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# 数学代写|Math111 Game theory

## Math111课程简介

The transition to the university is social. A large portion of university life is SOCIAL and NOT JUST STUDYING. We recognize this fact. One research study found that the average number of hours communicating in a face to face manner with friends is approximately 30 hours per week. Is important that you find friends that you can socialize with and rely upon in the pursuit of your academic goals. Especially as a freshman, you will find other students that are truly not interested in getting educated and more forward in the pursuit of life goals and a career. It is YOUR CHOICE with whom to socialize.

## Prerequisites

We hope you choose wisely. The people around you shape your future. I remember the “party animal”, the “all-night gamer”, the “stoner”–yes, I was a student once as well. I remember being pressured to go out on a Wednesday or Thursday night. I remember the fear of missing out. But, there is only one miracle, performance-enhancing drug, and it is called SLEEP. About the fourth week of class, look around at other students in a morning class. Count how many students look exhausted. In an exhausted state, it doesn’t matter how much you study or regularly attend class: VERY LITTLE will be learned. Keep the sleep/party trade-off in mind when making your decisions.

## Math111 Game theory HELP（EXAM HELP， ONLINE TUTOR）

Using the same payoff matrix as in the previous problem,

(a) describe the most conservative strategy each player can choose.

The game is a simultaneous move game and the players have two possible actions: play the red card or play the black card. We can represent the game in a payoff matrix, where the rows represent the actions of player $R$ and the columns represent the actions of player $C$. The entries in the matrix are the payoffs for each player, with player $R$’s payoff listed first.

(a) The most conservative strategy for player $R$ is to play Bottom (B) since this guarantees a minimum payoff of 2, regardless of what player $C$ chooses. The most conservative strategy for player $C$ is to play Left (L) since this guarantees a minimum payoff of 1, regardless of what player $R$ chooses.

(b) If you were offered the chance to play this game for real money as player $R$, would you play? Why or why not?

(b) As player $R$, I would not play this game for real money because the expected payoff for me is not very good. If player $C$ plays Left (L), then I will only get 1, and if player $C$ plays Right (R), then I will only get 2. Since player $C$ is likely to play Left (L) to ensure a minimum payoff of 1, my expected payoff is only 1.5, which is not very high. Thus, the risk of losing money is greater than the potential reward, so it is not a good gamble for me to take.

(c) Same question as part (b), but now you are offered the role of player $C$ ?

(c) As player $C$, I would play this game for real money because the expected payoff for me is better than for player $R$. If I play Left (L), then I am guaranteed a minimum payoff of 1. If I play Right (R), then my expected payoff is (0.75 x 2) + (0.25 x 6) = 3, which is better than my expected payoff if I play Left (L) (which is 2). Since my expected payoff is greater than my minimum guaranteed payoff, it is a good gamble for me to take.

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