Suppose that the speed limit is 70 miles per hour on the freeway and that 1: drivers simultaneously and independently choose speeds from '1'0 to 100. Everyone prefers to go as fast as possible, other things equal, but the police ticket any driver whose speed is strictly faster than the speeds of a frac- tion x of the other drivers, where x is a parameter such that 0 E x E 1. More precisely. for a given driver. let m denote the number of drivers that choose strictly lower speeds; then, such a driver is ticketed if and only if m/(n l) > x. Note that by driving 70, a driver can be sure that he will not be ticketed. Suppose the cost of being ticketed outweighs any benet of going faster. (3) Model this situation as a noncooperative game by describing the strat- egy space and payoff function of an individual player. (b) Identify the Nash equilibria as best you can. Are there any equilibria in which the drivers choose the same speed? Are there any equilibria in which the drivers choose different speeds? How does the set of Nash equilibria depend on x