Solve for the symmetric pure strategy Nash equilibrium

1. (25 points) There are 10 fishermen in a small fishing village. Each chooses a number of hours x; E [0, 10] to spend fishing each day. Each hour spent fishing reduces a fisherman's payoff by 50, but increases the number of fish he catches. The marginal product of a fisherman's time depends both on how much time he spends fishing (he experiences diminishing returns) and on how much time other fishermen spend fishing (the more time others spend fishing, the harder it is to catch a fish). Specifically, each hour that others spend fishing reduces marginal product by 1/10, while each hour he spends fishing reduces his marginal product by 2: When the strategy profile is x, fisherman i catches fi(x) = (15 - Xi - 10 Citi x;) x; fish. The fisherman then sells his catch at a price of p = 10 per fish, and receives a payoff of 10fi(x). Thus, fisherman i's payoffs are given by ui(x) = 10fi(x) - 50xi. Solve for the symmetric pure strategy Nash equilibrium of this game