Consider the game of two people approaching one another on a sidewalk. Each chooses right or left. If they make the same choice, they pass one another without a problem and each gets a payoff of $1.$ If they make opposite choices, they both get payoffs of $0.$ Find the three Nash equilibria of the game. $($One of them is a mixed equilibrium.$)$ Show that the payoff from the mixed equilibrium is only half as good for either player as either of the two pure equilibria.