Consider two tutoring companies $($A and B$).$ Each company has at their disposal very

effective, but very expensive marketing teams. Each company makes $$50,000$ in

revenue each year. If both A and B use their marketing team, it causes a spiral of

competitive ads, and each will ultimately spend $$100,000$ on marketing. If company A

acts first, using its marketing team, while B does not, then B will lose $$30,000$ in

revenue, and A will gain a net of $$10,000$ in revenue after marketing costs. This effect is

symmetric if B acts first. If both companies spend no money on marketing, their

revenues are unaffected.

a$.(4$ points$)$ Clearly state the players and strategy sets.

b$.(4$ points$)$ Write an equation to describe the revenue for Company A$,$ assuming

that it plays a mixed strategy while Company B does not use its marketing team

$($i$.$e$.,$ plays a pure strategy of not acting$).$

c$.(2$ points$)$ Describe the revenue for Company A assuming it plays a mixed

strategy while Company B acts to use its marketing team $($i$.$e$.,$ plays a pure

strategy of always acting$).$