Differentiate mixed strategies games from pure strategy games

The second

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*** Beginning of the Questions ***

Chapter 6. Game Theory

  1. 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)
  1. 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
  1. 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 ***

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