Solve the below problem:
Q. Consider an n-person game with the goal functions
fi ( x ) = a xi - båxj
j ÎN
and the strategies xi Î[0,1].
1.2.1. Find all pure strategy Nash equilibria.
1.2.2. Find all dominant strategy equilibria.
1.2.3. Find all Pareto-optimal strategy profiles.
1.2.4. What are the values of α and β that guarantee
Pareto-optimality of a Nash equilibrium?