数学代写|Math111 Game theory

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Math111课程简介

Course Objectives

1. Develop a sense of belonging.
2. Develop time efficient study strategies, especially pertaining to mathematics classes.
3. Examine the process of learning from a variety of perspectives.
4. Develop a broader perspective of a future career path through industry and faculty talks.

We are here to help you in this course. This course is intended to assist you in the transition from high school to the university-level environment. This transition requires change, and change is not always easy. You will presented with a number of learning strategies; we suggest you experiment with these strategies in a real and meaningful manner. Simply knowing that X is a good effective learning strategy is NOT the same as implementing X and seeing the benefits. You will most likely find that it is, in fact, MORE difficult and requires MORE time to implement these strategies in the BEGINNING. We want you to persist and continue to utilize these strategies. When you are accustomed to these strategies, you will spend LESS time and score MUCH HIGHER than your “average” classmate. If you are trying to implement X and you slip up and get off track and fail you use X, it is okay. This is the process of change. Simply accept that you failed to use X in one particular situation and start using it again. Don’t dwell on the failure.

Prerequisites 

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. 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）

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.

\begin{matrix} &\text{black card}& \text{red card}\ \text{black card}& 0,2 & -3,3\ \text{red card}& -3,3 & 0,2 \end{matrix}

In the matrix above, if both players play the black card, there is no payoff for either player, so the payoff is listed as 0,2 (player $R$’s payoff is 0, player $C$’s payoff is 2). If both players play the red card, player $R$ wins and gets a payoff of 3, while player $C$ gets a payoff of -3. If player $R$ plays the black card and player $C$ plays the red card, player $C$ wins and gets a payoff of 3, while player $R$ gets a payoff of -3. Finally, if player $R$ plays the red card and player $C$ plays the black card, player $R$ wins and gets a payoff of 2, while player $C$ gets a payoff of -2.

Note that since the game is symmetric, the matrix is also symmetric along the main diagonal. This means that if we swap the rows and columns, we get the same matrix, but with the payoffs swapped between the players.

To find the most aggressive strategies for each player, we need to find the dominant strategies for each player. A dominant strategy is a strategy that is always the best choice for a player, regardless of what the other player does.

Player $R$ has two strategies: strategy 1 (play row 1) and strategy 2 (play row 2). To determine which strategy is dominant, we need to compare the payoffs for each strategy against each of player $C$’s possible strategies. We can see that if player $C$ plays column 1, player $R$ gets a payoff of 1 with strategy 1 and a payoff of 5 with strategy 2. Therefore, strategy 2 is dominant for player $R$.

Player $C$ also has two strategies: strategy 1 (play column 1) and strategy 2 (play columns 2 and 3). If player $R$ plays strategy 1, player $C$ gets a payoff of 1 with strategy 1, and a payoff of 5 with strategy 2. If player $R$ plays strategy 2, player $C$ gets a payoff of -4 with strategy 1, and a payoff of -1 with strategy 2. Therefore, neither strategy is dominant for player $C$.

Since neither player has a dominant strategy, we cannot determine the most aggressive strategies for each player. Instead, we can look at the Nash equilibrium, which is a set of strategies in which neither player has an incentive to deviate from their chosen strategy.

To find the Nash equilibrium, we can look for a pair of strategies (one for player $R$ and one for player $C$) in which each player’s strategy is optimal given the other player’s strategy. In this case, the Nash equilibrium is (strategy 2, strategy 2), since neither player has an incentive to switch to the other strategy. If player $R$ plays strategy 2, player $C$ will play either column 2 or column 3, and if player $C$ plays either column 2 or column 3, player $R$ will play strategy 2. In this equilibrium, player $R$ gets a payoff of -4, while player $C$ gets a payoff of -1.

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