Explain the Prisoner’s Dilemma game the notion of dominant strategy and the concept of Nash equilibrium and cooperation.

Explain the Prisoner’s Dilemma game, the notion of dominant strategy, and the concept of Nash equilibrium and cooperation. Using these concepts, then, analyze the following duopoly game.

Philip Morris and R.J. Reynolds spend huge sums of money each year to advertise their tobacco products in an attempt to steal customers from each other. Suppose each year Philip Morris and R.J. Reynolds have to decide whether or not they want to spend money on advertising. If neither firm advertises, each will earn a profit of $2 million. If they both advertise, each will earn a profit of $1.5 million. If one firm advertises and the other does not, the firm that advertises will earn a profit of $2.8 million and the other firm will earn $1 million.

If the two companies decide to collude to maximize profits, what will each company do? What profit will each company earn?
What is the dominant strategy for each company, and what profit will each company earn if they follow those strategies?
Is the solution you found in the first question a Nash equilibrium?
Is the solution you found in the second question a N