Solve the following questions.
Use a matrix to model a two-player game of rock-paper scissors with a payoff of 1 if you win, - I if you lose, and Oil you tie Construct the payoff matrix for this game Player 1/Player 2 Rock Paper Scissors Rock Paper Scissors The Nash equilibrium Is O A Scissors/Paper O B. Paper/Scissors O C. Paper Rock OD. Rock/Rock O E. There is no Nash equilibrium Why should you use a mixed strategy to play this game? O A. Random behave generally leads to a Nash equilibrium O B. Mixed strategy has the advantage of requiring less effort to generate an optimal outcome O C. Predictable behavior by one player can be taken advantage of by the other plays O D. Pure strategy is a more efficient way to reach higher payoff outcomes,5. Suppose Russia is deciding to Invade or Not Invade its neighbor Ukraine. The U.S. has to decide to be Tough or Make Concessions. They will make their decisions simultaneously. Their payoffs are as follows: U.S. / Russia Not Invade Invade Be Tough U.S. gets 5 U.S. gets 7 Russia gets 4 Russia gets 3 Make Concessions U.S. gets 3 U.S. gets 1 Russia gets 5 Russia gets 9 a. What is U.S.'s best response when Russia chooses Not Invade? b. What is U.S.'s best response when Russia chooses Invade? C. What is Russia's best response when U.S. chooses Though? d. What is Russia's best response when U.S. chooses Make Concessions? e. What is the Nash equilibrium of this game?Imagine a game in which two drivers drive toward each other on a collision? course: one must? swerve, or both may die in the? crash, but if one driver swerves and the other does? not, the one who swerved will be called a? "chicken," meaning he is a coward. If they both go? straight, then they both? die, earning dash-10 happiness points each. If one goes straight and the other? swerves, then the brave driver gets 5 points of happiness and the? "chicken" loses 2 points of happiness. If both drivers? swerve, then it is a tie and nobody earns any happiness points.?? Construct the payoff matrix for Driver 1 and Driver 2.?? Driver 2 Driver 1 Go Straight Swerve ??Go Straight Box 1 Box 2 5 points/-2 points 0 points/0 points -10 points/-10 points -10 points/5 points -2 points/5 points ??Swerve Box 3 Box 4 -2 points/5 points 0 points/0 points -10 points/5 points -10 points/-10 points 5 points/-2 points Driver 1 has does not have a dominant? strategy, and Driver 2 has does not have a dominant strategy Identify the Nash? equilibrium(s):One of your coworkers, Freddie, really gets on your nerves and it would dramatically increase your happiness if he was fired. Freddie also dislikes you and wishes you would be fired. You have the option of going to your boss and lying about Freddie harassingyou, which you are sure will get him fired. Freddie has the same option to make up a lie about you to get you fired. Whoever gets fired will not have any credibility to have his lies believed afterward. Given these circumstances, it would be logical for you to wait for Freddie to lie first and then compain lie second to revenge yourself on Freddie lie first to get Freddie fired Do nothing The person who lies first in this situation has a commitment advantage second-mover advantage first-mover advantage reputational risk Now assume that your coworkers will know if either you or Freddie lie to get the other fired, and your coworkers will shun the liar and make life miserable for that person. Given these circumstances, it would be logical for you to wait for Freddie to lie first and then compain lie second to revenge yourself on Freddie lie first to get Freddie fired Do nothing The person who lies first in this situation has a first-mover advantage will be promoted suffers reputational damage incurs commitment advantage
