Question I. Practice finding PSNE.
For each of the following five games, are there Pure Strategy Nash Equilibria (PSNE)? Identify them, or explain why there are none. (Note all the Nash equilibria discussed in Unit 8 are PSNE. The other kind of Nash equilibria, mixed strategy NE, are discussed in Units 9 and 10.)
Game A Game B
Left Right Left Right
Top
0
0
–1
2 Top
–1
2
2
3
Bottom
3
–1
4
4 Bottom
0
1
2
1
Game C Game D
Left Right Left Right
Top
0
3
–1
0 Top
1
0
6
2
Bottom
–1
2
2
4 Bottom
5
4
0
1
Game E
Left Right
Top
0
0
3
–1
Bottom
3
–1
1
1
Question II. Electoral Coordination under Different Levels of Democracy and Development.
For Scenarios A, B and C below, do the following:
1. Depict the strategic interactions between North and South, the two players, as a game.
2. Identify all dominant and dominated strategies. If a player does not have a dominant strategy explain why.
3. Explain what a pure strategy Nash equilibria (PSNE) is. (You only have to do this once, in your answer for Scenario A). Find all of them in each scenario or explain why there are none.
4. Explain what a Pareto Efficient situation means (you only have to do this once, in your answer for Scenario A). For each PSNE, comment on whether the outcome is Pareto Efficient or not. Explain why.
5. For each scenario, discuss what the game theoretical analysis implies about the likelihood that the OLD regime stays in power. If there is more than one PSNE in a game, what can we predict about the game’s outcome?
SCENARIO A: Country X has long been ruled by a single political party, the Organization for Liberty and Democracy or OLD. OLD routinely wins elections despite a well–deserved reputation for corruption. In the upcoming presidential election, OLD is certain to get the votes of the rural and backward Center. In order to win the presidency, OLD also needs the support of one of the more economically advanced parts of the country, either the North or the South. If either the North or the
South support OLD in the election, it will win. OLD is being challenged by a new party, the Network for Empowerment and Wealth, or NEW, which is running on an anti–corruption platform. If both the North and the South support NEW, NEW will win the election.
Both North and South would prefer to see a NEW president. For each region, the utility of a NEW regime and its superioir policy choices is 5, compared to a baseline of 0 for the OLD regime’s policy.
Yet leaders in each region have benefited in the past from side–payments and other spoils (e.g. government jobs and contracts that pay well for little work) that OLD routinely provides to regions that have supported it. If OLD wins the election, it will deliver benefits of up to 6 units of utlity to its supporters in the North and South. (It will deliver some benefits to Center too, but we don’t need to worry about that here, because Center will support OLD no matter what.) If only North or only South
supports OLD, the supporting region will get all 6 units of side–benefits. If both regions support OLD, they get 3 units each. North and South decide simultaneously whether to support OLD or NEW. If NEW wins the election, there will be no side–payments, just the above–mentioned utility from better policy.
SCENARIO B: If the corruption of the OLD regime could be contained, North could attract more foreign investment, providing jobs and tax revenue for infrastructure development. This possibility increases the policy utility to North of a NEW government from 5 units to 10. South’s preferences stay the same as in Scenario A, as do both players’ preferences over side payments.
SCENARIO C: Now suppose both North and South value the NEW government’s policy at 10 units.
Everything else is the same as in Scenario A.
