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Game Theory and Strategic Choices - End of Chapter Problem

Founded in 1960, the Organization of Petroleum Exporting Countries (OPEC) is an intergovernmental organization of 14 nations that meets periodically to establish oil production quotas for each nation, resulting in greater profits overall. However, OPEC has a history of failing to enforce its own quota limits.

Consider a simplified example with just two countries: Venezuela and Kuwait. Currently, both countries are producing 2.5 million barrels per day. If both countries agree to cooperate, they will each restrict output to 2 million barrels per day, causing the price of oil to rise. If one country defects from the agreement, it will produce 2.5 million barrels, and total output will rise from 4 million barrels to 4.5 million barrels. As a result, the price will fall slightly. If both nations defect from the agreement, each nation will again produce 2.5 million barrels, and the price will fall to the original level. The payoffs for each possible outcome are illustrated in the accompanying payoff table.

\begin{tabular}{|c|c|c|}
\hline & Venezuela cooperates & Venezuela defects \\
\hline \begin{tabular}{l}
Kuwait \\
cooperates
\end{tabular} & \begin{tabular}{l}
Kuwait receives \\
[tex]$\$[/tex] 60[tex]$ million worth of profits. \\
Venezuela receives \\
$[/tex]\[tex]$ 60$[/tex] million worth of profits.
\end{tabular} & \begin{tabular}{l}
Kuwait receives \\
[tex]$\$[/tex] 40[tex]$ million worth of profits. \\
Venezuela receives \\
$[/tex]\[tex]$ 70$[/tex] million worth of profits.
\end{tabular} \\
\hline \begin{tabular}{l}
Kuwait \\
defects
\end{tabular} & \begin{tabular}{l}
Kuwait receives \\
[tex]$\$[/tex] 70[tex]$ million worth of profits. \\
Venezuela receives \\
$[/tex]\[tex]$ 40$[/tex] million worth of profits.
\end{tabular} & \begin{tabular}{l}
Kuwait receives \\
[tex]$\$[/tex] 50[tex]$ million worth of profits. \\
Venezuela receives \\
$[/tex]\[tex]$ 50$[/tex] million worth of profits.
\end{tabular} \\
\hline
\end{tabular}

a. In terms of their collective profits, the best outcome for Kuwait and Venezuela is that:
A. Both nations cooperate.
B. Kuwait cooperates, and Venezuela defects.
C. Venezuela cooperates, and Kuwait defects.
D. Both nations defect.

Sagot :

GinnyAnsweridn
To determine the best outcome for Kuwait and Venezuela in terms of their collective profits, we need to evaluate all possible outcomes and identify which scenario yields the highest combined profit for both countries. The payoffs for each possible outcome are given in the problem:

1. Both Cooperate:
- Kuwait receives \[tex]$60 million. - Venezuela receives \$[/tex]60 million.
- Collective profit = \[tex]$60 million + \$[/tex]60 million = \[tex]$120 million. 2. Kuwait Cooperates, Venezuela Defects: - Kuwait receives \$[/tex]40 million.
- Venezuela receives \[tex]$70 million. - Collective profit = \$[/tex]40 million + \[tex]$70 million = \$[/tex]110 million.

3. Venezuela Cooperates, Kuwait Defects:
- Kuwait receives \[tex]$70 million. - Venezuela receives \$[/tex]40 million.
- Collective profit = \[tex]$70 million + \$[/tex]40 million = \[tex]$110 million. 4. Both Defect: - Kuwait receives \$[/tex]50 million.
- Venezuela receives \[tex]$50 million. - Collective profit = \$[/tex]50 million + \[tex]$50 million = \$[/tex]100 million.

Now, we compare the collective profits from each scenario:

- Both Cooperate: \[tex]$120 million - Kuwait Cooperates, Venezuela Defects: \$[/tex]110 million
- Venezuela Cooperates, Kuwait Defects: \[tex]$110 million - Both Defect: \$[/tex]100 million

Clearly, the highest collective profit is achieved when both Kuwait and Venezuela cooperate, leading to a combined profit of \$120 million.

Thus, in terms of their collective profits, the best outcome for Kuwait and Venezuela is that both nations cooperate.
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