Elon and Richard are billionaires who want to go to Mars. Each owns a company that is currently researching a new type of technology that will allow them to conduct the first human mission to the red planet. Currently, both companies are close to making a breakthrough and securing a patent on the new technology. Consider the following setup:

- Both Elon and Richard are four "research steps" away from noshing the technology and getting the patent.

- Elon and Richard take turns deciding how much they want to invest into their company's research, with Elon choosing first. Each can observe the choice of the other.

-The value of the patent is $20 billion, but is only awarded to the owner of the company that finishes the research first.

-During their turn, each player has 3 options.

1) Invest $0 and take 0 research steps

2) Invest $4 billion and take 1 research step

3) Invest $11 billion and take 2 research steps

- Payoffs to each player are given by the value of the patent (if they get it) minus the total investment into research.

Solve the game. What will Elon and Richard do to maximize their payoffs. Explain in detail.