Question:
Consider trade relations between the Country A & Country B. Assume that the leaders of the two contries believe the payoffs to altrenative trade policies are as follows:
,,,,,,,,,,,,,,,,,,Country A
,,,,,,,,,,Low Tarriffs|High Tarriffs
,,,,,,,,,,A 25 Billion|A 30 Billion
Country B,,,,,,,,,,,,,|
Low ,,,,,,,,,,,,,,,,,,|
Tarriffs,,B 10 Billion|B 10 Billion
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
High ,,,,,A 10 billion|A 20 Billion
Tarriffs,,,,,,,,,,,,,,|
,,,,,,,,,,B 30 Billion|B 20 Billion
What is the dominate strategy for the Country A?
The maxtrix confuses me. I picked A should be with the High Tariff and gain 30 billion. I am not sure if this is correct?
I do not think you are correct.
First, check; does A have a maximizing strategy which is independent of what B does. If A chooses a low tarriff, the best that A can win is 25 and the worst it could win is 10. If A chooses a high tarriff, the best A can win is 30 and the worst it can win is 20. A's position, right now is uncertain.
Now check B. If B chooses low, the best it can win is 10. If B chooses High, the WORST it can win is 20. So, B will choose a High Tarriff.
Ok, so now A sees that B will choose a high tarriff, it's best call is to choose a low tarriff and gain 25.
To determine the dominant strategy for Country A, we need to analyze the payoffs for each possible combination of trade policies chosen by Country A and Country B. In this case, the payoffs are represented in the matrix you provided, where the rows represent Country A's trade policy choices (Low Tariffs or High Tariffs), and the columns represent Country B's trade policy choices (Low Tariffs or High Tariffs).
Let's break it down step by step:
1. When Country A chooses Low Tariffs and Country B chooses Low Tariffs, the payoff for Country A is 25 billion, and the payoff for Country B is 10 billion.
2. When Country A chooses Low Tariffs and Country B chooses High Tariffs, the payoff for Country A is 30 billion, and the payoff for Country B is 20 billion.
3. When Country A chooses High Tariffs and Country B chooses Low Tariffs, the payoff for Country A is 10 billion, and the payoff for Country B is 30 billion.
4. When Country A chooses High Tariffs and Country B chooses High Tariffs, the payoff for Country A is 20 billion, and the payoff for Country B is 20 billion.
To determine the dominant strategy, we need to compare the payoffs of Country A when it chooses Low Tariffs versus High Tariffs, while considering all possible choices of Country B.
When Country B chooses Low Tariffs, Country A receives a higher payoff (25 billion) when it chooses Low Tariffs instead of High Tariffs (10 billion).
When Country B chooses High Tariffs, Country A receives a higher payoff (30 billion) when it chooses High Tariffs instead of Low Tariffs (20 billion).
Therefore, irrespective of the choice made by Country B, Country A's dominant strategy should be to choose High Tariffs, as it consistently yields higher payoffs for Country A compared to Low Tariffs. Thus, your initial choice of High Tariffs for Country A is indeed correct.