Two competing firms decide simultaneously which consumer group to target in their advertising campaigns. One consumer group is L(arge) and, if targeted, yields a payoff of x; the other group is S(mall) and, if targeted, yields a payoff of 20. If the two firms target the same group, they share the payoff equally, but if they pick different groups, each enjoys the whole payoff. Each firm can target only one group with a view to maximizing their own expected payoffs

(a) Draw the payoff matrix of the game.

(b) For what values of x does each firm have a strictly dominated strategy?

(c) For what values of x does the game have a mixed strategy Nash equilibrium?