Practice Problems
1) Sticker Sale
Suppose Ashley and Kat are both selling stickers. Like the lemonade stand example, this chart can be used to represent their payoffs in setting the price of their stickers:
What is each person’s dominant strategy?
Considering each person's dominant strategy, what is likely to be the outcome? How much money will each person make?
2) Disarmament
Two countries, A and B, are threatened by each other. They would each both rank their options in this order:
1. Military dominance (via the others’ disarmament).
2. Mutual disarmament (equality without economic hardship).
3. Arms race (equality with economic hardship).
4. Military inferiority (via its own disarmament).
Make an prisoner’s dilemma chart where each country has the option to arm or disarm. (Hint: if you use the ranking as the number in the chart, lower numbers win)
What is each country’s dominant strategy?
Considering each country’s dominant strategy, what is likely to be the outcome?
3) Balancing the Budget
When balancing the budget, congress and the federal reserve both have different preferences.
Congress’ preferences: Fed’s preferences:
1. Deficit and low rates 1. Balanced budget and low rates
2. Balanced budget and low rates 2. Balanced budget and high rates
3. Deficit and high rates 3. Deficit and high rates
4. Balanced budget and high rates 4. Deficit and low rates (most inflationary)
Make a prisoner’s dilemma chart
What is each party’s dominant strategy?
Considering each party’s dominant strategy, what is likely to be the outcome?
4) More Nash Equilibrium
For each of the following examples, indicate each person’s dominant strategy and the Nash equilibrium(s), if any exist:
Solutions
- Sticker Sale
1) Both Ashley and Kat have the dominant strategy to set low prices.
2) The most likely outcome is they both set a low price and make a total of $4 each.
2. Disarmament
1)
2) the dominant strategy of both countries is to disarm
3) Arms race (3, 3) is the chosen outcome
3. Balancing the Budget
1)
2) congress: always go with deficit
fed: no dominant strategy
3) high interest rates, budget deficit (3,3) is the chosen outcome
4. More Nash Equilibrium
These problems are from Ashley Hodgson’s video, Nash Equilibrium Examples. To view her worked-out solutions to each problem see this video
