Nancy commits to her own effort level. What is the subgame - perfect equilibrium of the game where the joint profits are 5m + 4n+ mn, the costs of their efforts to Monica and Nancy are m2 and n2, respectively, and Monica commits to an effort level first? Compare the payoffs to Monica and Nancy with those found in Exercise U10 in Chapter 5. Does this game have a first-mover or second - mover advantage? Using the same joint profit function as in part (a), find the subgame - perfect equilibrium for the game where Nancy must commit first to an effort level. U10. Return to the game between Monica and Nancy in Exercise U10 in Chapter 5. Assume that Monica and Nancy choose their effort levels sequentially instead of simultaneously. Monica commits…See page 561 02 Question John and Daniel greatly enjoy each other's company but have different tastes regarding the best form of entertainment. John prefers the lowbrow entertainment of professional wrestling that disgusts Daniel. Meanwhile, Daniel likes highbrow opera, which bores John. However, each finds it preferable to spend the evening together rather than disagree about what to do and end up staying home angry. This interaction is modeled in the normal-form game below: Evening Entertainment John Part 1 Wrestling Opera Choose one or more: Daniel Wrestling 12.00, 4.00 0,0 Identify any pure strategy equilibria of this game. A. (wrestling, wrestling) B. (wrestling, opera) OC. (opera, wrestling) Part 2 Opera 0,0 6.00, 18.00 D. (opera, opera) DE. There are no pure strategy equilibria. Find the mixed strategy Nash equilibrium of this game. In it, John will choose wrestling with probability choose wrestling with probability (Give your answers to two decimal points.) See H See Hir ,and…
- Here is a table representing the gains for the server if he serves on his opponent's forehand or backhand and for the receiver the gains if he returns on his forehand or backhand. Each player can choose to play the forehand or the backhand of the other player : Server D R D 50,50 80, 20 R 90,10 |20, 80 Receiver D Determine the Nash equilibrium(s) (pure strategies and mixed strategies).The U.S. government has decided to build a new off ramp for Interstate 5 in California. Exxon and Shell are both interested in building a gas station near the new off ramp. They can build the gas station near the off ramp for northbound traffic or they could build the gas station near the off ramp for southbound traffic. The profits for each outcome are illustrated in the accompanying payoff table: Shellnorthbound Shellsouthbound Exxon northbound Exxon receives$60,000 profitShell receives$50,000 profit Exxon receives$110,000 profitShell receives$100,000 profit Exxonsouthbound Exxon receives$80,000 profitShell receives$120,000 profit Exxon receives$50,000 profitShell receives$50,000 profit a. Select the Nash equilibrium, or equilibria, that occur if Exxon and Shell make these decisions simultaneously. Exxon builds northbound and Shell builds northbound. Exxon builds southbound and Shell builds northbound. Exxon builds southbound and Shell builds southbound.…The world has changed a bit. Microsoft and Google could still either cooperate or compete in the market for social media video software currently captured by Tik Tok, but their payoffs have changed. The table below shows their profits in billions of USD in each scenario. Use your mouse to point and click on the Nash equilibrium outcome(s). [There may be more than one so make sure you work out all the best response strategies]. Microsoft Cooperate 3,3 4,0 Cooperate O Don't cooperate O Google Don't cooperate O O 0,4 1,1
- Mr. and Mrs. Ward typically vote oppositely In elections and so their votes “cancel each other out.” They each gain two units of utility from a vote for their positions (and lose two units of utility from a vote against their positions). However, the bother of actually voting costs each one unit of utility. Diagram a game in which they choose whether to vote or not to vote.Consider the following game : Stag Rabbit Stag 9, 9 0, 8 Rabbit 8, 0 7, 7 The first payoff is that of player 1 and the second that of player 2. a. ) Draw the extensive form of the simultaneous game. Find all the Nash equilibrium. p. Suppose player 1 moves first or we are in a sequential game now. Draw the extensive form in the sequential version. c. What is the subgame perfect Nash Equilibrium (SPNE) in the sequential version? d. ) Explain why it is an SPNE.To Vote or Not to Vote Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain two units of utility from a vote for their positions (and lose two units of utility from a vote against their positions). However, the bother of actually voting costs each one unit of utility. Diagram a game in which they choose whether to vote or not to vote. Mrs. Ward vote. don't vote Mr. Ward Vote. -1, -1. 1, -2 don't vote. -2, 1. 0,0?
