Economics

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Economics

Game theory is the study of mathematical configuration of contention and cooperation between reasonable, sound decision makers. The games that are studied in game theory are made up of sets of players, strategies available to the players, and the payoff or reward specific to each combination of strategies. A normal form game can be exemplified by a matrix which shows the players, strategies, and payoffs. Each player has a number of strategies stipulated by the number of rows and columns while the payoffs are expressed in the interior. The focus of game theory is the strategies applied by the players known as equilibria in these games.

1. For two players, A and B engaged in a coin-matching game, each shows a coin as either heads or tails. If the coins match, B pays A $1 and if they differ, A pays B $1. Depicting this game in tabular form provides a visual presentation of the players’ strategies and their respective payoffs. B’s strategies

Heads Tails

A’s strategies Heads +1, -1 -1, +1

Tails -1, +1 +1, -1

The payoffs are based on the choices made by the players although this choice is unknown to the other player. The players’ payoffs or utility are balanced in the sense that one player’s gain in utility is an inverse of the second player.

The Nash equilibrium is not exhibited in this instance since there is no available channel for the players to maximize their payoffs. Though the players have adequate aptitude to deduce the solution, the equilibrium remains unknown owing to the intricacy of the game. A zero-sum game as depicted above can be solved by adopting linear optimization.

2. For two players, Smith and Jones playing a number matching game with the choice of the numbers 1, 2 or 3, if the numbers match, Jones pays Smith $3 and if they differ, Smith pays Jones $1. The payoff matrix for this game is shown below:

Smith’s strategies

1 2 3

1

Jones’ Strategies 2

3

The payoff of this game exhibits a zero-sum game although the players may adopt different strategies to vary their utility. The matrix does not have a Nash equilibrium strategy pair because a change in strategy by either of the players will benefit that player. There is no equilibrium because each strategy pair offers one of the players an incentive to adopt another strategy. In addition, it is not mandatory that each player will choose the numbers with equal probability.

In a mixed strategy, there exists equal probability of the players to choose the numbers. This can be proved by calculating the mixed strategy Nash equilibrium. If the probability of Jones playing 1 is assigned p while his probability of playing 2 is represented by r while that of playing 3, (1-p+r). The probabilities of Smith playing the numbers 1, 2 and 3 are represented by s, t and (1-s+t) respectively. Thus the payoffs E can be calculated and compared to determine the random selection of the numbers with equal probability of a third. This game is valuable in exhibiting the mixed strategies that can be applied in Nash equilibrium games.

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Economics

Economics

I believe that students not only learn by being good listeners but also through observation and interaction with the important aspects in their surroundings. However, most students have limited themselves to learning in the classrooms. They neglect the chance of experiencing what is around them. In addition, I consider diverse campus environment to be a learning ground. This is because meeting people of different cultures and backgrounds give me a wider view on the environment. Most of this has improved my knowledge and some have inspired me to do extraordinary things. Therefore, I intend to help the university to promote learning in the Jesuit Catholic tradition. This will enable students to acquire knowledge, skills and values they need to succeed.

I consider myself lucky to study abroad. However, I am disappointed by the fact that learning has become dull. I prefer learning things first hand. Therefore, I intend to help the university in incorporating these learning tactics. Since being in group discussions has always enhanced my learning, I intend to encourage students to interact socially. This will enable them to improve their learning skills through the group discussions. In addition, sharing their experiences and ideas will help in improving the group discussions. This is because of the diverse environment. These diverse environments will enable the students to understand the behaviors and thoughts of people in different situations. The students will also be able to realize the positive influences that benefit the society.

My dream is to help create a better learning environment for the underprivileged. I will be able to fulfill this dream if I get the chance to join the University of San Francisco. Here, I intend to major in economics. I also intend to help the university to enhance its learning in the Jesuits catholic tradition. This tradition appreciates the principles importance. The students’ ability to rationalize is important. The utilitarian approach ascertains that if people are able to rationalize, then they will not be able to solve the ethical cases. However, in order to do this perfectly, they must practice the principles that are applicable in every circumstance. In addition, I will embrace the university’s mission statement by involving myself in the leadership opportunities offered by the student leadership and engagement. I will also practice the core values by taking learning as a humanizing and social activity rather than a competitive act. I hope to be able to help the community since I share similar values as the university. I also intend to be involved in the Jesuit tradition. My personal goals are to learn in order to be able to help the needy.

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