Midterm Review

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# Midterm Review
## ECON 316 • Game Theory • Fall 2021
### Ryan Safner Assistant Professor of Economics <a href="mailto:safner@hood.edu">safner@hood.edu</a> <a href="https://github.com/ryansafner/gameF21">ryansafner/gameF21</a> <a href="https://gameF21.classes.ryansafner.com"> gameF21.classes.ryansafner.com</a>

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# Major Concepts I

- Sequential Games (1.3)
    - game trees
    - strategy
    - rollback equilibrium
    - order advantages
- Simultaneous Games (1.4)
    - Nash equilibrium (detection):
        - Successive elimination of dominated strategies
        - Best response
    - Nash equilibrium refinements (1.5):
        - Focal points
        - Pareto efficiency
        - Payoff dominance
        - Risk dominance
        - Rationalizability

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# Major Concepts II

- Types of Games:
    - Constant sum game
    - Prisoners' dilemma
    - Coordination games (1.5):
        - (Pure) Coordination
        - Assurance (Stag Hunt)
        - Battle of the Sexes
        - Chicken (Hawk-Dove)

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# Major Concepts III

- Economics of oligopoly (2.1-2.4)
    - Oligopoly as prisoners' dilemma
    - Cartels
        - problems and mechanisms to overcome
    - Bertrand competition
    - Cournot competition (& collusion)
    - Stackelberg competition
    - Contestable markets (2.5)
- Mixed strategies (3.1)
    - Opponent indifference principle

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# Don't Worry About

- Harder questions on HWs/in class (meant to challenge you in low-stakes environment):
  - Simultaneous games with `$>2$` players
  - Cournot competition with `$>2$` firms
  - Mixed strategies for `$>2$` strategies (e.g. Rock-Paper-Scissors)

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# Review Questions

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# Question 1

- Name several different refinements of Nash equilibrium.

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# Question 2

- Explain the differences between the three different models of oligopoly.

- Which is most/least profitable to each firm?

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# Question 3

- What is the Nash equilibrium of a contestable market? What conditions are required for a market to be contestable?

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# Question 4

- Name the four types of coordination games and describe the major features of each.

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# Question 5

- Explain the differences between a *prisoners' dilemma* and a *stag hunt.*

You can draw example payoff tables, and let each player choose between "Cooperate" and "Defect" for each game.

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# Question 6

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- Consider the game to the right:
- Find all Nash equilibria
- Which is/are Pareto efficient?
- Which is/are payoff dominant?
- Which is/are risk dominant? 
- Which outcome/s is/are rationalizable?

]

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.center[
![](../images/review_game_6.png)
]
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# Question 7

- Two firms are competing simultaneously over quantity, have constant marginal costs of \$0, and share the market demand

`$$\begin{align*}
p&=12-Q\\
Q&=q_1+q_2\\
\end{align*}$$`

- Find the Cournot-Nash equilibrium profit for each firm.

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# Question 8

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- Find all Nash equilibria (in pure and mixed strategies) for the following game:

]

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![](../images/review_game_8.png)
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