Answer :
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.
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.