Review feedback from your instructor (in Grades) on your final draft of Writing Project 1 and/or the half draft of this project, from your peers (in M05 Peer Response–Writing Project….

## Differentiate mixed strategies games from pure strategy games

**The second**

Page limit: **6** pages in total. References, tables and figures do not count towards the page count.

- Use either Times New Roman (12 font size) or Ariel (11 font size); double-space; at least 1-inch margin on all sides.
- Every material you referred to must be listed in the bibliography attached to the end of your paper. Any reference style is acceptable.

**Academic Honesty**

- This is an individual assignment. Copying and pasting others’ work will evoke the policy stated in the syllabus.
- Direct coping and pasting of any material, including my script, PowerPoint Slides, Textbook, is NOT allowed. You must paraphrase it in your own words. If you have to include a direct quote, it should be in double-quotation marks (“ “). The use of such direct quotes should be minimal (no more than 2 sentences throughout your paper).
- Please refer to Spartan Code of Honor in the syllabus.
- The course policy for plagiarism is as follows: first offense – 0.0 points for the entire assignment; second offense – 0.0 for the entire course.

**Overarching grading rubric **

- Your answers must closely reflect the content discussed in this course.
- Your answers must be comprehensive. In other words, partially answering questions will not get you the full grade.
- Refrain from copying random content you found on the web (e.g., Wikipedia). Vague answers, such as, “because everyone is connected through social media…” will not earn you any credit.

- You will earn 100% of the grades assigned to a question if your answer covers the entire content pertinent to the given question in the textbook, lectures, and recitations.
- E.g., What are the reasons for triadic closure?
- Your textbook lists 4 reasons over Chapters 3 and 4, and you listed all four.

- E.g., What are the reasons for triadic closure?
- You will earn 80% of the grades assigned to a question if your answer covers only partial content pertinent to the given question in the course materials (e.g., textbook, lectures, and recitations).
- E.g., What are the reasons for triadic closure?
- Your textbook lists 4 reasons over Chapters 3 and 4, but you listed only three.

- E.g., What are the reasons for triadic closure?
- You will earn 50% of the grades assigned to a question if your answer does not cover any material pertinent to the given question in the course materials (e.g., textbook, lectures, and recitations) but is based on the content you found on the web or common sense.
- E.g., What are the reasons for triadic closure?
- Your textbook lists 4 reasons over Chapters 3 and 4, but you listed none of these but list some information you found on Wikipedia.

- E.g., What are the reasons for triadic closure?

***** Beginning of the Questions *****

**Chapter 6. Game Theory**

- Explain how Nash equilibrium was achieved in the PowerPoint-keynote game (p. 151) AND the battle of the sexes (p. 153), as an example of a coordination game vs. unbalanced coordination game, respectively. (10 points)

- Differentiate mixed strategies games from pure strategy games. What is the most prominent difference between the two? Then, explain what a mixed strategies game is (in terms of the three key concepts of mixed strategies) and how it is played. Use Matching Pennies game as an example. (10 points)

- Explain why outcomes that are socially optimal must also be Pareto optimal, but not the other way around. In so doing, describe what social optimality and pareto optimality are. (10 points)

- Consider the two-player game described in the payoff matrix below.
- Find all pure-strategy Nash equilibria for this game (5 points)

- Find if there are any mixed-strategy Nash equilibria (5 points)

**Chapter 10. Matching Markets**

- Explain how prices decentralize the allocation of goods to people. In your answer, make sure you use the three rounds of the Housing Market example where sellers’ price changes result in perfect matching (p. 255) (10 points)

- Explain the four rounds of the housing market prices whereby a perfect matching can be achieved between only one seller and three buyers. (10 points)

- Suppose we have a set of three sellers, labeled
*a*,*b*, and*c*, and a set of three buyers, labeled*x*,*y*, and*z*. Each seller is offering a distinct house for sale, and the valuations of the buyers for the houses are as follows.

Suppose that *a *charges a price of 4 for his house, *b *charges a price of 1 for his house, and *c *charges a price of 0. Is this set of prices market clearing? If so, explain which buyer you would expect to get which house; if not, say which seller or sellers should raise their price(s) in the next round of the bipartite-graph auction procedure from Chapter 10. (10 points)

**Chapter 12. Bargaining and Power in Networks**

- Explain the four reasons why power can be a property of a network. Refer to page 303. (10 points)

- Describe why only Figure Fig. 12.8(b) is a balanced outcome while Fig. 12.8(a) and 12.8(c) are not. Make sure you use the definition of Nash bargaining solution and balanced outcome, and the
**actual mathematical formulas****and numbers**to conclude that only (b) is a balanced outcome. Refer to the video lecture where I explain the mathematical steps. (10 points)

- Suppose a network exchange theory experiment is run on the graph depicted in the figure below using the one-exchange rule with $10 placed on each edge

- Say which node or nodes you would expect to make the most money (i.e. receive the most favorable exchanges), and give a brief (1-3 sentence) explanation for your answer. You do not need to give actual numbers for the amounts of money the nodes would receive. (5 points)

- Now the experimenters vary the network: they introduce a sixth node f, which is attached by a single edge to just the node c. A new person is brought in to play the role of f, and a new round of experiments is performed with this new six-node network. Explain what you think will happen to the relative power of the participants, compared to the situation in (a), and give a brief (1-3 sentence) explanation for your answer. Again, you do not need to give actual numbers for the amounts of money the nodes would receive. (5 points)

***** End of the Questions *****