Consider the following zero-sum game.

The strategy set of each player is the closed real interval [0,1].

In what follows we use (and you should, as well) variables x and y to
denote the strategies of players 1 and 2.

The payoff function of player 1 is

p(x,y) = 4xy - 2x - y + 3.

Find all Nash equilibria of this game.

Hint. Use the results of Chapter 6.