Mary and Nathan are Business Partners. The profit level of their business depends on the amount of effort each person puts into the business. Let m denote Mary’s effort level and let n denote Nathan’s effort level. The profit of their business is given by:

5m+4n+mn

Mary and Nathan will split the profit equally however they will separately incur the cost of their own effort. The cost of Mary’s effort is m^2. The cost of Nathan’s effort is n^2.

What are Mary and Nathan’s payoff function?

Suppose Mary chooses her effort level first. Nathan, after observing Mary’s effort level, chooses his effort level. Determine the effort levels that Mary and Nathan choose.