Game DF Questions

I need support with this Business question so I can learn better.

Answer the questions below at least 150 words each.

1.In the button-pushing game from Lecture 1, you looked at which lines of reasoning, if any, were rational. In Lecture 2, Professor Stevens explained that being rational means that a person makes decisions in a way that leads to his or her own best expected payoff. One person’s payoff may not be the same as another person’s. Give an example of at least one situation in which two rational people could make different decisions. How can thinking in this way help with real-life decision making?

2.You, along with three strangers, see a burglar smash a store window and take a piece of jewelry. All of you could identify the perpetrator. As you leave the scene, you decide whether to call the police. Assume as common knowledge that the benefit from the criminal being apprehended is greater than the cost of becoming involved for each witness. What are the Nash equilibria of the game? What difficulties exist in reaching an equilibrium? What would you do if this actually happened?

3.Consider the button game from Lecture 1. Each of 101 players has a button. Pressing the button has two effects.

1. It costs all other players $2.
2. If other players have pressed their buttons, it cuts the losses you take from them in half.

What is the Pareto-optimal solution in this game? What are the the two Nash equilibria of the game? Suppose that before the game is played, the players met in a room and all agreed not to push. Pushes are still anonymous. Would you push? Would you expect others to? Why or why not?

https://www.youtube.com/watch?v=_2sHRJlJrh8 (button Game)