Problem 5: There are two countries fighting over an oil well. The first country
ID: 1110527 • Letter: P
Question
Problem 5: There are two countries fighting over an oil well. The first country has K > 2 tanks available for war, and the second country has L > 2 tanks available for war. Currently, the oil well is occupied by the second country. The rules of engagement are as follows:
• If one country declares peace, then peace is established and the game ends.
• If one country attacks the current occupier of the well, both countries loose a tank.
• If the invading country has tanks left over after the attack, then the invading country occupies the well with one tank.
• If the invading country is reduced to 0 tanks after the invasion, but the defending country still has tanks available, the defending country keeps the oil well.
• If, after an attack, both countries are reduced to 0 tanks, then no one takes control of the well.
• Assume that K > L and that occupying the oil well is more valuable than a tank, but less valuable than 2. Find the SPNE of this game. Who, if anyone, gets possession of the well?
• Now assume that L > K, find the SPNE of this game. Who, if anyone, gets possession of the well?
• (extra credit, 0.33) Still assuming that L > K, assume now that the utilities change: High command has informed the generals that the well has more oil than previously assumed, so the well is now worth more than 2 tanks (but less than 3). Solve the SPNE of the game. Do your predictions on who wins the oil well change?
Explanation / Answer
Q5) Since an oil well is not worth 2 tanks and atleast 2 tanks will be lost if the first country decided to wage a war and win it (l>2), the first country will decide not to go to war even when k>l.The second country will continue to possess the well. When l>k, then the first country cannot win the war and also it don't want to due to the reason just stated. Hence, the well remains with the second country in both the cases.
Utilities changed
When L>k, the first country can never win the war and the oil well. The well will remain with second country.