Please fully explain and clearly state if the statements are true or false.

1. In a two-player game, a Nash equilibrium is the outcome that maximizes the sum of the players' payoffs.

2. In a Nash equilibrium in a two-player game, both players must have selected a dominant strategy.

3. Repeatedly playing the Prisoner's Dilemma may or may not result in a cooperative solution.

4.In the models of oligopoly considered in the recorded lectures, the equilibrium price will be strictly lower if there are n + 1 firms than if there are n firms.

5. In the models of oligopoly considered in the recorded lectures, consumers are no better off than in a perfectly competitive market.