Part II : Game Theory Exercises

In a competitive situation, game theory can tell you how to be smart. In a cooperative situation, game theory can tell you how to be fair.

1. Use your search engine to find the meaning of "Oligopoly."
   In complete sentences explain how oligopoly pertain to game theory.
2. A card game is played with two players who select one card at a time to use against their opponent. Both players have cards that add points and cards that subtract points. Cards are marked by colors and number value.
   Player A has two strategies, yellow and green, and player B has two strategies, red and blue. The game is played simultaneously with both players playing pure strategies and being able to see the other player’s actions. The game, with strategies and payoffs, is given by the following payoff matrix:
   
3. Fill-in the blanks:
   For player A, ___ dominates ____ since ______ and ____.
   For player B, ___ dominates ____ since ___ and ____.
4. How does Nash’s equilibrium in the Prisoner’s Dilemma relate to this game?
5. Suppose the game now has the following payoff matrix. If red would dominate blue for player B, and if yellow would dominate green for player A, then what is the minimum value that could be substituted in for x that would impact on the Nash equilibrium? Explain why you chose that value.

Part III - Donald in Mathmagic Land

Answers all items in COMPLETE sentences.

1. Recall: Who were the "Pythagoreans?" What was their purpose?
2. What did the video say about the ratio of a musical octave?
3. The game played on a pool table is called billiards. In three cushion billiards, the cue ball must hit two ___ and three ___.
4. The method used in billiards is called ______.
5. Name conics that we can make from slicing a sphere or a cone.
6. Use the internet to identify at least two of the mathematic contributions made by Pythagoras.
7. What is the Golden Triangle? Search the internet to report on our uses the Golden Triangle. In which occupations is it important?
8. Pythagoras wrote, "Everything is arranged according to number and mathematical shape." Use the internet to find out what he meant by that? Do you agree? Why?
9. The video refers to a number of games that rely on geometric or other math principles in order to be played. What were some of these games and how is math used in them?
10. Who was John Forbes Nash? Search to find out and report on his contributions to game theory and report on his contributions to economics.
11. Why is math "beautiful?" Support your answer with examples from the net.
12. The video spans three millennia and shows mathematical achievements from ancient to modern times. What are some inventions that exist today that weren’t shown in the video? Name some ways that math is used in your named modern achievements.

Part IV: Chess

Playing the game of chess on a regular basis right from the childhood teaches the importance of being disciplined in life. Such an exercise provides mental clarity to the child. Mental clarity and mental dexterity is required for solving problems, analyze consequences, and formulate future tactics. Prepare a well written paragraph that discusses how chess can help the brain and discuss what is good about playing chess. Support your points with references to the internet.

Look at https://www.chess.com/blog/masmasi2907/health-benefits-of-playing-chess (Links to an external site.)

Assignment: You will need to submit the following.

Write a well developed reactionary paragraph to the chess article on the web site.

The paragraph is to contain a complete topic sentence, five supportive sentences, and a concluding sentence.

The supportive sentences should contain explanations of why you are interested in the topics discussed.

They should discuss how the topics are applicable and purposeful to life of the learner (you).

A clincher sentence should conclude the paragraph with meaningful points.

Price: $24.61

Solution: The downloadable solution consists of 6 pages, 1984 words and 2 charts.
Deliverable: Word Document